Wake Vortex Dynamics Study in Temperature Inversion Conditions

Baranov N.A.

Dorodnicyn Computing Centre, Federal Research Center “Computer Science and

Control” of Russian Academy of Sciences

Abstract

The presented results have been obtained following numerical modeling of aircraft

wake vortex dynamics in the conditions of surface temperature inversion of the

atmosphere. Modeling was based on data from surface temperature profile

monitoring, which took place in winter and spring at Sochi airport using MTP-5

meteorological temperature profiler. A comparative analysis of the wake vortex

dynamics in the absence and presence of a side wind of varying intensity was

carried out for a number of temperature inversion cases, such as surface inversion,

elevated inversion with different layer altitude inversion, elevated inversion with

surface isothermy.

The work was supported by the Russian Foundation for Basic Research under

Project 16-07-01072.

Introduction

One of the factors which determine flight safety is the problem of wake vortex

safety provision. Different countries conduct researches on the analysis of the

wake vortex evolution generated after the aircraft specifics in different

meteorological conditions, assessment of the persistence level depending on

atmospheric conditions and the level of hazard to aircraft of different weight

categories [1]. It is important to mention WakeNet-Russia, WakeNet-USA,

WakeNet3-Europe, FP7 Project "UFO - UltraFast wind sensOrs for wake-vortex

hazards mitigation", and a number of projects under European SESAE project/

The wake vortex dynamics is determined not only by the existence of wind and

level of atmospheric turbulence, but also depends on atmospheric stratification [2,

3]. The impact on the wake vortex behavior of the stratification type of the surface

atmosphere layer is analyzed via mathematical modeling in this paper

Assumptions and input data

A numerical algorithm based on the method of discrete vortices was used. It

takes into account the changes in the wake vortices lowering speed and their

additional decay due to the temperature stratification of the atmosphere [4, 5].

Wake vortex was calculated on the basis of the hypothesis quasi-plane-parallel

flow.

As the example was taken low-altitude flight of the B-747-800 aircraft.

Flight altitude was chosen so that the wake vortex dynamics was determined by

viscous interaction with the boundary layer of earth. It was assumed that the flight

is conducted in the landing configuration with maximum landing weight. Time of

the calculation was 100 sec.

The data from the surface monitoring of temperature profiles in the-winter-

spring period at the Sochi airport gathered with the meteorological temperature

profiler MTP-5 (rpoattex.com) was used for modeling. The spatial resolution of the

temperature profile height was 25m to a height of 100m and 50m - more than

100m, accuracy of the estimation (RMSD) – 0.2°C to 0.5°C in first 500 m

(temperature accuracy decreases with altitude and depends upon the temperature

profile shape).  Four types of profiles were used for the analysis (Figure 1.):

profile 1 – elevated inversion at 200m,

profile 2 – surface inversion,

profile 3 - elevated inversion with surface isothermal,

profile 4 – elevated inversion at 100m.

During the analysis the impact of the weak side wind on the dynamics of the

wake vortex at different conditions of temperature inversion has been also

considered

Figure 1 – Considered temperature profiles

A brief description of the model

During the modeling of the wake vortex dynamics was used a two-phase

model of the vortex intensity decay, whereby it was assumed that at the first stage

the slow decay of the wake vortex intensity took place, and from a certain point in

time, the vortex trail enters a phase of rapid decay. [3]

The influence of temperature profile on wake vortex decay is taken into

account by modifying the time of the vortex life which determines decay

circulation rate: instead of the function of dimensionless time of vortex life

Tdemise(η) a function is considered

demisedemisedemise 185,0exp, TTT NN ,

where η is turbulence kinetic energy speed dissipation, N - Brent-Vaisal

dimensionless frequency:

20 with max ,0 max ,0

p

g dT g g dt N N

T dz c dz

N .

T(z) – temperature profile, cp – heat capacity at constant pressure, and g – gravity

acceleration.

8 10 12 14 16 T0

200

400

600

800

1000 h

Profile 1Profile 2Profile 3Profile 4

Besides the change of wake vortex circulation decay rate the model takes

into account the wake lowering, due to stratification influence according to the

following equation

strat2

22

strstrstrat

dt

zdv

dt

d , strat

2

2

02

strstr 21

dt

zdb

dt

d ,

0

22

2( )

z

zstrat

d zN z dz

dt

,

where αstr , βstr are given model coefficients, z and z0 respectively are the current

and initial height of vortices [1].

Viscous interaction of wake vortices with the surface was taken into account

by secondary vortices simulation which shows separation of the boundary layer of

the earth.

Results

The figure 2 shows the influence of the various types of temperature

stratification on the wake vortex dynamics in the absence of a crosswind. A change

in his attitude in terms of the adiabatic temperature profile is shown as the wake

vortex sample trajectory

It is possible to see, that in the adiabatic conditions at first the wake vortex

rises. It is explained by the interaction with the separated boundary layer. Then the

speed of rising is decreased and it almost stops moving at a certain height.

Simultaneously the wake vortices are shifted to the axis of the wake vortex pair

symmetry.

Figure 2 – Wake vortex vertical position change at different temperature profiles in

the absence of wind

In terms of surface inversion wake vortex dynamics changes radically: there is no

stabilization height wake vortex lift. In the conditions of the elevated inversion,

including surface isotherm, the height of the stabilization occurs earlier than under

adiabatic conditions, wherein the vortex lifting height depends on the surface

gradient and the height of the inversion layer. It should be noted that despite the

fact that under adiabatic conditions the vortex height stabilization occurs at an

altitude of less than 100m the vortex dynamics is influenced by the presence of the

inversion layer at an altitude of 200m, due to a change in the temperature gradient

in the height range 50 ... 100m: even weak variations of the temperature gradient (

0.5 ... 1С for 100m altitude) affect both lifting height and change in the lateral

position of the wake vortex.

The figure 3 shows the results of the wake vortex modeling in the conditions of

weak side wind

0 30 60 90 z0

25

50

75

100

125 yProfile 1Profile 2Profile 3Profile 4Adiabatic

T(z) Wind 1m/s Wind 2m/s

1

2

3

4

Figure 3 – Wake vortex vertical position change at different temperature profiles in

the conditions of weak side wind

-100 0 100 200 z0

15

30

45

60 y

left vortexright vortex

-100 0 100 200 300 z0

15

30

45

60 y

left vortexright vortex

-100 0 100 200 z0

30

60

90

120

150 y

left vortexright vortex

-100 0 100 200 300 z0

30

60

90

120

150 y

left vortexright vortex

-100 0 100 200 z0

20

40

60

80 yleft vortexright vortex

-120 0 120 240 z0

20

40

60

80 yleft vortexright vortex

-100 0 100 200 z0

20

40

60

80 yleft vortexright vortex

-100 0 100 200 300 z0

20

40

60

80 yleft vortexright vortex

The shown data shows that the side wind presence depending on the stratification

type can lead to nearly hanging of one of the vortices in the vicinity of the aircraft

trajectory. This phenomenon is an unfavorable factor for the aircraft to land, as the

flight of the aircraft takes place on the same trajectory and the presence of a wake

vortex increases the risk of an accident. The most unfavorable conditions are

isothermal surface and slightly lifted inversion in low crosswind.

For comparison figures 4 and 5 show the disturbance rolling moment distribution

in the wake vortex of a B-747-800 aircraft which encounters the wake vortex of B-

767 type aircraft 60sec and 100sec after generator passing. The results obtained by

modeling the case of the wake vortex dynamics in the surface isothermal

conditions (temperature profile number 3) with weak side wind 1m /sec. The

Figure 6 shows the disturbance rolling moment distribution for the case with

100sec parameter and elevated inversion (profile number 4) with weak side

wind 1m/s.

The results reflect the high sensitivity of the dynamics of the wake vortex to the

parameters of temperature stratification.

Figure 4 – Rolling moment distribution after 60 sec from the case of elevated

inversion with surface isotherms

-50 0 50 100 150 200 2500

20

40

60

80

100

120

140

160

180

200

z

y

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Figure 5 – Disturbance rolling moment distribution after 100 sec for the case of

elevated inversion with surface isotherms

Figure 6 – Disturbance rolling moment distribution after 100 sec for the case of

surface inversion (profile number 4)

Conclusion

The conducted research, based on numerical simulations show that the

change in the spatial position of wake vortex essentially depends on the type of the

temperature stratification of the atmosphere. In this regard, the wake vortex

-50 0 50 100 150 200 2500

20

40

60

80

100

120

140

160

180

200

z

y

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-50 0 50 100 150 200 2500

20

40

60

80

100

120

140

160

180

200

z

y

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

attitude prediction models in different meteorological conditions is necessary to

assimilate the data on the temperature profile in the surface layer. These results

show that even small variations in the temperature profile can significantly change

the attitude of the vortex disturbance zone. Preliminary estimation based on

mathematical modeling data show that the measurement accuracy of the

temperature profile should not be below 0.5 with spatial resolution of height 25-

50m.

Reference list

1. Holzäpfel F. et al. Aircraft Wake Vortex - State-of-the-Art & Research

Needs. 2015, DOI 10.17874/BFAEB7154B0

2. Sarpkaya T., Day J.J. Effect of ambient turbulence on trailing vortices.

J.Aircraft, 1987, 24, № 6, 399-404.

3. Sarpkaya T. New model for vortex decay in the atmosphere. . J.Aircraft,

2000, 37, № 1, 53-61.

4. Baranov N.A., Turchak L.I. Investigation of aircraft vortex wake structure.

AIP Conference Proceedings, 2014, Volume 1629, Issue 1, p.44-55. DOI:

10.1063/1.4902258.

5. Turchak L. I., Baranov N.A. Modeling of Aircraft Vortex Wake Structure.

Fifth International Conference on Application of Mathematics in Technical

and Natural Sciences, 24-29 June 2013, Albena, Bulgaria. Book of

Abstracts, p. 69 – 73.