National Aeronautics and Space Administration

NASA Technical Memorandum 104262

Stratospheric TurbulenceMeasurements and Modelsfor Aerospace Plane Design

L.J. Ehernberger

December 1992

National Aeronautics andSpace Administration

Dryden Flight Research Facility

Edwards, California 93523-0273

1992

NASA Technical Memorandum 104262

Stratospheric TurbulenceMeasurements and Modelsfor Aerospace Plane Design

L.J. EhernbergerNASA Dryden Flight Research FacilityEdwards, California

STRATOSPHERIC TURBULENCE MEASUREMENTS ANDMODELS FOR AEROSPACE PLANE DESIGN

L.J. Ehernberger*

NASA Dryden Flight Research FacilityP.O. Box 273

Edwards, California 93523-0273

Abstract

Progress in computational atmospheric dynamics isexhibiting the ability of numerical simulation to describeinstability processes associated with turbulence observedat altitudes between 15 and 25 km in the lower strato-sphere. As these numerical simulation tools mature, theycan be used to extend estimates of atmospheric perturba-tions from the present gust database for airplane design ataltitudes below 15 km to altitudes between 25 and 50 kmwhere aerospace plane operation would be at hypersonicspeeds. The amount of available gust data and number oftemperature perturbation observations are limited at alti-tudes between 15 and 25 km. On the other hand, in-situgust data at higher altitudes are virtually nonexistent. Theuncertain potential for future airbreathing hypersonicflight research vehicles to encounter strong turbulence athigher altitudes could penalize the design of these vehi-cles by undue cost or limitations on performance. Be-cause the atmospheric structure changes markedly withaltitude, direct extrapolation of gust magnitudes and en-counter probabilities to the higher flight altitudes is notadvisable. This paper presents a brief review of turbu-lence characteristics observed in the lower stratosphereand highlights the progress of computational atmospher-ic dynamics that may be used to estimate the severity ofatmospheric transients at higher altitudes.

Nomenclature

CAT clear air turbulence

Fr Froude number,

g acceleration caused by gravity, m/sec2

NFr

*Associate Fellow, AIAA.Copyright 1992 by the American Institute of Aeronautics and

Astronautics, Inc. No copyright is asserted in the United States underTitle 17, U.S. Code. The U.S. Government has a royalty-free license toexercise all rights under the copyright claimed herein for Governmentalpurposes. All other rights are reserved by the copyright owner.

h geopotential altitude, km

rate of change of altitude, m/min

HAT high-altitude turbulence

HICAT high-altitude clear air turbulence

L height of the flow barrier in the Froude number

MSL mean sea level

p pressure, mb

PSD power spectral density

rms root mean square

T temperature, K

U horizontal windspeed component

Ude derived equivalent gust velocity

second derivative of U with respect to altitude

USAF United States Air Force

w vertical velocity component

x horizontal coordinate

β atmospheric static stability parameter,gδθ ⁄ θδh

δ derivative operator

∆ finite difference operator

θ potential temperature, T(1000 ⁄ p)0.286

ρ atmospheric density

Introduction

Advanced hypersonic research vehicles, such as theNational Aero-Space Plane, require discrete atmosphericperturbation models for design at altitudes above thepresent gust and turbulence design criteria based on in-situ measurements. Recent developments indicate thatnumerical simulation of small-scale atmospheric dynam-ics could assist in the specification of these discrete

h

U

atmospheric perturbation models for hypersonic aircraftdesign, especially at high flight altitudes. The atmo-spheric turbulence environment specified for design ofcivil and military aircraft is described as a function of al-titude in terms of discrete and random gust inputs.1–2

These discrete inputs are given as the derived equivalentgust velocity.3

Continuous random inputs are specified by a powerspectral density (PSD) shape, wavelength scale factor,and root-mean-square (rms) value.4 These design dataare based on extensive gust loads surveys aboard opera-tional aircraft and on true gust velocity measurementprograms on specially instrumented military and re-search aircraft.5–8 The adequacy of these criteria for gustloads design of subsonic aircraft to altitudes of approxi-mately 15 km has been demonstrated on narrow- andwide-body transport aircraft.5 For the higher altitudes,gust loads and true gust velocity data have been obtainedby U-2 aircraft (Lockheed Corporation, Burbank, Cali-fornia) to altitudes of approximately 20 km.9–10 Thesedata have also been obtained by supersonic researchaircraft to altitudes of 25 km.11–14

Because hypersonic flight research will use altitudes toapproximately 50 km, these existing in-situ atmosphericturbulence data cover approximately one-half of the alti-tude range required. Moreover, subsonic transport air-plane design has emphasized gust input effects on thelimit load and fatigue life design. In contrast, hypersonicvehicles are more likely to require emphasis on propul-sion and flight control systems responses. Response ofhot structures to high-altitude turbulence and gusts willalso be required. In flight regimes where more than onesystem is sensitive to the perturbation inputs, the inter-acting responses will probably involve more than one ofthe input perturbation components. For example, criticalresponses may simultaneously involve vertical and hori-zontal gust components as well as combinations of gustvelocity and ambient density or temperature. In this re-gard, a chief limitation of the present gust database anddesign criteria is that they have only been established forsingle, independent perturbation component inputs. Thatis, for present conventional aircraft design, combinationsof vertical and horizontal gusts are prescribed as beingstatistically independent. In addition, present aircraft de-sign criteria do not link either the horizontal or verticalgust components with perturbations in temperature,density, or pressure.

These concerns for hypersonic aircraft design applynot only to the present database altitudes below 25 kmbut also become even more critical at altitudes from 25 to50 km where higher speed airbreathing aerodynamicflight will be pioneered. Thus, two major aspects of the

turbulence environment remain to be explored for hyper-sonic aircraft. The first aspect is statistical characteriza-tion of the intensity and amount of turbulence throughoutthe stratosphere. The second aspect involves descriptionof the nature of coupling between gust motion compo-nents and pressure, density, and temperature state pertur-bations. Formulation of higher altitude design criteriaand perturbation models addressing both of these aspectsrequires use of advanced numerical simulation tech-niques for small-scale atmospheric perturbations. In ad-dition, appropriate observations to validate thesimulations for these applications are needed.

This paper provides a brief overview of the character-istics of turbulence observed in the lower stratosphere.Current studies for the use of small-scale, two-dimensional, numerical atmospheric dynamics simula-tions for specification of the higher altitude perturbationenvironment are also discussed. Finally, a simple, gener-ic, discrete atmospheric perturbation model proposed forassessment of hypersonic aircraft sensitivity to combina-tions of atmospheric gusts and thermodynamic transientsis described.

Metric units have been used throughout this paper.For the convenience of readers who are more familiarwith the U.S. Customary System, conversion factors areas follows:

Grateful appreciation is extended to the followingcollaborating researchers: Dale Durran, University ofWashington, Seattle, Washington; Terry Clark, Nation-al Center for Atmospheric Research, Los Angeles, Cali-fornia; and Morton Wurtele and his team at theUniversity of California, Los Angeles, California. Sup-port for this work from NASA through NCC 2-374 andfrom the National Aero-Space Plane Program is alsogratefully acknowledged.

Atmospheric Structure

Figure 1 shows the atmospheric layers with respect tothe average January conditions at Edwards, California.These data are based on rawinsonde observations to

U.S. Metric Conversion factor

Celsius, °C Kelvin, K °C = K – 273.15

Fahrenheit, °F Kelvin, K K = (5 ⁄ 9)(°F + 459.67)

Feet, ft Meters, m m = ft × 0.3048

Millibar, mb Hectopas-cal, hPa

mb = hPa

Nauticalmiles, n. mi.

Kilome-ters, km

n. mi. = km × 0.54

2

30-km altitude and nearby rocketsonde data for altitudesfrom 30 to 70 km and serve as a representative exampleof midlatitude winter conditions.15 In the troposphere,temperature generally decreases about 6.5 K/km altitude,and windspeed generally increases up to the tropopauselevel at the base of the stratosphere. In the lower strato-sphere, temperature tends to be nearly constant with alti-tude (isothermal), and windspeed generally decreases tominimum values at altitudes between 20 or 25 km. In theupper stratosphere, the rate of temperature increasereaches approximately 2.8 K/km. Windspeeds increasewith altitude through the upper stratosphere into themesosphere, where the temperature again decreases atrates of 2 to 4 K/km altitude. The division between thestratosphere and mesosphere is termed the stratopause.

In the lower troposphere, sensible heat is activelyexchanged by mixing processes which bring air into con-tact with the earth and sea surfaces. Low altitude warm-ing predominates during the day at lower latitudes.Conversely, cooling prevails at night and at higher lati-tudes. Much heat is also exchanged throughout the tropo-sphere by moisture phase changes. Solar radiative heatinput to the atmosphere is located predominantly in theupper stratosphere where chemical species, such asozone, absorb solar ultraviolet radiation. Between thesetwo heat source regions, temperatures are cooler in theupper troposphere and lower stratosphere. Basically, allatmospheric layers are subject to infrared radiative heatloss which, at the surface, may be notably limited bycloud cover.

Because air is compressible, temperature changesexperienced by atmospheric airparcels are not limited toheat gain or loss. These changes are also affected by adi-abatic expansion and compression when airparcels riseand descend. As airparcels are displaced adiabatically,that is, without heat gain or loss, up or down in the atmo-sphere, the temperatures change by a rate of nearly10 K/km of altitude displaced. Cooling occurs for up-ward displacements, and warming results from down-ward displacements. Thus when vertical motion is notuniformly distributed in the atmosphere, airparcels withthe most relative displacement experience the greatesttemperature differences from the surrounding airmass.Subsequently as rising airparcels become cooler andmore dense than the surrounding airmass, the force ofgravity causes buoyancy effects to restore the airparcelstoward their original altitude levels. Conversely, as de-scending airparcels become warmer or less dense thanthe surrounding ambient air, these parcels also experi-ence restoring buoyancy which forces them toward theiroriginal altitude.

Because ambient temperatures increase with altitudein the stratosphere, the airparcel temperature contrastgrows at rates of 10 to 13 K/km displaced, causing the

buoyancy forces to act as a stiff spring. In comparison,weaker spring force effects are experienced in the tropo-sphere and mesosphere, where airparcel temperaturecontrast grows at rates from 4 to 8 K/km displaced. Thiseffect, in which airparcel altitude displacements are op-posed by buoyancy forces, is much stronger in thestratosphere than in either the troposphere or the mesos-phere. As a result, the term stratosphere is quite appro-priate for this deeply stratified region of the atmosphere.The differences between wind and temperature structurein the troposphere and stratosphere also lead to inherentdifferences in atmospheric turbulence characteristics.Differences in turbulence characteristics are believed toinclude gust magnitudes, length scales, horizontal andvertical patch dimensions, patchiness or spacing be-tween patches, and characteristics of associated temper-ature perturbations. As indicated in the next section,these characteristics have only been partially observedto date.

Turbulence Observations in the Lower Stratosphere

Early operation of the U-2 airplane in the 1950’s pro-vided gust loads data to altitudes near 23 km over sever-al representative areas of the world.9 The USAF High-Altitude Clear Air Turbulence (HICAT) Program subse-quently conducted true gust velocity measurements inthe stratosphere with the U-2 airplane over various ter-rain and geographical areas.10 The XB-70 (NorthAmerican Rockwell, Los Angeles, California) andYF-12 (Lockheed Corporation, Burbank, California)prototype supersonic cruise aircraft also provided high-altitude gust acceleration data and true gust velocitymeasurements as a part of aeronautical flight researchprograms.11–14

Results from these flight programs (fig. 2) generallyindicate that the amount of turbulence expressed as a per-centage of total flight distance decreases from a maxi-mum near the jetstream and tropopause altitudes to aminimum near altitudes of 20 or 25 km. Figure 2 showsthat the fraction of miles in clear air turbulence (CAT) foruse with PSD criteria also decreases significantly in thelower stratosphere.7 The altitudes at which the amount ofturbulence decreases most changed somewhat from onesampling program to another. Presumably, these changesin the altitude of turbulence decrease were caused by sea-sonal differences in the atmospheric structure as well asgeographical area.13

The number of gust loads or normal accelerationpeaks cumulated from large to small and experienced asa function of overall flight distances also decreasesdramatically (fig. 3) at the higher altitudes of the

3

supersonic airplane data. The cross-hatched area onfig. 3 shows that the range of gust loads acceleration ex-perience for subsonic transport jet aircraft is close to thesupersonic aircraft experience at altitudes between ap-proximately 12 to 17 km. In contrast at altitudes above18 km, gust accelerations experienced in supersonicflight are markedly less than those experienced in eithersubsonic or supersonic flight at lower altitudes. Because25 km is generally near the altitude of minimal wind-speed, gust loads are expected to remain relatively mildat altitudes between 20 to 25 km. At higher altitudes,however, winds generally increase although the directionmay reverse. Such changes in windspeed indicatethat the amount and intensity of turbulence may beexpected to increase at altitudes of 30 to 50 km in theupper stratosphere.

Some insight into the observed decrease in turbulenceat altitudes in the lower stratosphere is provided by in-spection of seasonal trends, geographical patterns, andempirical associations with attending meteorologicalfeatures. Figure 4 shows the seasonal variation in therelative amount of turbulence encountered in the lowerstratosphere by the YF-12 airplane on flights made fromEdwards, California.13 These data are smoothed by a3-month moving mean for the altitude layer from 12 to17 km in the lower stratosphere. They depict a maxi-mum in the winter and early spring when lower alti-tude jetstream and airmass frontal activity is greatestand a minimum in the summer and early fall when thewinds in the lower stratosphere are weak and havereversed to easterlies.15

Meteorological Features of Turbulencein the Lower Stratosphere

On individual days, meteorologists have noted the as-sociation of high-altitude turbulence (HAT) at altitudesabove 12.5 to 25 km with mountain-wave activity andstrong winds blowing over the tops of large cumulonim-bus clouds.10,16–17 The association with wave activitywas examined further for several of the XB-70 turbu-lence encounter days.18–19 These findings not only sup-ported the indications from studies by HICATmeteorologists10,17 but also demonstrated the associa-tion of HAT with both rawinsonde balloon rise rates andwith a parameter important to mountain-wave behavior,that is, the curvature of the lower altitude wind profile.Nominal rawinsonde balloon rise rates are typically from250 to 300 m/min. These nominal rise rates may changegradually with balloon material characteristics, amountof inflation, and atmospheric temperature. Variationsaround the nominal rise rate will sometimes occur as aresult of up- or down-drafts associated with cloud orwave activity in the atmosphere.

Large and cyclic variations in the balloon rise rates areindicative of mountain waves and turbulence encoun-tered in the stratosphere.18 Examples of the balloon riserate variations associated with high-altitude turbulenceconditions are shown by the profiles in Figs. 5(a) to (d).18

These profiles represent two balloon ascents for a daywith mountain-wave conditions and HAT and two as-cents for another day with neither mountain waves norHAT. For HAT cases, nearby balloon rise rate variationsin the troposphere are generally in the range of 50 to150 m/min. Nonturbulent cases generally have rise ratevariations from 30 to 70 m/min. This study encompassed112 balloon ascents from 7 locations over 39 high-altitude flight days. The criteria for large and cyclic bal-loon rise rate variations correctly indicated 80 percent ofthe HAT encounters on these days.

Another parameter associated with HAT is an increasein the wind profile curvature between altitudes from 3 to7.6 km. Curvature is the second derivative of windspeed,

with respect to altitude divided by windspeed. Acurvature increase between two altitudes is conducive to the formation of large amplitude moun-tain waves.19 These findings were developed by identi-fying areas of expected mountain-wave activity andthose with positive curvature parameter changes in thelower troposphere between layers centered near 3 and7.6 km and examining these areas with respect to turbu-lence encountered along the flight track of the XB-70airplane (Fig. 6). For evaluation of the forecast, skillsprovided by the curvature parameter nonturbulence re-gions were also specified in smooth areas of the flighttrack where altitude changes were minimal. The flightexample shown in Fig. 6 has two HAT encounters in ar-eas of expected mountain-wave activity where the cur-vature criteria were fulfilled, one smooth segment of thetrack in another area of expected wave activity, and foursmooth track segments which were outside of these ar-eas. Overall evaluation of this forecast parameter on15 high-altitude flights resulted in correct identificationof 40 turbulence encounters out of a total of 47 encoun-ters and one false alarm in 43 nonturbulence areas. Thus,the role of lower altitude wave activity has been empiri-cally established by independent investigators for a sig-nificant portion of HAT cases encountered by bothsubsonic and supersonic aircraft. This finding was sig-nificant but not surprising because mountain waves hadbeen known to increase the severity of CAT at passengerjet cruise altitudes. Many researchers have been instru-mental in the analysis and demonstration of CAT en-hancement by mountain-wave-induced vertical dis-placement of shear layers to cause Kelvin-Helmholtzwave amplification and instability.20–25

U U ,⁄∆U U 0>⁄( )

4

These convincing demonstrations of the Kelvin-Helmholtz instability role in CAT were undoubtedly alarge part of the answer to explaining the generation ofmany CAT encounters. However, the Kelvin-Helmholtzinstability explanations did not suffice as a large part ofthe solution to the CAT forecast and avoidance problembecause its application would rely on forecasting thevertical displacement of windshear layers. Accurateforecasts of windshear layer displacements with thenecessary detail in time and space are not feasible. Therelated atmospheric processes often involve such localphenomena as mountain waves with small-scale atmo-spheric variations which entail subgrid phenomena.None the less, mountain-wave field studies and theoreti-cal analyses of the attending atmospheric dynamicshave made considerable progress in the concepts ofmountain-wave propagation behavior.26–28

An example of upward propagating mountain-waveactivity which causes turbulence in the lower strato-sphere is depicted by the temperature and wind fields an-alyzed for a case of in-situ aircraft observations inFig. 7.28 Moderate and severe turbulence was encoun-tered at several aircraft sampling altitudes as denoted bythe “hats” in the figure. Potential temperature is the tem-perature that the airparcel would have if adiabaticallycompressed to 1000 mb, that is, approximately 100 mmean sea level (MSL) pressure altitude. In Fig. 7, poten-tial temperature contours are denoted by solid lines. Hor-izontal wind contours (isotachs, lines of constant speed)are shown as dashed lines. Upstream windspeeds exceed60 m/sec near 7.5- and 12-km altitudes. At higher alti-tudes, the upstream winds generally decrease to less than20 m/sec at 20-km altitude. The potential temperaturecontours, which approximate trajectory streamlines,show the downslope winds over the mountain ridge.Successive wave crests indicate partially trapped wavecomponents at 5 to 7 km in the middle troposphere.

Although wave amplitudes are diminished near 11 km,a large amplitude jump is generated at the 14- to 17-kmlevel. At 16-km altitude, upstream of the jump, the zeroisotach indicates a narrow region of flow reversal. Suchreversals suggest that cooler, more dense air from loweraltitudes has been brought above warmer air to form a lo-cal layer of convective overturning. Unfortunately, themeasurement scale was not sufficiently detailed to indi-cate the cell sizes of instabilities involved in this region.Strong horizontal temperature gradients are noted in thejump and downstream of the peak. At 16 km, the hori-zontal windspeed increases from less than zero in theblocked or overturning region to 40 m/sec in the peak ofthe jump. The windspeed then decreases to between20 and 30 m/sec in a pronounced horizontal temperaturegradient with strong turbulence. Near 19 km, the highest

measurement altitude, light turbulence was stillobserved, and wave amplitudes and wavelengths weredecreased. Wave cases are seldom identical and oftenchange measurably over periods of an hour or more. Justthe same, the features of this case are representative ofwave character changes from the lower troposphere tothe tropopause and lower stratosphere when moderateand severe stratospheric turbulence occurs. Note that thesharp density changes resulting from strong temperatureperturbations in similar cases are often on the order of5 percent. Such changes would have measurable impactson aerodynamic coefficients and propulsion system massflow for an aerospace plane.

Numerical Simulation of WavePropagation

Relevant progress in applying numerical simulationto atmospheric gravity wave propagation, particularlyinto the lower stratosphere, has been recently re-viewed.29 Several numerical simulation codes are nowavailable and may have a role in advancing the quantita-tive understanding of small-scale perturbations ob-served in the lower stratosphere and in the prediction ofdisturbances at altitudes above the present airplane de-sign criteria database.30–33 Numerical techniques areparticularly applicable to the study of perturbations inthe lower stratosphere because quantitative treatment ofmountain-wave behavior by closed form solution is lim-ited to simple analytical profiles of wind and thermalstructures and to small obstacles or flow barriers. Multi-ple layers must be used to represent the irregular atmo-spheric wind and temperature profiles frequentlyassociated with most cases of strong turbulence. Be-cause the juncture between the troposphere and strato-sphere at the tropopause and jetstream level is also aninherent, first-order, atmospheric discontinuity, multiplelayers are also involved for estimating the amplitude ofwaves propagating into the stratosphere. Therefore, it isappropriate to seek numerical solution techniques to ad-equately account for the influence of irregular tempera-ture and wind profiles on mountain-wave propagationand turbulence in the stratosphere.

An initial experiment to ascertain the viability ofnumerical simulations for application to small-scalestratospheric perturbations is described in the next threesubsections.34 A brief overview of other related numeri-cal simulation studies follows in a later section.

Intercomparison Cases

In this initial comparison experiment, observed casesof disturbances in the lower stratosphere were com-pared with numerical simulation codes having various

5

underlying physical assumptions, numerical formula-tions, and topographical representation schemes.34 Sim-ulation input consisted of the topographic or barrierdescription as the lower boundary and the upstream pro-files of atmospheric temperature and wind as the inputcondition at every vertical gridline. This comparison ex-periment was initiated to identify differences betweenthe numerical codes that would be important to applica-tions in the stratosphere and to provide a practical assess-ment of the capability for specifying the atmosphericprofiles and topography for the numerical simulationinitial conditions in applied cases. Moreover, agreementbetween observation and models indicates the viabilityof using the numerical simulation models to specifyperturbation characteristics at altitudes above availableobservations.

Six cases of documented in-situ wave observations inthe stratosphere27–28,35–37 were selected for the pilotproject intercomparisons of simulations by the numeri-cal codes.30–33 These simulation codes can run withoutrestrictions of linearity or hydrostatic equilibrium. Dif-ferences in these codes include treatment of compress-ibility, topographic representation, grid structure (fixedcartesian versus variable-grid resolution and orthogonalcurvilinear), and viscid effects.

Three topographic reliefs relative to the barrier arerepresented by the following cases:

• Sierra-Nevada and White Mountains

• Rocky Mountain Continental Divide west ofDenver, Colorado

• Rocky Mountain ridgeline east of Alamosa,Colorado

The Sierra-Nevada and White Mountains have lower ter-rain upstream than downstream. The Rocky MountainContinental Divide has higher terrain upstream thandownstream. The Rocky Mountain ridgeline has approx-imately the same terrain elevation upstream as it doesdownstream from the barrier.

All six cases had in-situ aircraft observations at multi-ple altitudes from the upper troposphere to 18 km in thestratosphere. In four cases, strong turbulence was en-countered in the stratosphere. The other two cases exhib-ited well-established wave activity in the lowertroposphere but did not report notable turbulence orwave activity above 14 km. In the atmospheric layer atand below the mountain ridge level altitude, the casesrepresent an inverse square root of the Froude number

These cases range from approxi-mately 0.8 to 3.5 and, therefore, cover more than a nar-row range of dynamic flow conditions near the

topography. This application to the atmosphere differsslightly from the Froude number as conventionally usedin hydrodynamics. Here, U is the windspeed upstream ofa mountain ridge height, L, and the atmospheric stability(gβ or gδθ ⁄ θδh) is used in place of g alone because ofatmospheric buoyancy.29 The analyzed atmosphericwind and temperature data for the wave propagationevent depicted in Fig. 7 is an example of the in-situ dataused for comparison with the numerical simulations forthese cases.28

Case Preparation for Numerical Model Input

Upstream atmospheric wind and temperature profileswere prepared for input to the numerical models fromroutinely archived upper air network rawinsonde dataand synoptic charts. Figures 8 and 9 show examples ofthe original upper air observations and the resulting tem-perature and wind input profiles. For the first stage of theintercomparisons, preparation of the input atmosphericprofiles and topographic representation was accom-plished independently from the numerical modeling.These atmospheric data were interpolated in time andspace to give representative values of wind and tempera-ture at 1-km altitude intervals. As suggested by the scat-ter of the observed data around the input profiles, thisdata value selection process was subjective with atendency to produce constant wind shear and lapse ratelayers over large altitude segments.

Topographic barrier descriptions for the simulationlower boundary condition were also specified by a three-way, subjective compromise among aircraft groundtrack, ridge layer wind direction, and topographic irreg-ularities. These independently prepared input data werethen given to the numerical modeling personnel at theUniversities of Washington (Seattle) and California (LosAngeles) without identification of the dates or in-situcase observations. Implementation of these input data inthe models and selection of grid resolution, time step,model domain, and output simulation times were notrigidly restricted. Instead, such decisions were left to theexpert judgment of the individual modelers.

Preliminary Comparison Results

Results of the initial intercomparisons betweensimulations and observed wave and turbulence werehighly encouraging.34 As an example, Figs. 10(a) to (d)show the strong contrast between simulations producedfor wave perturbation cases, with and without strong tur-bulence in the stratosphere, for the potential temperatureand horizontal windspeed fields. All three models whichsimulated these two cases exhibited similar contrastbetween the one with and the one without turbulencein the stratosphere. This turbulence case simulation

NFr U**2 Lg⁄=( ).

6

corresponds to the in-situ measurement analysis shownin Fig. 7. The simulation replicates the diminished waveamplitudes near 11 km, potential temperature jump be-tween 14 and 17 km, large horizontal windspeed changesat 16 km, and decreased wave amplitudes and wave-length above 19 km.

Preliminary assessment of the simulation results forthe six cases was based on inspection of qualitative wavepropagation features. The qualitative features includedwave character in the troposphere, wave amplitude prop-agation behavior in the tropopause zone, and wave-breaking tendency indicative of turbulence in the lowerstratosphere. Inspection of the analyzed aircraft observa-tion data for the 6 cases yielded 15 of these qualitativefeatures for evaluation of the initial outputs availablefrom 2 models. For the 30 qualitative wave propagationfeatures examined on the simulations, agreement wasjudged as good for 21, as fair for 4, and as poor for 5 ofthe evaluated features.

Quantitative comparison of amplitudes for the largerwave perturbations at the flight data altitudes were alsoassessed. Quantitative examination emphasized the pre-dominant perturbation wave heights, vertical velocity,and windspeed changes. Magnitudes of these featureswere generally estimated from contour plots for the ob-served and the numerical model output data. More than50 percent of the 92 comparisons agreed to within a fac-tor of 2.34 In judging the goodness of this agreement, thefollowing factors were considered:

• Perturbation magnitudes vary by more than a factorof 2 between subjective turbulence intensity-ratingcategories.

• Aircraft measured perturbation magnitudes typi-cally change by 10 to 100 percent for repeated dataruns at given altitudes within a 3-hr period.

• Manual data extraction from contour presentationsis not precise.

• Strong perturbations are not expected to be steadystate in either the atmosphere or the numericalsimulations.

In view of these considerations, the present intercompar-ison results are judged to be excellent and very encour-aging for the application of numerical simulation to waveperturbation phenomena in the stratosphere.34

Further assessment will consider the sensitivity of theindividual models and comparisons among them to thefollowing parameters:

• Resolution and smoothing of topographic featuresas well as representation by grid blocks (restrictedto horizontal and vertical surfaces) versus terrain-following constructions

• Computational grid resolution in horizontal andvertical space dimensions as well as in the time-step size

• Duration of the simulations in atmospheric time

• Resource requirements in terms of computer time,cost, and user expertise

These assessments will consider present and futureapplications which may include extension to altitudesabove 50 km and finer grid resolutions to study the influ-ence of shear layers with Kelvin-Helmholtz instability.

Related Wave Propagation Studies

Generation of atmospheric turbulence in the strato-sphere is basically the result of buoyant imbalance andmotion stresses much the same as in the lower atmo-sphere. In the troposphere, however, buoyant imbalanceis frequently caused by heating of the ground or clouds,releasing of latent heat in condensation processes, mix-ing as winds blow over rough terrain, or strengthening ofupper air wind and temperature gradients. In contrast, alarger portion of turbulence in the stratosphere is causedby wave processes triggered by mountains, cloud barri-ers, or irregular jetstream dynamics which amplify asthey propagate upward. In the troposphere, vertical prop-agation of some wave energy is frequently prevented byairmass layers. These layers have negative or neutralstatic stability, that is, no buoyant restoring force. Propa-gation is also prevented by reflection caused by strongchanges in windspeed with altitude on the underside ofthe jetstream or by significant directional shifts in thewind profile. As wave motion components which escapethe aforementioned limitations propagate upward, am-plitude and velocity perturbations of these componentstend to grow approximately with the inverse square rootof the density ratio between altitudes.29,38 Thus, upwardwave leakage amplifies until it generates its own instabil-ities or meets other limiting factors in the wind ortemperature static stability profile.

Ground-based measurements and satellite observa-tions are among methods used to gather evidence ofwave amplification and instability with propagationto higher altitudes in the mesosphere and thermo-sphere.39–41 The extremely low density at these altitudesleads to large amplitude disturbances which are observ-able by remote means. These phenomena are believed toexplain much of the atmospheric density variations in-ferred from space shuttle entry trajectory data.42 Themost dramatic of these was the alleged “density hole”which strongly perturbed the Space Shuttle Columbiacausing a jolting response similar to heavy turbulenceduring atmospheric entry near 76-km altitude on STS-4.

7

Most concern for airbreathing hypersonic flight researchis, however, at much lower altitudes where dynamicpressures will be sufficient for acceleration and levelcruise. Thus, the need for realistic specification of atmo-spheric perturbations for hypersonic flight is most criti-cal at altitudes from 25 to 50 km. These altitudes areabove the limit of most in-situ data, yet they are stillsomewhat below most of the remote observation studies.

The mechanisms involved in wave propagation fromthe middle stratosphere to the mesosphere have beenstudied by a limited number of numerical simulationswhich have required considerable computer time.43

These simulation studies have illustrated the amplifica-tion and instability processes and have provided usefuladditions to conventional theoretical interpretations. Asan example, Figs. 11(a) to (d) show the potential temper-ature contours resulting from a numerical simulation ofwave propagation between altitudes of 30 and 50 km.43

The wave response is triggered by a barrier located50 km downstream from the inflow boundary and at thebase altitude of the simulation, 30 km. The potentialtemperature contours, which approximate flow stream-lines for nearly steady conditions, show the wave ampli-tude increases with altitude. At 10-hr simulation time(Fig. 11(a)), the upward motion becomes very steep inpatches between 40- and 50-km altitude. In local regionswhere the potential temperature contours slant back tothe left as they go up, the simulation produces colder,more dense air over warmer, lighter air. The prevailingleft-to-right wind decelerates and begins to reverse. Con-tinuation of this process (Figs. 11(b) and (c)) leads tofurther reversal of the wind in these local regions and towave breaking or overturning as the small areas of coldair accelerate downward. Turbulence and mixing inthese small areas develop regions of nearly constant po-tential temperature as noted by the tendency to formpockets of separated potential temperature isotherms(Fig. 11(c)) at 14 hr into the simulation. Finally at 16 hr(Fig. 11(d)), the wave perturbations and turbulence de-cay before the onset of another cycle of wave propaga-tion, growth, and overturning.

In spite of the value of this upper stratosphere numer-ical simulation work, many questions of wave behaviorremain to be answered in the lower stratosphere (below30 km) before the knowledge of higher altitude wave be-havior can contribute to design risk definitions for hyper-sonic vehicles. These questions involve the frequency ofsignificant wave component generation at, or propaga-tion through, the tropopause. The critical layer behaviorin the lower stratosphere must also be ascertained. Stud-ies of the instability zone associated with the criticallevel will greatly assist in this effort.

Wave propagation studies have recently addressed thelower stratospheric structure where wind decreases withaltitude. Theoretically, critical levels occur where thewindspeed equals the wave-phase speed (or zero wind-speed for a standing wave). Results of this work empha-size the following facets of wave propagation behavior:

• Critical level behavior, wherein propagating waveenergy is converted to turbulent and kinetic energy,is commonly manifested a few kilometers belowthe actual critical level altitude where the primaryupward propagating wave meets reflected wavecomponents which are propagating downward.44

• Critical level criteria do not need to be completelyfulfilled to induce a layer of instability in the lowerstratosphere.45 That is, the windspeed decreasewith altitude does not actually need to reach zero(or reverse) with respect to the wave.

• Because of the effects of Earth rotation, longerwavelength inertial-gravity wave propagation caninduce instabilities at multiple levels over a broador deep altitude zone depending on the atmosphericprofile structure and mode wavelength or wavenumber.29,45

• Nonhydrostatic effects impact the momentumflux and cause wave perturbations in the strato-sphere to occur further downwind than predicted bysolutions based on the simplifying hydrostaticassumption.46

Figures 12(a) to (d) show an example from the previ-ously cited studies.44 This example depicts instabilitydevelopment in a deep layer of decreasing wind with anupward propagating wave component approaching thecritical level. Wave propagation behavior in this simula-tion study corresponds to what may be expected in the al-titude band from 15 to 30 km at times. In this case, theinput upstream windspeed decreases with constant shearfrom 10 m/sec at 15 km (the base altitude of the layer) to0 m/sec at 25-km altitude (the critical level) and contin-ues in reverse direction to –5 m/sec at 30-km altitude.Figures 12(a) to (d) show the streamfunction resultingfrom monotonic excitation having a wavelength of10 km and an amplitude less than 150 m introduced atthe base altitude of 15 km of the nonlinear, spectral sim-ulation. For clarity of illustration, Figs. 12(a) to (d) showthe streamfunction patterns for only the 20- to 26-kmaltitude section of the simulation at times of 4, 9, 10, and12 hr after introduction of the 10-km wave at the lowerboundary. In addition to delineate the instability pattern,the streamfunction contour interval resolution isdecreased by a factor of 10 just below the 22-km altitude.

8

The first phase, depicted in Fig. 12(a) at 4 hr into thesimulation, shows the wave crests and troughs slope up-stream with altitude as they propagate to higher altitudes.As the propagation process continues, critical level inter-actions reflect wave energy which modifies the form ofthe upward propagating wave. This interaction subse-quently produces sloping zones of reverse flow at alti-tudes between 23 km and the critical level at 25 km asshown in Fig. 12(b) for 9 hr into the simulation. At thistime, rapid development of smaller scale instabilities isinitiated and becomes evident between altitudes of22 and 24 km just 1 hr later as shown in Fig. 12(c). As theinstability processes enter their later stages at 12 hr intothe simulation time (Fig. 12(d)), note that the small-scaledisturbances not only extend below 22 km but some alsobegin to propagate above the critical level at 25 km. Thisinstability zone below the critical level, somewhat abovethe tropopause and jetstream altitudes, will often be at al-titudes where airbreathing vehicles accelerate from su-personic to hypersonic speeds. This progress innumerical wave propagation and simulation studies indi-cates that atmospheric dynamics can have a greater rolein the quantitative understanding of small-scale pertur-bations observed in the lower stratosphere and in the pre-diction of disturbances at altitudes above the presentdatabase for aircraft design criteria. The challenges andrecommendations for further progress in the definition ofstrong discrete perturbations at stratospheric altitudes areclear. Meteorological observations and in-situ atmo-spheric data from the troposphere and lower stratosphereare required to provide the basic statistical characteriza-tion of perturbation activity at these levels. Definition ofperturbations at higher altitudes requires numerical sim-ulation of the upward propagation dynamics. Such defi-nition would help in determining how theseperturbations are affected by the atmospheric structureand under what meteorological conditions instabilitieswill result in strong perturbations and turbulence at high-er altitudes. As numerical simulation studies progress,their realism can be evaluated in stages by comparisonwith in-situ perturbation measurements, with wave am-plitude observations by rawinsonde balloon rise rate inthe middle stratosphere, and with remotely detectedwave activity in the mesosphere. Such work should sig-nificantly improve the accomplishment of two basicgoals. These goals are as follows:

• To predict the nature of wave propagation andinstabilities at higher altitudes

• To improve estimates of the perturbation-lengthscales and maximum magnitudes for hypersonicaircraft design purposes

These accomplishments will inherently support thedefinition of hypersonic vehicle design criteria and theformulation of simple, discrete models for characteriz-ing perturbations in the vertical and horizontal windcomponents as well as the pressure, density, andtemperature states.

Discrete Perturbation Model Concept

This section describes a simple, initial, genericconcept for a combined discrete atmospheric perturba-tion model. Such models may be used for design sensi-tivity assessment. However, their use as design criteriathroughout the stratosphere will not be warranted untilthe appropriate magnitudes, scale lengths, and risk levelsare better estimated for the higher altitudes.

The traditional derived equivalent gust velocity, Ude, isbasically a discrete perturbation form which has servedits purpose well as an airframe lifetime gust loads predic-tor for altitudes which were surveyed with similar air-craft.5 Its one-minus-cosine load shape, in which the gustencounter builds up in the positive direction and decaysback to zero over a distance of 25 wing chord lengths, isa one-sided model for the vertical gust component alone.As airframe structures became more flexible, it becameprudent to characterize gust data in terms of the turbu-lence PSD for the evaluation of second-order responses.4

For some preliminary design studies, simple, repeatableinputs of sharp, two-sided transients which represent thelarger magnitude perturbations embedded in continuousturbulence are desirable. Hypersonic vehicle airworthi-ness may depend on gust-induced responses for severalsubsystems, such as propulsion, flight control, and basicsensor capabilities, in addition to the gust loads on thestructure. Therefore, the discrete perturbation modelmust include all physical components of the atmospherictransients that may affect the vehicle.

One simple, generic model that combines all of theperturbation variables is a vortex with solid body rotationin the core and velocity components outside the core de-caying inversely with distance from the core. This pertur-bation form is generally characteristic of atmosphericobservations for phenomena including vortex-ring seg-ments accompanying downburst outflows, dust devils,and higher altitude rotor formation resulting fromKelvin-Helmholtz instability and other familiar vortexshedding phenomena.21,47 Generation of the instabilitycells results from wave amplification which brings upcolder, more dense air and brings down warmer, lessdense air. Figure 13 shows potential temperatureisotherm distortion leading to formation of a strongturbulent perturbation.

9

When vortex formation occurs with the axis of the corein the horizontal plane, the gust velocity component per-pendicular to the flightpath achieves maximum perturba-tion velocity along trajectories through the center of thecore. The perturbation component parallel to the flight-path attains maximum amplitude for trajectories tangen-tial to the outer edge of the core. For illustration of theresulting perturbations, the maximum gust velocity of10 m/sec with the vortex core radius dimensioned to200 m is selected. This combination of maximum gustvelocity and core radius produces an arbitrarily strongmaximum shear of 0.05 sec–1.

Figure 14(a) shows the vertical gust velocity for ahorizontal flight trajectory through the center of the core.In comparison, note that the peak-to-peak perturbationamplitude through the core is approximately the same asprescribed for maximum cruise speed at 15 km.1 Thehorizontal component for this trajectory directly throughcore center of the idealized perturbation does not experi-ence any variation. Both horizontal and vertical compo-nents experience comparable perturbation magnitudesfor horizontal trajectories through the upper or loweredges of the core.

Figure 14(b) illustrates the horizontal and verticalcomponents of the discrete perturbation model for a tra-jectory tangential to the (that is, through the) upper edgeof the core. Again, note that the amplitudes of this dis-crete model are approximately the same as the Ref. 1 cri-teria for design loads criteria at maximum dive speed atan altitude of 15 km. For the temperature change, a valueof 10 K with buildup and drop-off distances of 400 m isused. This value appears to be reasonably conservativeon the basis of previously reported aircraft measure-ments.48 Because temperature transient peaks often donot coincide with peaks in the gust velocity components,the coldest temperature is offset 200 m to the updraft sideof the core as illustrated with the attending ambient den-sity variation in Fig. 14(c). This configuration of cold airrelative to the motion components is highly arbitrary be-cause neither the most prevalent nor the most critical pat-terns are known. Pressure is approximated by use ofBernoulli’s equation and the equilibrium assumption thatthe pressure gradient force balances the centrifugalforce. For this model, the pressure perturbation is lessthan 0.1 percent at the outer edge of the core. This per-turbation is not illustrated because it results in a nearlynegligible effect on density.

Specification of such simple, discrete perturbationmodels as well as their geometric dimensions and pertur-bation magnitudes is reasonably straightforward for thealtitudes of available in-situ data below approximately20 km. At higher altitudes above available in-situ data,

selection of the gust and thermodynamic perturbationmagnitudes as well as the appropriate geometric lengthscales becomes highly questionable. Discrete perturba-tion model specification for hypersonic aircraft design atthese higher altitudes requires the use of numerical sim-ulation of the small-scale dynamic atmospheric process-es which lead to strong perturbations in gust velocities,temperature, and density.

Concluding Remarks

Vehicle design criteria for lower altitudes have servedtheir purpose well for structural design of subsonic air-craft to altitudes of approximately 15 km. However,these criteria do not incorporate combined perturbationinputs for either the motion components or the tempera-ture, pressure, and density states. These states are expect-ed to be more significant to airbreathing hypersonicvehicles. In addition, the amount of in-situ data for estab-lishing gust design criteria decreases markedly betweenaltitudes of 15 and 25 km. Above these altitudes, essen-tially no in-situ data have been gathered. Available datafor turbulence and temperature transients encountered byaircraft in the lower stratosphere often show an associa-tion with lower altitude mountain-wave activity. There-fore, improved understanding of upward wave pro-pagation processes is a key element in the formulation ofatmospheric perturbation design criteria for higheraltitude aircraft.

Recent advances in numerical simulation of wavepropagation processes are making such improvements inunderstanding the conditions and atmospheric structuresassociated with the development of wave instabilitieswhich cause turbulence and strong gusts. A current ex-periment comparing in-situ observations of mountain-wave-induced perturbations in the lower stratospherewith two-dimensional, numerical, atmospheric dynamicssimulations made by separate codes was described. Ini-tial results from these comparisons indicate numericalsimulations will provide useful descriptions of higher al-titude perturbations. An example of a simple, generic,discrete perturbation model combining motion compo-nents and thermodynamic (pressure, density, and temper-ature) disturbances was given. Definition of appropriatedisturbance magnitudes and length (dimensional) scalesfor such discrete atmospheric perturbation models at al-titudes of 25 to 50 km is needed for hypersonic vehicledesign. These perturbation magnitudes and length scalescan be defined by studies which combine these numer-ical atmospheric simulation tools with higher altitudeobservations in the middle and upper stratosphere.

10

References

1 U.S. Dept. of Transportation, Federal AirworthinessRegulations, Airworthiness Standards: Transport Cate-gory Airplanes, pt. 25, app. G, change 19, 1974.

2 USAF, Military Specification, Airplane Strength andRigidity Flight Loads, MIL-A-8861B, Feb. 1986.

3 Pratt, Kermit G. and Walter G. Walker, A RevisedGust-Load Formula and a Re-Evaluation of V-G DataTaken on Civil Transport Airplanes From 1933 to 1950,NACA-1206, 1954.

4 Houbolt, John C., Roy Steiner, and Kermit G. Pratt,Dynamic Response of Airplanes to Atmospheric Turbu-lence Including Flight Data on Input and Response,NASA TR R-199, 1964.

5 Zalovcik, J.A., J.W. Jewel, Jr., and G.J. Morris, Com-parison of VGH Data From Wide-Body and Narrow-Body Long-Haul Turbine-Powered Transports, NASATN D-8481, 1977.

6 Rhyne, Richard H. and Roy Steiner, Power SpectralMeasurement of Atmospheric Turbulence in SevereStorms and Cumulus Clouds, NASA TN D-2469, 1964.

7 Hasty, Paul L., A Description of the Atmospheric Tur-bulence Environment Derived From the Critical Atmo-spheric Turbulence (ALLCAT) Program, AFFDL-TR-77-4, 1977.

8 Murrow, Harold N., “Measurements of AtmosphericTurbulence,” Atmospheric Turbulence Relative to Avia-tion, Missile, and Space Programs, NASA CP-2468,1986, pp. 73–92.

9 Coleman, Thomas L. and Roy Steiner, AtmosphericTurbulence Measurements Obtained From Airplane Op-erations at Altitudes Between 20,000 and 75,000 Feet forSeveral Areas in the Northern Hemisphere, NASA TND-548, 1960.

10 Crooks, Walter M., Frederic M. Hoblit, Finis A.Mitchell, et. al., Project HICAT—High Altitude ClearAir Turbulence Measurements and Meteorological Cor-relations, AFFDL-TR-68-127, vol. I, 1968.

11 Wilson, Ronald J., Betty J. Love, and Richard R.Larson, Evaluation of High-Altitude Turbulence En-counters on the XB-70 Airplane, NASA TN D-6457,1971.

12 Reukauf, Paul J., Frank V. Olinger, L.J. Ehernberg-er, and Craig Yanagidate, “Flight-Measured TransientsRelated to Inlet Performance on the YF-12 Airplane,”Proceedings of YF-12 Experiments Symposium, NASACP-2054, vol. III, 1978, pp. 427–473.

13 Ehernberger, L.J. and Betty J. Love, High AltitudeGust Acceleration Environment as Experienced by a Su-personic Airplane, NASA TN D-7868, 1975.

14 Ehernberger, L.J., “The YF-12 Gust Velocity Mea-suring System,” Proceedings of YF-12 Experiments Sym-posium, NASA CP-2054, vol. I, 1978, pp. 135–154.

15 Range Commanders Council, Range Reference At-mosphere, Edwards AFB, California, 0–70 km Altitude,MG 366-83, 1983.

16 Ehernberger, L.J., Atmospheric Conditions Associ-ated With Turbulence Encountered by the XB-70 Air-plane Above 40,000 Feet Altitude, NASA TN D-4768,1968.

17 Ball, John T., Cloud and Synoptic Parameters Asso-ciated With Clear Air Turbulence, NASA CR-111778,1970.

18 Incrocci, Thomas P. and James R. Scoggins, An In-vestigation of the Relationships Between Mountain-Wave Conditions and Clear Air Turbulence Encounteredby the XB-70 Airplane in the Stratosphere, NASA CR-1878, 1971.

19 Possiel, Norman and James R. Scoggins, “Curva-ture of the Wind Profile in the Troposphere Versus Re-gions of CAT and Non-CAT in the Stratosphere,” Mon.Wea. Rev., vol. 104, no. 1, Jan. 1976, pp. 57–62.

20 Harrison, Henry T., The Mountain Wave, NASACR-315, 1965.

21 Clark, James W., Richard C. Stoeffler, and Paul G.Vogt, Research on Instabilities in Atmospheric Flow Sys-tems Associated With Clear Air Turbulence, NASA CR-1604, 1970.

22 Dutton, John A. and Hans A. Panofsky, “Clear AirTurbulence—A Mystery May Be Unfolding,” Science,vol. 167, no. 3920, Feb. 1970, pp. 937–944.

23 Atlas, D., J.I. Metcalf, J.H. Richter, and E.E. Gossa-rd, “The Birth of ‘CAT’ and Microscale Turbulence,” J.Atmospheric Sciences, vol. 27, Sept. 1970, pp. 903–913.

24 Browning, K.A., A. McPherson, and J.R. Starr, “Si-multaneous Measurements of Clear Air Turbulence at theTropopause by High-Power Radar and Instrumented Air-craft,” Nature, vol. 228, 1970, pp. 1065–1067.

25 Metcalf, J.I. and D. Atlas, “Meteorological Struc-ture of Thin Clear Air Scatter Layers Observed by Ultra-High Resolution Radar,” Proceedings of the 15th RadarMeteorology Conference, Urbana, Oct. 10–12, 1972, pp.242–274.

11

26 Holmboe, Jörgen and Harold Klieforth, Investiga-tion of Mountain Lee Waves and the Air Flow Over theSierra Nevada, AFCRC TR-57-204, 1957.

27 Lilly, D.K., Y. Pann, P. Kennedy, and W. Touten-hoofd, Data Catalog for the 1970 Colorado Lee WaveObservation Program, NCAR-TN/STR-72, 1971.

28 Lilly, D.K., “Observations of Mountain-InducedTurbulence,” J. Geophys. Res., vol. 76, 1971, pp. 6585–6588.

29 Wurtele, M.G. and A. Datta, “Lee Waves, Benignand Malignant,” Measurement and Modeling of Environ-mental Flows—1992, American Society of MechanicalEngineers, New York, 1992, pp. 109–122.

30 Pihos, Gregory G. and Morton G. Wurtele, An Effi-cient Code for the Simulation of Nonhydrostatic Strati-fied Flow Over Obstacles}, NASA CR-3385, 1981.

31 Durran, D.R. and J.B. Klemp, “A CompressibleModel for the Simulation of Moist Mountain Waves,”Mon. Wea. Rev., vol. 111, 1983, pp. 2341–2361.

32 Sharman, R.D., T.L. Keller, and M.G. Wurtele, “In-compressible and Anelastic Flow Simulations on Nu-merically Generated Grids,” Mon. Wea. Rev., vol. 116,1988, pp. 1124–1136.

33 Kim, Young-Joon and Akio Arakawa, “Assessmentof Gravity-Wave Parameterization Schemes Using a Me-soscale Gravity-Wave Model,” Preprints Ninth Confer-ence on Numerical Weather Prediction, Am. Meteor.Soc., Boston, 1991, pp. 380–383.

34 Ehernberger, L.J., Dale R. Durran, Peter P. Miller, S.Ward, M.G. Wurtele, R.D. Sharman, A. Datta, Y.J. Kim,T.L. Keller, and Terry L. Clark, Comparison of 2-D Nu-merical Simulations With Observed Wave and Turbu-lence Activity in the Lower Stratosphere. (Scheduled forpublication as a NASA report in 1993. Forward requestsfor this document to L.J. Ehernberger.)

35 Helvey, R.A., Observations of Stratospheric ClearAir Turbulence and Mountain Waves Over the Sierra Ne-vada Mountains—An Analysis of the U-2 Flights of 13--14 May 1964, AFCRL-68-0001, 1967.

36 Waco, David E., “Temperature Gradients in Strato-spheric Turbulence,” J. Appl. Met., vol. 11, 1972, pp. 99–107.

37 Nicholls, J.M., “Measurements of StratosphericAirflow and Clear Air Turbulence, up to 63,000 ft, Overand Downwind of Mountainous Terrain,” Proceedings ofRAeS/CASI/AIAA International Conference on Atmo-spheric Turbulence, London, 1971.

38 Hines, C.O., “Internal Atmospheric Gravity Wavesat Ionospheric Heights,” Canadian J. Phys., vol. 38,1960, pp. 1441–1481.

39 Fritts, D.C., “Gravity Wave Saturation in the MiddleAtmosphere: A Review of Theory and Observations,”Rev. Geophys. Space Phys., vol. 22, 1984, pp. 275–308.

40 Philbrick, C.R. and B. Chen, “Transmission ofGravity Waves and Planetary Waves in the Middle Atmo-sphere Based on Lidar and Rocket Measurements,” Adv.Space Res., vol. 12, no. 10, 1992, pp. (10)303–(10)306.

41 Fetzer, E.J., A Global Climatology of Middle Atmo-sphere Inertia-Gravity Waves, Ph.D. Thesis, U. of Colo-rado, 1990.

42 Findlay, J.T., S.P. Berube, and G.D. Qualls, Shuttle-Derived Density Profiles in the Middle Atmosphere,NASA CR-4109, 1988.

43 Bacmeister, J.T. and M.R. Schoeberl, “Breakdownof Vertically Propagating Two-Dimensional GravityWaves Forced by Orography,” J. Atmos. Sci., vol. 46, no.14, 1989, pp. 2109–2134.

44 Landau, D.M. and M.G. Wurtele, Resonant Back-scattering of a Gravity Wave From a Critical Level, Pro-ceedings of Eighth Conference of Atmospheric andOceanic Waves and Stability, Am. Meteor. Soc., Boston,1991, pp. 244–247.

45 Datta, A., Propagation of Gravity, Inertia-Gravity,and Lee Waves in Two Dimensions, M.S. Thesis, U. ofCalifornia, Los Angeles, 1991.

46 Keller, T.L., M.G. Wurtele, and R.D. Sharman, “Im-plications of the Hydrostatic Assumption on Atmospher-ic Gravity Waves,” Proceedings of Eighth Conference ofAtmospheric and Oceanic Waves and Stability, Am.Metero. Soc., Boston, 1991, pp. 320–323.

47 Wingrove, R.C., R.E. Bach, Jr., and T.A. Schultz,“Analysis of Severe Atmospheric Disturbances FromAirline Flight Records,” Flight in Adverse Environmen-tal Conditions, AGARD CP-470, 1989, pp. 3-1 to 3-7.

48 Schweikhard, W.G., G.B. Gilyard, J.E. Talbot, andT.W. Brown, Effects of Atmospheric Conditions on theOperating Characteristics of Supersonic Cruise Air-craft, Presented at XXVII Congress of the InternationalAstronautical Federation (I.A.F.), Anaheim, California,I.A.F. 76-112, Oct. 16, 1976.

12

Fig. 1 Representative atmospheric structure, January average for Edwards, California (Ref. 15).

Fig. 2 High-altitude turbulence survey results for amount of turbulence expressed as the percent of flight distance (Ref. 13).

920675

Temperature, K, deg300

80

h, km above

MSL

70

60

50

40

30

20

10

0Zonal westerly windspeed, m/sec

100755025 275250225200

Mesosphere Stratosphere Troposphere

24

20

16

120 2 4

Flight distance in turbulence, percent6 8

h, km

USAF design recommendation (Ref. 7) Supersonic aircraft

YF-12A (Ref. 13) XB-70 (Ref. 12)

Subsonic aircraft Western U.S. (Ref. 9) All data (Ref. 9) HICAT (Ref. 10)

920676

13

Fig. 3 Cumulative frequency distributions of peak accelerations caused by turbulence.

Fig. 4 Seasonal variation of turbulence encountered in the lower stratosphere between 12 and 17 km.

920677Peak normal acceleration, g.5

Cumulative frequency,

km-1

10-1

10-2

10-3

10-4

10-5.4.3.2.10

h, km12.2 to 13.7 13.7 to 15.2 15.2 to 16.8 16.8 to 18.3 18.3 to 19.8 < 12.2 combined ± acceleration

YF-12A airplane (Ref. 13)

Subsonic transport (Ref. 5)

June September December March June

16

12

8

4

0

Percent

3-month moving mean from 12- to 17-km band

920678

14

Fig. 5 Rawinsonde balloon ascent rate profiles for turbulence and nonturbulence areas encountered in high-altitudesupersonic flight (Ref. 18).

16

14

12

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8

6

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0

h, km

200 300 400Ascent rate, m/min

920679

Ely, Nevada

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16

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200 300 400Ascent rate, m/min

920680

Winnemucca, Nevada

100

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200 300 400Ascent rate, m/min

920681

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200 300 400Ascent rate, m/min

920682

Ely, Nevada

100

(a) Rate variations of 50 to 150 m/min for turbulencenear Ely, Nevada.

(b) Rate variations of 50 to 150 m/min for turbulencenear Winnemucca, Nevada.

(c) Rate variations of 30 to 70 m/min for nonturbu-lence near Las Vegas, Nevada.

(d) Rate variations of 30 to 70 m/min for nonturbu-lence near Ely, Nevada.

15

Fig. 6 Mountain-wave turbulence forecast verification (modified from Ref. 19).

Turbulent aircraft flight segment Nonturbulent aircraft flight segment Expected mountain-wave areas Expected mountain-wave areas where ∆(U/U) > 0 Upper air observation sites

920683

Flight track

16

Fig. 7 Cross-section of potential temperature and windspeed analyzed from in-situ aircraft data for mountain-waveturbulence (Ref. 28).

20

h, km

19

18

17

15

16

14

13

12

11

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0 50 100 150 200

Rocky Mountain profile

Distance, km920684

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20310

305

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Potential temperature, K Windspeed, m/sec Turbulence encountered along flight track

17

Fig. 8 Input temperature profile and rawinsonde observation data for simulation of mountain-wave turbulence in thestratosphere.

Fig. 9 Input wind profile and rawinsonde observation data for mountain-wave turbulence in the stratosphere.

40 x 103

35

30

25

20

15

10

5

0–80 –70 –60 –50 –40 –30 –20 –10 0 10 20

Ambient temperature, °C

h, m

Final input profile

Flight area values from morning upper air charts

Flight area values from evening upper air charts

Morning rawinsonde from Denver, Colorado

Morning rawinsonde from Winslow, Arizona

Morning rawinsonde from Salt Lake City, Utah

920685

40 x 103

35

30

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0–10 0 10 20 30 40 50 60 70 80 90

Windspeed, m/sec

h, m

920686

Final input profile

Flight area values from morning upper air charts

Flight area values from evening upper air charts

Morning rawinsonde from Denver, Colorado

Morning rawinsonde from Winslow, Arizona

Morning rawinsonde from Salt Lake City, Utah

18

(a) Potential temperature contours (K, deg) for strong turbulence.

(b) Horizontal velocity contours (m/sec) for strong turbulence.

Fig. 10 Vertical and horizontal cross-sections for numerical simulations of potential temperature and wind contourswith and without observed turbulence in the stratosphere.

19

(c) Potential temperature contours (K, deg) without turbulence.

(d) Horizontal velocity contours (m/sec) without turbulence.

Fig. 10 Concluded.

20

21

(a) At 4 hr, monotonic wave upward propagation approaches the critical level at 25 km.

(b) At 9 hr, critical level interaction induces zones of reverse flow between 22.5 and 25 km.

Fig. 12 Numerical simulation streamfunction field showing instability development beneath the critical level at 25 kmresulting from upward propagation of a monotonic wave at an altitude of 15 km (Ref. 44).

920695Distance, km

30

h, km

26

24

22

20

Critical level

4 hr

150

920696Distance, km

30

h, km

26

24

22

20

9 hr

150

22

(c) At 10 hr, smaller scale perturbations develop.

(d) At 12 hr, perturbations have developed at smaller scales and propagate to both higher and lower altitudes.

Fig. 12 Concluded.

920697Distance, km

30

h, km

26

24

22

20150

10 hr

Critical level

920698Distance, km

30

h, km

26

24

22

20150

12 hr

23

Fig. 13 Schematic of distorted atmospheric potential temperature stratification leading to instability and vortex wrap up.

Stratification distorted by wave growth

920699

Cold, more dense air

Warm, less dense air θ + ∆θ

θ

θ – ∆θ

Relative motion Instability zone of turbulent mixing Temperature contours

24

(a) Vertical component for horizontal trajectory through the core center.

(b) Components for a trajectory through the core top.

(c) Thermodynamic perturbations for a trajectory through the core top.

Fig. 14 Discrete, small-scale, two-dimensional, atmospheric perturbation model.

10

5

0

–10

–5

–15–1000 –800 –600 –400 –200 0 200 400 600 800 1000

Horizontal distance from core, m

Velocity, m/sec

Vortex model perturbation though center of core

920700

Perturbation schematic

x, U

h, w

5

0

– 5

–10–1000 –800 –600 –400 0

Horizontal distance from core, m200 400 600 800 1000

Temperature, K, and

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920702

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25

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Stratospheric Turbulence Measurements and models forAerospace Plane Design

WU 763-21-51

L.J. Ehernberger

NASA Dryden Flight Research FacilityP.O. Box 273Edwards, California 93523-0273

H-1865

National Aeronautics and Space AdministrationWashington, DC 20546-0001 NASA TM-104262

Progress in computational atmospheric dynamics is exhibiting the ability of numerical simulation to describeinstability processes associated with turbulence observed at altitudes between 15 and 25 km in the lowerstratosphere. As these numerical simulation tools mature, they can be used to extend estimates of atmosphericperturbations from the present gust database for airplane design at altitudes below 15 km to altitudes between25 and 50 km where aerospace plane operation would be at hypersonic speeds. The amount of available gustdata and number of temperature perturbation observations are limited at altitudes between 15 and 25 km. Onthe other hand, in-situ gust data at higher altitudes are virtually nonexistent. The uncertain potential for futureairbreathing hypersonic flight research vehicles to encounter strong turbulence at higher altitudes couldpenalize the design of these vehicles by undue cost or limitations on performance. Because the atmosphericstructure changes markedly with altitude, direct extrapolation of gust magnitudes and encounter probabilitiesto the higher flight altitudes is not advisable. This paper presents a brief review of turbulence characteristicsobserved in the lower stratosphere and highlights the progress of computational atmospheric dynamics thatmay be used to estimate the severity of atmospheric transients at higher altitudes.

Clear air turbulence; Discrete gust models; Hypersonic aircraft; Mountain waves;Numerical simulations; Stratosphere

A03

29

Unclassified Unclassified Unclassified Unlimited

December 1992 Technical Memorandum

Available from the NASA Center for AeroSpace Information, 800 Elkridge Landing Road, Linthicum Heights, MD 21090; (301)621-0390

Presented at the AIAA Fourth International Aerospace Planes Conference, December 1–4, 1992,Orlando, Florida.

Unclassified—UnlimitedSubject Category 47