Subaqueous “yardangs”: Analogs for aeolian yardang evolution

Paul A. Carling1

Received 3 November 2011; revised 20 October 2012; accepted 26 October 2012.

[1] Landforms, morphologically similar to aeolian yardangs but formed by erosion ofbedrock by currents on an estuarine rock platform, are described for the first time. Thegeometries of the “yardangs” are described and related to semi-lemniscate shapes thatminimize hydraulic drag. The processes of bedrock erosion by the reversing sediment-laden tidal currents are described, and a semi-quantitative model for landform evolution isproposed. The model casts doubt on the “simple” role of the maximum in the two-dimensional vertical suspended sediment flux distribution and the consequent distributionof potential kinetic energy flux in the process of shaping the rock wall facing the ebb flow.Rather, although the kinetic energy flux increases away from the bed, the sedimentbecomes finer and abrasion likely is insignificant compared with coarse sand abrasionlower in the profile. In addition, the vertical distribution of sediment flux is mediated bytopographic forcing which raises the elevation at which bed load intersects the yardangprow. Consequent erosion leads to ebb-facing caprock collapse and yardang shortening. Incontrast, the role of ebb-flow separation is paramount in mediating the abrasion processthat molds the rock surface facing the flood flow. The length of yardangs is the leastconservative dimension, reducing through time more rapidly than the height and width.Width is the more conservative dimension which implies that once the caprock isdestroyed, scour over the obstacle is significant in reducing body height, more so thanscour of the flanks which reduces width. The importance of vertical fissures in instigatingthe final breakdown of smaller yardangs and their extinction is noted. Similarities toaeolian yardang geometries and formation principles and processes are noted, as are thedifferences. The model has implications for aeolian yardang models generally.

Citation: Carling P. A. (2013), Subaqueous “yardangs”: Analogs for aeolian yardang evolution, J. Geophys. Res., 118,doi:10.1029/2011JF002260.

1. Introduction

[2] Yardang is a Turkmen word introduced by [Hedin1903] as a term for wind-abraded desert ridges that has beenapplied widely to aeolian-sculpted hillocks [Goudie, 1999].The length scales of these streamlined landforms can rangefrom centimeters (microscale), through meters (mesoscale)to kilometers (megascale: in the terminology of [Cookeet al. 1993]). Widely described in arid and semiarid environ-ments on Earth [McCauley et al., 1977a; Laity, 1994;Livingstone and Warren, 1996; Breed et al., 1997], in thegeological record [Tewes and Loope, 1992] and on Mars[Ward, 1979; Hynek et al., 2003; Carter et al., 2009;Zimbelman and Griffiths, 2009], the morphology is variableand can include long parallel ridges but at the mesoscale, theobstacle commonly consists of a streamlined form of finitelength, which minimizes drag in the prevailing wind [Ward

and Greeley, 1984], commonly with an overhanging upwindprow and rounded “whaleback” lee [see Goudie, 1999,Figure 8.2; McCauley et al., 1977b, Figure 14]. The overallshape of these mesoscale landforms is thought to be formedprimarily to aeolian abrasion by saltation and tractiontransport of sediment. Sediment is concentrated close to thebed and so erodes the lower portion of the upwind nose andflanks of the yardang more than those portions at a higherelevation (which are rounded by suspension load), thusresulting in the overhanging profile [Greeley and Iversen,1985; Laity, 1987] and leeside rounding. In some instances,the plan view morphology is influenced by jointing patternsin the bedrock [e.g., Vincent and Kattan, 2006]. A hardercaprock may characterize the top of soft-rock yardangs, andthis structure can lead to a more pronounced overhang onthe upwind side [de Silva et al., 2010]. At the simplest, theoryhas shown that the vertical location (the invert) of themaximum in the recession rate of the profile may be relatedto the maximum in the vertical sediment flux distributionand the consequent maximum in the distribution of kineticenergy flux of the approaching flow [Sharp, 1964; Anderson,1986; Cooke et al., 1993; Bridges et al., 2005]. However,there are no field or wind tunnel experiments to demonstratethe relationship of this theory to the development of aeolianyardang forms in any detail.

1Geography and Environment, University of Southampton, Southampton,UK.

Corresponding author: P. A. Carling, Geography and Environment,University of Southampton, Southampton SO17 1BJ, UK. (p.a.carling@soton.ac.uk)

©2013. American Geophysical Union. All Rights Reserved.2169-9003/13/2011JF002260

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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 118, 1–12, doi:10.1029/2011JF002260, 2013

Journal Code Article ID Dispatch: 00.00.00 CE: Dorio, LynetteJ G R F 2 0 0 1 3 No. of Pages: 12 ME:

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[3] In this paper, estuarine bedrock landforms withstreamlined shapes that are similar to aeolian yardangs aredescribed. Because of the similarity of form to aeolianyardangs, these water-sculpted features are termed “yard-angs” in the following text, in accord with the typology ofRichardson and Carling [2005]. These features developedsubaqueously, and so the primary aim of the paper is todemonstrate the relationships between sediment-ladenaqueous flows, bedrock erosion, and the form of the bedrockobstacles. However, the morphological similarity of theestuarine landforms to aeolian mesoscale yardangs spurredthe equally important secondary aim: to provide somegeneric observations from water flows that might be appli-cable to aeolian yardangs. A benefit of the estuarine envi-ronment is the high frequency of predictable tidal flowswhich allows a more detailed appreciation of the flow fieldin the vicinity of bedrock obstacles than has been reportedfor field examples of aeolian yardangs. Although there areimportant differences, the typical air-flow patterns andsediment transport pathways associated with wind fieldsaround yardangs [Whitney, 1983; Ward and Greeley,1984] broadly should be similar to those that occur aroundstreamlined obstacles within water flows [Allen, 1982], soa degree of analogous development might be anticipated.In particular, the distribution of kinetic energy flux of theapproaching flow is examined, and conclusions are drawnwith respect to the erosion processes over both aeolian andsubaqueous yardangs. Specifically, the hypothesis is testedthat the heights of the erosional inverts in the yardangprofiles are constrained by the vertical distribution of poten-tial kinetic energy of suspended sediment.

1.1. Location and Site Description

[4] The yardangs are on Hills Flats, an intertidal bedrockplatform in the Severn Estuary, UK (FigureF1 1) [Allen andFulford, 1996]. The geology is the Triassic Mercia Mud-stone Group [Welch and Trotter, 1961], parallel-beddedlayers, 0.5 to 1m thick, dipping a degree or two to the north-west. Gray sandstone forms the platform, above whichhigher elevation beds, brick-red sandy marl with thin inter-calations of gray sandstone, are now truncated further tolandward by small vertical cliffs (0.5 m to 1.5 m high). Eachyardang, clustered around 51�40042.600N: 2�32026.200W, hasa sandstone base but consists of approximately 0.5 to 1mthick unit of marl commonly exhibiting a 0.08 to 0.16mthick cap of sandstone.[5] Two intersecting sets of vertically orientated fis-

sures occur in the beds [Allen and Fulford, 1996] whichare <0.02m wide to hairline and extend a few metersonly with 0.5 to 1.0m spacings. Yardangs show no align-ment with fissures, but their structural integrity is affectedby the presence of the fissures, as is shown in section 3.A sample of 58 fissure orientations showed that there aretwo distinct populations. One group, with a range ofstrikes between 265� and 287�, has an average strike of276�. The other group range between 145� and 222�,with an average strike of 183�.[6] On the platform, there is a thin, patchy veneer of

shale gravel, sand, and mud (Figure 1b). Thus, a sparsecoarse bed load passes individual yardangs. Althoughthe bed load moves up estuary with the flood tide,

Figure 1. (a) Location of the Hills Flats study area inthe Severn Estuary of S.W. England. Dark gray area isthe rock platform with a field of gravel dunes shownin white. P1, P2, and P3 are current-metering locations(see text for details). (b) Location (black dots) ofthe most prominent measured yardangs at the outermargin of the Hills Flats rock platform with bare rockand mud areas labeled. (c) Orientation of long axesof yardangs.

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residual sediment transport is down estuary with the ebbtide [Carling et al., 2005].[7] The tidal flat experiences a semidiurnal, macro-tidal

regime with marked diurnal and lunar-monthly inequalities.At Avonmouth, (Figure 1a), the extreme astronomical tidalrange of 14.8m ranges from a low of �0.2m below chartdatum (�6.7m Ordnance Datum (O.D.)) to a high of14.6m (8.1m O.D.). Mean high-water Spring tides lie at13.2m (6.7m O.D.), and mean high-water Neap tides lie at9.8m (3.3m O.D.) [Allen and Duffy, 1998]. The yardangswarm is subtidal during Neap tides but is exposed for briefperiods during low water Spring tides.[8] In subtidal channels, suspended fine sediment includ-

ing approximately 23% quartz grains [Bryant and Williams,1983] is present at high concentrations for all tidal states[Hydraulics Research Station, 1981; Crickmore, 1982;Kirby, 1986] and the lower 2m of the concentration profileis well mixed [Kirby and Parker, 1983]. Deposited sandconstitutes between 5 and 10% of material on the flats, with11 to 12% clay and the remainder chiefly silt and organicdetritus [Allen and Dark, 2007Q1 ]. The platform is not subjectto intense wave action; Allen and Duffy [1998] calculated<0.4m average wave heights which raise the grain size ofsuspended silt but the grain size of suspended sand is notaffected [Allen and Dark, 2007].

2. Method

[9] The study required an integrated investigation ofhydrodynamics, rock hardness, and erosion rates as wellas the geometry of the yardangs. For clarity, the nomencla-ture applied to define different parts of the yardangs isdefined in FigureF2 2a. A low angle (1� to 3�) pediment mayexist between the horizontal platform and the pedestal butis frequently absent. The pedestal is that part of the land-form between the pediment (or platform) and the caprock(where present) and may display a distinct invert (at heightź above the platform) between the lower pedestal and theupper pedestal at which point the upper profile becomesoverhanging. The invert is usually best developed on theebb-facing facet with less well-defined inverts alongthe flanks. Inverts occasionally occur on the flood-facingfacets, but commonly, the invert, the upper pedestal, andthe caprock are absent on these latter facets which then havewhaleback forms.

2.1. Yardang Geometry

[10] The locations of 41 yardangs were mapped usinghandheld GPS accurate to within� 4m on the survey days.The surveyed yardangs represent the majority of the well-defined landforms. Less distinct examples forming the scab-land to the west were not measured, and additional examplesmay exist in subtidal locations further to the north. Thegreatest length (L), the greatest width (W) orthogonal to L,and the greatest height (H) of each yardang were measuredusing a graduated tape, meter rule, and spirit level. Thealignment of the long axis in degrees relative to magneticnorth was determined using a sighting compass sightedalong an axis determined by two ranging poles positionedat the ends of the greatest length of each feature. The yard-angs appear to have semi-lemniscate planforms. Conse-quently, the plan view was approximated as Joukowski

semi-lemniscate, or ellipsoid, bodies (Tables T11 and S1) assuch approximations have been used to define the plan viewof streamlined bodies [Baker and Kochel, 1978; Clark et al.,2009].1 Assuming a semi-lemniscate body, a dimensionlessshape parameter (k) can be defined:

k ¼ L2p4A

; (1)

where A is the plan view area of the yardang.[11] Assuming an ellipsoidal approximation, then

A ¼ pab; (2)

and

P ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 a2 þ b2ð Þ

p; (3)

where a and b are the semi-lengths (i.e., L/2 andW/2) and Pe

Figure 2. (a) “Classic” yardang form (February 2006) withnotation used in this paper. In the background, other yard-angs are emerging during a falling tide. Length approxi-mately 2.5m. Ebb flow right to left. (b) Close up of thesame yardang in December 2009. Partial loss of the capstonehas resulted in significant erosion of the prow. The cameralens cap is placed just left of the fissure arrowed in Figure 2a.

1Auxiliary materials are available in the HTML. doi:10.1029/2011JF002260.

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is the perimeter length. The values of parameters k, A, and Pare included in Table 1 to demonstrate the typical plan viewproperties of the yardangs.

2.2. Rock Hardness and Rock Erosion Rate

[12] A Schmidt hammer (Mastrad Ltd., Douglas, UK),range 10 to 70Nmm�2, was used to obtain compressivestrengths of (1) caprock of gray sandstone, (2) red marlpedestals, and (3) sandstone platform. The sandstone tendsto weather by grain or flake removal. The appellation “marl”[Welch and Trotter, 1961] is imprecise; the rock has theappearance of a shale, sometimes exhibiting faint horizontallamination but which weathers into 1000 to 5000mm3

“cuboids,” rhombs, or irregular-shaped blocks of rock ratherthan flaking along bedding planes. The marl is a brittle mate-rial and should be subject to erosion by individual grainremoval and propagation of fine networks of cracks rather thanby scratching which characterizes erosion of ductile materials[Bitter, 1963a, 1963b]. Debris, when only partially detached,can remain in situ as a patchy surfaced weathered layer (lessthan approximately 10mm thick), but areas of unweatheredrock, from which weathered material has been eroded andremoved, occur widely. All reported data consist of readingsobtained from flat clean surfaces of unweathered rock awayfrom the edges of the yardangs to avoid a resonant response.[13] To monitor erosion, on the 26 February 2004, a rect-

angular pit (40mm by 40mm in plan and 35mm deep) wascut in the marl of the invert of an ebb-facing prow. A similarpit was cut in the platform 0.20m up estuary from the prow.The site was revisited frequently, and by 10 July 2008, theplatform pit was undetectable and the invert pit was extremelyfaint. The erosion rates are obtained by considering the totalperiods of tidal inundation as determined in section 2.3.

2.3. Hydrodynamics

[14] In order to provide information on Spring tidal flowspeeds, flow directions, flow depths, periods of inundation,and suspended sediment concentration data in the yardangfield for a series of Spring tides, an S4 InterOcean Systemscurrent meter (threshold: 0.03m s�1) and a McLane Phyto-plankton sampler were deployed at 0.40m above the bedat location P3 (Figure 1a). The meter recorded current speed

and direction, and water depth at 2 s intervals from 2 Decem-ber 2005 for a series of six typical Spring tidal cycles. Thephytoplankton sampler was modified to sample suspendedsediment (2mm>D50< 0.7 mm) and calibrated in thelaboratory to give concentrations with less than 10% errorof target values. The sampler collected twenty-four 1 lsamples at 20min intervals throughout a 12.88m tide. Todetermine the grain size distribution of sediment above thebed, suspended sediment was collected in six vertical80mm diameter cylinders with openings located at 0.25m,0.35, 0.45, 0.55, 0.65, and 0.75m above the bedrocksurface. It was not possible to sample closer to the bed as tur-bulence re-suspended sediment from cylinders shorter than0.25m. A bed load sample was obtained by amalgamatingsamples of the gravel on the bedrock surface during low-tideexposure. The size distribution of the sediment was deter-mined by settling through a 2m column [Amos et al.,1981] using the method of Dyer [1986].

3. Results

3.1. Yardang Alignment

[15] The average alignment for 41 yardangs is 244� with aSD of 21.4� (Figure 1c). Occasionally, two or rarely threeclosely spaced yardangs occur in line, which alignment isinterpreted to represent the breakup of one long yardang intoseveral shorter examples.

3.2. Yardang Shape

[16] Halimov and Fezer [1989] proposed that a planesurface subject to unidirectional flow can be dissected pro-gressively to produce flat-topped mesas at first elongatedridges and finally low streamlined whaleback landforms thatpresent semi-lemniscate shapes to the flow and thus mini-mize drag. The optimal W/L ratio for such bodies is 0.27[Fox and McDonald, 1979], as longer bodies have excessiveskin drag. Setting the length equal to unity, the general scal-ing relationship for a smoothed elongate body is ~L/W/H= 1/0.2/0.1 using aeolian yardang data obtained from bothfield measurements and laboratory experiments [Fage et al.,1929;Halimov and Fezer, 1989;Ward, 1979] and L/W=1/0.33to 1/0.25 using data from experimental water flows [Hoerner,1965]. Broadly similar L/W water flow scaling ratios areobtained from analyses of streamlined “islands” [Baker andKochel, 1978; Komar, 1983, 1984; Wyrick, 2005], but in thecase of islands, the landforms are not submerged.[17] Table 1 and Figure F33 summarize the dimensional

characteristics of the yardangs. Fifteen yardangs showeddistinctive inverts in the ebb-facing prows ( �z0 = 0.16m;SD=0.015m) with inclined lower pedestals of angle, a,facing the ebb flow (�a=33�; SD=4.4�) and overhangs abovethe inverts (Table S2). Note that the position of the invert is notusually at the interface between the pedestal marl and the sand-stone capstone but commonly is within the marl. The heighthistogram is strongly skewed because the caprock limits theheight of yardangs to less than 0.7m. In Table 1 and Figure 3,it is evident that the Hills Flat yardangs exhibit geometries thatare not dissimilar to the streamlined forms reported by[Halimov and Fezer 1989] but tend to be broader for givenlength. [Halimov and Fezer 1989] noted that as aeolian yard-angs became smaller, they tended to retain the expected shaperatios noted in Table 1. The same principle does not apply to

Table 1. Summary Statistics for Hills Flat Yardangs

L (m) W (m) H (m)

Av. measured (m) 2.94 1.08 0.43SD (m) 1.56 0.30 0.40SE (m) 0.22 0.04 0.02N= 48

L W/L H/LExpected ratiosa 1 0.2 0.1

Av. observed ratios 0.43 0.17SD observed ratios 0.15 0.08SE observed ratios 0.02 0.01

Ae (m2) Pe (m) k (-)

Av. observed values 3.08 7.30 2.73SD observed values 2.15 3.43 1.01SE observed values 0.31 0.49 0.15

aSetting the yardang length to equal unity, the relationship is givenbetween the observed ratios at Hills Flats and the expected ratios for mini-mized obstacle drag (the latter after Halimov and Fezer [1989]).

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the Hills Flat yardangs; despite scatter, the width is reducedlinearly as the length is decreased until residual small formsremain that have elongate whaleback forms with W/L ratiosapproaching 0.25 (FigureF4 4a and Table 1) or are near conical.In addition, there is no clear relationship betweenW/L and thepresence or absence of a caprock. In Figure 4a, only yardangswith a height of ≥0.6m have caprock present, and as W/Lreduces, the height does not reduce systematically nor is thereany threshold response to W/L once the caprock is lost.[18] Figure 4b shows that few yardangs exhibit L/H ratios in

excess of the expected value of L=10H (Table 1) for a stream-lined form and the majority have L/H ratios which are low.These results indicate that height is more conservative thanlength as yardangs erode. Figure 4c shows that only a minorityof yardangs exhibitW/H ratios less than the expected value ofW=2H (Table 1) for a streamlined form and themajority of ra-tios are too high. These results indicate that width is more con-servative than height as yardangs erode.[19] None of the yardangs exhibit any evidence of horse-

shoe-shaped scoured furrows cut into the platform aroundthe obstacles. Such furrows commonly form readily aroundbluff obstacles [Greeley et al., 1974] but are absent whenerosion by suspended sediment is dominant, in contrast todominance by bed load-induced erosion [Allen, 1982, p.185]. However, once streamlined bodies have developed,furrow scour is minimized [Allen, 1982, p. 186]. Note thatthe majority of yardangs have overhanging prows ofsandstone facing into the ebb flow and have well-roundedwhalebacks of the marl facing into the flood flow (Figure 2).However, some of the larger landforms have overhangingprows at both ends of the obstacle. Both ebb and flood prowsmay collapse if sufficiently prominent (Figure 2b), a processaided by vertical transverse fissures (Figure 2b).

3.3. Rock Hardness and Rock Recession Rate

[20] Twenty-nine readings of unweathered caprock hard-ness yielded an average value of 16Nmm�2 (SD= 3.68)within a range of 12 to 26Nmm�2. Ten readings of the ped-estal rock hardness yielded an average value of 13Nmm�2

(SD= 3.24) within a range of 10 to 20Nmm�2. Ten read-ings of the platform hardness yielded an average value of27Nmm�2 (SD= 3.41) within a range of 22 to 30Nmm�2.All weathered surfaces returned values <10Nmm�2.

Figure 3. Histograms of yardang dimensions (N= 48).

Figure 4. (a) Relationship between length, width, andheight. Height is color coded: blue =>0.60m; green =>0.5m< 0.60m; red =>0.4m< 0.5m; black =>0.3m< 0.4m;white =>0.2m< 0.3m; yellow =>0.1m< 0.20m; purple =0m< 0.10m. See text for details. (b) Relationship betweenheight and length in comparison with ideal H:L ratio forstreamlined body. (c) Relationship between height and widthin comparison with ideal W:H ratio for streamlined body.

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The recession rate (R) of the ebb-facing prow averaged0.0219mmd�1, which, although a single-point estimate, pro-vides some information on the rapidity of yardang extinction.[21] The recession rate, R, of an impacted near-vertical

surface is

R ¼_A

rt¼ T qke

rt(4)

where Å is the mass of the target material removed from thesurface area per unit time, rt is the density of the targetmaterial, T is the susceptibility of the target material to de-tachment by the kinetic energy, and qke is the instantaneousflux of kinetic energy to the unit surface area per unit timeperpendicular to the flow [Rosenberger, 1939; Anderson,1986]. Thus, for a given rock mass, the rate of erosion is di-rectly proportional to the applied kinetic energy, an issueconsidered in section 4.

3.4. Hydrodynamics

[22] Tidal flow data are presented here, in some detail, asthese data are used in section 4 to explain aspects of the formof the yardangs. FigureF5 5a presents the flow direction datafor a tide of predicted height at Avonmouth of 12.88m.The characteristics of this tide are similar to the other fiveSpring tides sampled and so are considered representativeof median Spring tides. The flood tide has an averagebearing of 52� (SD = 6.82�; n = 1167) over the period ofstrongly accelerating and decelerating flood tide betweentime increments 636 and 2970 s. As the flood tide weakens(Figure 5b), the bearing of the current swings toward the

north. The period of high “slack” water lasts 6min duringwhich the flow direction is variable. At the beginning ofthe ebb tide, the flow has a northerly bearing directly towardthe main ebb-dominated channel before assuming a steadyaverage bearing of 236� (SD= 4.96�; n= 3100) over theperiod of strongly accelerating and decelerating ebb tidebetween time increments 5600 and 11,800 s before low“slack” water is approached.[23] The maximum water depth (hmax) above the yardang

field was 8.38m with maximum flood velocity of 1.65m s�1

and maximum ebb velocity of 1.85m s�1, during whichReynolds numbers (Re=Uh/n) ranged between 2� 107 and4� 107 and between 4� 107 and 8� 107 during the periodof strongest flood and ebb currents, respectively. The yardangsare deeply submerged through 95% of the tidal cycle(Figure 5c). The duration of the ebb tide is around 1.7 timesthe duration of the flood tide and velocities during the ebbare sustained at more than 0.5m s�1 for twice as long as duringthe flood. Thus, the yardang field is ebb dominated both interms of sustained current speeds and duration. All flows aresubcritical with maximum Froude numbers approaching0.3 on both flood and ebb. The shear stresses applied tothe bed were not measured at location P3 but at locationsP2 and P1 (Figure 1a)Williams et al. [2006, 2008] measuredpeak average Spring tidal current speeds between 1.30ms�1 and 1.79m s�1 and average stresses of between 0.89and 4.9 Nm�2, with occasional excursions to 10Nm�2,with the flood peak typically being 1.6 Nm�2 and the ebbpeak being 4.9 Nm�2. Location P1 is slightly to landwardof the yardang field and in shallower water (hmax = 5.48m)during Spring tides. Thus, the slightly higher velocities atthe yardang field are as expected, and the range of shearstresses imposed on the bed within the yardang field shouldcover the same range, although including more occasionswith the higher values reported by [Williams et al. 2006,2008]. In general, ebb-flow parameters (excluding depth)at P3 have twice the values of the flood tide, and thus, theebb is assumed to be approximately twice as erosive.[24] Suspended sediment concentrations, at 0.40m above

the bed, increased monotonically during the flood tide froman initial value of 148mg l�1 to a value of 654mg l�1 justbefore high slack water. Concentrations fell at high water,spiked on the first ebb-flow to 749mg l�1 (presumably asslack-water settled sediment was resuspended from thebed) and then oscillated during the ebb flow (average ebbconcentration: 145mg l�1; SE = 22mg l�1). The grain sizedata in Figure F66 show that whilst fine gravel is transportedpredominately as a traction load, there is a significant coarsesand/granule component in suspension up to 0.45m abovethe bed. Above this elevation, the grain size distribution isuniformly similar at all elevations ranging from silt to0.25mm sand but with a variable, random, component ofcoarser grains at each elevation.

4. Discussion

4.1. General Consideration

[25] The alignments of the yardangs (average 244� with aSD of 21.4�) are consistent with their being eroded andaligned by the rectilinear reversing Spring tidal flow (floodtide: 52� (SD 6.82�); ebb tide: 236� (SD 4.96�). The bearingof the flood tide is essentially 180� out of phase with the ebb

Figure 5. Summary tidal parameters for Spring tide of 2December 2005, predicted height at Avonmouth of12.88m. (a) Tidal flow bearing. (b) Tidal current velocity.(c) Tidal water depth.

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tide, and so it cannot be stated that the yardangs are betteradjusted in terms of alignment to the bearing of the ebb orflood tide. However, other morphological characteristics, asdiscussed below, indicate an ebb dominance in term of form.The difference between the average yardang alignment andthe average bearing of the two fracture patterns is 32� and61�, and so there is no structural control on the yardangalignment. However, fractures transverse to the long axesare important foci for enhanced erosion that sometimes leadsto the breakup of individual long yardangs into two or morealigned smaller yardangs and in the erosion of yardangs gen-erally. These results indicate that the yardangs develop theirdistinctive form and orientation due to tidal abrasion. Similarobservations of lack of structural control have been madewith respect to some aeolian yardangs [Breed et al., 1989].[26] The relationship between W and L is described by

W ¼ 0:1468Lþ 0:6499 r2 ¼ 0:58 (5)

or:

W ¼ 0:73L0:38 r2 ¼ 0:58 (6)

[27] Despite variance, the data trend in Figure 4a is wellrepresented by the linear function (equation (5)) but powerfunctions have been used widely in other studies of stream-lined bodies to describe W/L relationships so equation (6)also is considered here. Equations (5) and (6) are developedusing W/L data for individual yardangs (Figure 4a). If theergodic principle is adopted and the smaller yardangs areassumed to have evolved from larger ones, it is evident thatthe trend line reflects evolution of large yardangs, which arerelatively narrow (e.g., equation (5): predicted W/L for 7mlong yardang is 0.24), to smaller yardangs which are rela-tively broad (e.g., equation (5): predicted W/L for 1m longyardang is 0.80). Baker and Kochel [1978], Kehew and Lord[1986], andWyrick [2005] obtained power functions relatingW to L for streamlined islands, and their regression coeffi-cients usually are not statistically different from 1.0 [see alsoKomar, 1984], indicating proportionate changes in W/Lacross the data range. However, their data represent bodiesthat are orders of magnitude larger than the yardangs, andisland shapes are subject to channel-width constraints andchannel bend migration effects—which effects do not apply

to isolated submerged bluff bodies in wide flows. A regres-sion with the coefficient constrained to equal unity doesnot follow the trend of the yardang data and is statisticallysignificantly different to equation (5) (Figure 4a). The formof equation (5) implies that larger obstacles are betterstreamlined than smaller bodies. This observation impliesthat the mass of each of the larger yardangs is sufficient thatdespite erosion, the bodies can survive long enough tobecome optimally streamlined. However, small yardangs,formed by the structurally influenced divisions of largeryardangs, do not have the body mass to survive long enoughto become optimally streamlined. Equation (5) also suggeststhat although the flanks of the yardangs are eroded throughtime, the bulk losses through time are greatest in terms oflength, as has been suggested with aeolian yardangs [Wardand Greeley, 1984]. Given an ebb tidal flow dominanceand field evidence for caprock collapse primarily at the upestuary end of yardangs, the length losses are greatest dueto ebb flows. The difference in the yardangs and streamlinedislands results may reflect scale issues or, more likely, theimmersed versus non-immersed status of the yardangsversus islands, respectively.

4.2. Drag Force of Yardangs

[28] A drag force results from the presence of a yardang inthe tidal flow. This drag can be minimized by tidal scoureroding the obstacle to provide a body shape that minimizesflow resistance. The total drag is composed of (1) the skindrag, which is proportional to the surface area of the body,and (2) the form drag which is dependent on the shape ofthe body and the consequent degree of flow separationaround the body. Streamlining will reduce the wake zoneand thus reduce the form drag [Schlichtling, 1960, p. 269];an approximately exponential reduction in width and heightof the distal portion largely minimizes separation [Patterson,1938; Chow, 1981] which explains the whaleback form.[29] The drag force is the product of the dynamic pressure

and the reference area (A) which is typically defined as the areaof the orthographic projection of the object on a plane perpen-dicular to the direction of fluid motion [Hoerner, 1965]:

Fd ¼ 0:5rU2� �

CdWH ; (7)

where the product of the maximum values of the width (W)and the height of the obstacle (H) are taken to represent Aand r is the sediment-laden fluid density. As the drag variesas the velocity squared, drag is maximized during peak flowspeeds, so U is defined as the maximum velocity of the fluidfor flood or ebb (aligned with the long axis of the body) andCd is a non-dimensional drag coefficient.[30] Typical values of the drag coefficient are 0.47 for a

sphere settling in water, 1.05 for a cube settling in water,and 0.04 for a streamlined “tear drop” settling in water[Prandtl, 1949]. For a Hills Flat yardang, the most appropri-ate similitude is a half tear drop fixed to a plane surface(Figure 2a) which has a drag coefficient of 0.09 [Hoerner,1965] when the bluff end is facing into the ebb flow; thedrag increases if the flow is angled against the tear dropobstacle [Andreas, 1995]. No data have been identified todetermine the drag coefficient of a half tear drop with the tailfacing into the flood flow. Reviewing geometries similar totear drops, [Andreas 1995] concluded that Cd for the bluff

Figure 6. Grain size distributions of sediment at givenheights above the bedrock platform. Susp. is the height ofsampling of suspended load.

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case was 0.1 and three times this value where the flow wasreversed by 180�. The bluff case Cd values reported byHoerner [1965] and Andreas [1995] agree within 10%,and consequently, Andreas’s multiple (0.09� 3) is appliedto yardangs subject to flood flows.[31] Solutions of equation (7) for each of 41 yardangs with

significant bluff profiles were obtained assuming ebb-flowdominance (Cd = 0.09) and using a maximum flood velocityor maximum ebb velocity and fluid densities based uponsuspended sediment concentrations reported in section 3.4.The average value of drag for the 41 cases has a standarddeviation of 37% which largely reflects the variation in Wand H between yardangs. For the flood tide, Fd = 279N;for the ebb tide, Fd= 98N. Thus, in low-density ebb flows,fluid drag is minimized. The enhanced drag in flood flowsis as expected [see Hoerner, 1965, p. 2–3] due to augmentedwakes that develop downstream of the bluff (ebb eroded)noses that face up estuary.[32] Flow separation will occur around a bluff body once

Re ≥ approximately 50 to 100 [Hoerner, 1965], and so atHills Flats, flow separation is universal given the recordedRe numbers and enhanced drag will occur in high Reynoldsnumber flows (Re> 107) unless the W/L ratios are less than~0.4 [Baker and Kochel, 1978]. Bodies do not elongatemuch beyond W/L= 0.33 because the skin friction increasesthe resistance to flow. About half the yardangs have ratios0.4, and consequently, these less-streamlined bodies aresubject to significant flow separation. To minimize the valueof Fd for any given flow conditions, the drag coefficientwould need to be reduced. Such a reduction can be accom-modated by minimizing the ratio of W/L! 0.27 [Fox andMcDonald, 1979]. However, it is evident from Table 1 andFigure 4a that the average ratio is not optimal; in part, the rea-son is the effect of scour associated with wakes noted above.Only four yardangs approach the optimal ratio (i.e., 0.18,0.22, 0.23, and 0.23) as yardangs with optimum W/L ratiosbecome structurally unstable due to the presence of fissures.[33] Fissures play a fundamental role in altering rock resis-

tance on shore platforms [Naylor and Stephenson, 2008],and in the majority of yardang cases, both pedestals and cap-rock exhibit occasional vertical fissures, such that the long,narrow yardangs breakdown readily. In the presentexamples, long yardangs can become “dissected” once thecaprock breaks up to form two yardangs each of shorterlength whilst each maintains a width similar to the “parent”body and thus do not exhibit optimal streamlining. Further,it is evident that there is a scale dependence inasmuch assmaller, or narrower, yardangs appear more susceptible tostructural breakdown than larger bodies. Once the caprockis destroyed, rapid erosion of the exposed pedestals occursand yardang extinctions follow.

4.3. Model of Yardang Erosion

[34] The peak fluid stresses across Hills Flats duringSpring tides are typically in the range 0.89–10Nm�2

[Williams et al., 2006, 2008]. Fluid stresses act as a tractiveforce on the bedrock surfaces, and the critical value forerosion is proportional to, but less than, the rock hardness[Sunamura and Matsukura, 2006]. [Sunamura andMatsukura 2006] measured the erodibility of mudstones insediment-free and sediment-laden flows of similar characterto those at Hills Flats. With reference to their results and the

rock hardness data, the fluid stresses alone are inadequate toerode the weathered or unweathered bedrock; rather, theimpacts of bed load and suspended grains must beaccounted. The tidal flows (z=0.40m) typically can havesuspended sediment concentrations of <654mg l�1, whichtranslate into a volume concentration of <0.03%. Such con-centrations are typical of sand-laden fluids [Bagnold, 1963;Hanes, 1986] in a dilute flow rather than a grain collisional re-gime. In dilute flows, fine grains such as silts and clays behaveas the fluid phase and produce minimal values of shear stresseson any surfaces [Anderson, 1986; Nakagawa and Imaizumi,1992; Laity and Bridges, 2009]. Therefore, only the highconcentrations of suspended load of sand in the unmeasurednear-bed parts of the tidal flows (Figure 6) and any bed loadtransport should be responsible for abrading the yardangs. Asimple conceptual model of this process is developed below.[35] The shape results show that in plan view, the inter-

tidal yardangs are broader than the ideal for minimizationof drag (Table 1 and Figure 4a). Thus, as a first approxima-tion, flow around the flanks of the broader subaqueousyardangs and in the lee should be similar in behavior to flowaround a conical obstruction. Flow slows immediately up-stream of such an obstacle [Paola et al., 1986], and coherentvortices accelerate along the flanks [Maunder and Rodi,1983] before forming a series of less coherent but highlyturbulent vortices in the lee between the main flow and thewake [Calvert, 1967;Werner et al., 1980]. The approachingflow abraded those facets directly facing upstream[Richardson and Carling, 2005], while the vorticity alongthe lateral margins and in the lee abrades the flanks andthe leeside platform. The possibility of enhanced scour in thelee [see Whipple et al., 2000a] is in contrast to conditions inair, where the low viscosity and low density of air comparedwith water results in poor entrainment of sediment in leewardvortices and consequent aeolian leeside deposits are common[Greeley and Iversen, 1985]. In water, deposition may stilloccur in the wake [Paola et al., 1986] but is minimizeddownstream of optimally streamlined obstacles and no wakedeposits were ever seen at Hills Flats during periods of plat-form exposure.[36] In principle, high suspended sediment concentrations

and hence increase in fluid density and viscosity [Julien,1995] might suppress turbulence intensity [Best and Leeder,1993; Wang and Larsen, 1994; Baas and Best, 2002] and soreduce pressure drag, such thatW/L ratios should be larger inturbid flows than clear-water flows [Wyrick, 2005]. How-ever, despite this possibility, fluid densities are not greatlyaugmented by the measured suspended sediment concentra-tions and turbulence levels are high (Re ~ 107 to 108) and soan increased incidence of leeside or stoss-side scour in sub-aqueous environments, in contrast to aeolian environments,is the preferred explanation for the larger, less-streamlined,W/L ratios recorded for the intertidal yardangs (Table 1and Figure 4a) as such strong scour will result in greatertruncation of lengths rather than reduction in widths.[37] Obstruction of the flow on the upstream side of a bluff

body causes localized vertical downflow and scour along theupstream flanks for obstacle cones with slopes >15≤ 30�[Okamoto et al., 1977; Paola et al., 1986; Schär andDurran, 1997]. On cones with shallower slopes, the scour-ing effect is small but flow deceleration can cause sedimentdeposition at the nose of the obstacle which would blanket

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the bedrock and prevent further basal scour. Steeper brit-tle faces abrade faster than shallow ones due to the angle-dependent flux of sediment [Pugh, 1973, p. 151] againstthe bedrock surface as well as nonlinear effects of momentumtransfer efficiency and rebound effects that are proportional toincident angle [Bridges et al., 2004, 2005]. As explainedbelow, these principles are mediated by the structure of thevelocity profile and the sediment concentration profileupstream of the obstacle.[38] For conditions at Hills Flats, where there is an unlim-

ited supply of fine and coarse suspended sediment, thesuspended sediment concentration, and thus, the particleimpact rate should scale with the fluid velocity [Whippleet al., 2000a, 2000b]. As was noted in section 1 for aeoliansystems, abrasion by bed load, including traction and salta-tion, should dominate close to the bed [Sklar and Dietrich,2004] with abrasion by suspension loads being importantfor bedrock outcrops, such as yardangs, protruding high intothe flow [Hancock et al., 1998; Whipple et al., 2000a;Richardson and Carling, 2005]. Thus, below, the hypothesisis tested that the heights (ź) of the erosional inverts in theyardang profiles are constrained by suspension abrasion pro-cesses, and the conclusions derived should equally apply toaeolian and subaqueous yardangs.[39] Although the variation in the velocity distribution in

the vertical at the study site has not been explored, it is reason-able to assume that during the strongly accelerating phases ofthe tide, the vertical flow profile immediately above the planarplatform is logarithmic, with velocity increasing with height[Soulsby and Dyer, 1981; Lamb et al., 2008]:

Uz ¼ u�k

ln z=zoð Þ (8)

where Uz is the reference velocity at a height z in the watercolumn, u* is the shear velocity, zo is the roughness length,and k is von Kármán’s constant (0.40).[40] In the same vein, it might be expected that the relative

concentration of grains (S) being well mixed [Kirby andParker, 1983] and the relative grain size (D), being fine, willaccord with the Rouse profile [Vanoni, 2006] and approach1.0 near the platform surface (FigureF7 7). The shear velocityand the roughness length are estimated using the quadraticstress law:

u� ¼ Cdref12Uref (9)

where Cdref for a gravel-strewn rock bed is in the range0.0025 and 0.004 [Sternberg, 1972; Thompson et al.,2004] for the peak ebb tidal reference current speed of1.85m s�1 and

zo ¼ p exp �kCd�0:5

� �(10)

[41] Allowing for unsteadiness in the tidal flow [Soulsbyand Dyer, 1981; Dyer, 1986] and using equations (9) and(10), u* ranges between 0.07 and 0.14m s�1, typicallybetween 0.08 and 0.12m s�1 (consistent with the shear stressmeasurements of Williams et al. [2006, 2008] at P1 and P2),and zo =O 0.001m� 60%.[42] The Rouse equation describes the vertical profile of a

suspended sediment size class in water flows:

Sz ¼ Sa z=að Þ�Ws=bkU� (11)

where Ws is the estimated settling velocity of the grains[Jimémez and Masden, 2003 Q2, equation (12)] and Sz is theconcentration at a given height, z, relative to Sa, the concen-tration at reference height, a [Vanoni, 2006]. The referenceheight relates to the shedding of suspended sediment upwardfrom a bed load layer, and the reference height in this case isthe height of the top of the bed load layer from the fixed bed[Robinson and Brink, 2005]. The coefficient b is usuallyclose to one (ranging between 0.2 and 1.5).[43] If a static or near-static granular layer exists on the

platform, then the granular bed is dominated by frictionalforces (S ~ 1.0) with no flux or small flux of grains, littlekinetic energy expenditure, and consequently little or noabrasion [Sklar and Dietrich, 2004]. Above the bareplatform or sediment bed level, active bed load transport willoccur in traction and in saltation such that S< 1, D reduceswith height above the bed, collision forces dominate graininteractions and kinetic energy expenditure, and potentialabrasions thus are maximized at some height above the plat-form. As saltation is replaced by suspension dynamics athigher levels, the concentration profile and the average sizeof the constituent grains will reduce further (S<<1) suchthat abrasion should decrease with increased height. In water,as in air, finer sediment has less abrasive power, even in thefaster flows higher in the velocity profile [Nakagawa andImaizumi, 1992; Laity and Bridges, 2009]. It might beexpected therefore that the vertical distribution of the kineticenergy flux imposed on the bedrock surface of a pedestaland prowwill exhibit a peak in the region of collisional forces.[44] Susceptibility to abrasion is proportional to the kinetic

energy of an impacting particle [Rosenberger, 1939, p. 65;Greeley and Iversen, 1985]. The power expended per unittime is equal to the product of the kinetic energy and thenumber of impacting grains [Momber, 2008, p. 33]. Thus,assuming the speed of the suspended particle, Up, is similarto the speed of the flow, Uz:

qkeN / 4=3prsr3

2gUz

2N ¼ SU 2

2g(12)

where the number of spherical grains of diameter, D, isN= S/[rs(4/3)p r3], where r is D/2.

Figure 7. Mass sediment flux: examples for 7mm, 3mmgranules, and 1mm suspended sand.

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[45] Calculated vertical mass suspended sediment fluxesfor sand-sized and finer sediment do not demonstrate anypeak in the individual grain-size profiles. However, gran-ule-sized sediments (10mm>D> 1mm), which are foundin suspension below 0.35m height (Figure 6), do exhibitpeaks in the mass flux profiles in the range 0.08m< z’< 0.2m for all reasonable values of b. Figure 7 shows two exam-ples for granules and for 1mm sand; peakedness is increasedas the grain size coarsens. It is evident that the mass fluxintegrated over a range of coarser grain sizes peaks in the vi-cinity of, or just below, the heights of the inverts. The levelof the maximum kinetic energy flux will fluctuate as tidalstate, concentration, and grain size vary and will rise or fallas any bed layer of gravel aggrades or deflates. However, afixed bedrock surface (with a small bed load flux) is presentfor most of the time, and so the average and the varianceof the heights of the inverts noted above as �z0 = 0.16m(SE = 0.015m) in the upstream facing facet of yardangs(relative to the platform level) should demarcate thetypical height range over which the height of the kineticenergy flux maximum varies in a suspension dominatedflow [cf. Sharp, 1964; Anderson, 1986: Cooke et al.,1993; Bridges et al., 2005]. However, for the suspendedsediment at Hills Flats, there is no peak in the distribu-tion of the potential kinetic energy for any suspendedgrain size; rather, the kinetic energy increases with heightabove the bed (FigureF8 8) as is the case for the potentialabrasive power of the coarser suspended grain-sizefractions (FigureF9 9).

[46] The results shown in Figures 7–9 demonstrate that al-though the heights of the inverts correlate approximatelywith the peak in the mass flux of coarser grains, it is notpossible to relate the invert geometry in any simple mannerto potential kinetic energy or potential abrasive powerexpenditure of the suspended load when the distribution ofthese parameters are considered as two-dimensional verticalprofiles alone. The primary explanation is that the profiles ofpotential expenditure do not allow for whether particlesdetach from the flow (coarser grains) and impact the surfaceor follow the flow field (finer grains). The driver for invertdevelopment must consider only the kinetic energy of thesuspended load which impacts the surface together withthe bed load (both traction and saltation load) all of whichare mediated by the complex fluid stressing that occursaround the prow of any bluff body in fluid flow [e.g., Kiyaand Arie, 1972, 1975; Gowda et al., 1985; Nigro et al.,2005]. The development of the pediment and lower pedestalthrough time should allow bed load (traction and saltation)to be advected to higher elevations thus raising the elevationof the peak expenditure of kinetic energy due to the unmea-sured bed load. Similarly, Udo et al. [2009] also concludedthat the effect of a saltation load on the overall sedimentconcentration profile had been underrepresented in apprecia-tions of near-bed aeolian concentration profiles. Thus, in air,as well as in water, the distribution of abrasive power expen-diture will be significantly conditioned by the ability ofcoarser sediment particles to decouple from the flow andabrade the surface whilst fine sediment follows the deflect-ing flow lines around the yardang. Further study of thecomplex bluff body sediment-laden flow field would be re-quired to determine the exact controls on invert elevation.[47] Retreat of the steep-faced, near-vertical invert will

cause the lower pedestal to reduce in angle, reducing erosionacross the lower pedestal [Schoewe, 1932; Bridges et al.,2004] and enhancing the propensity for occasional burialby bed load. In the same fashion, the upper pedestal over-hang above the invert will reduce in angle as the invertretreats faster than the leading edge of the harder capstone.Nevertheless, the progressive removal of pedestal rock masswill weaken the support given to the prow such that caprockdisintegration will occur in due course due to gravitationalfailure and by “jacking” of caprock slabs and flakes inducedby turbulent uplift pressures [Clement, 1988]. The collapseof the prow then results in a steep facet being exposed againbut without the protective presence of the cap. At this stage,the distinct invert in the upstream facet is lost (Figure 2b).[48] Aeolian yardangs frequently present a whaleback

form downwind of the prevailing wind direction [Greeleyand Iversen, 1985, p. 135], but this form has not be consid-ered beyond noting that the form minimizes drag [Ward andGreeley, 1984]. Thus, in reversing tidal currents, an interest-ing problem is why some yardangs have developed whale-back forms for their down estuary extremities but not at allfor their up estuary extremities. This orientation is additionalevidence for the dominance of the ebb flow in molding theyardang form by erosion. The whaleback form, in the pres-ent examples, requires breakup of the caprock. Whereasthe ebb-facing prows of caprock are commonly underminedby erosion of the softer pedestals, as detailed above, theflood caprock is rarely are undermined significantly. Rather,the whaleback morphology implies strong turbulent flow is

Figure 8. Kinetic energy profile for 3mm particles.

Figure 9. Abrasive power profile for 3mm particles iskinetic energy multiplied by the number of grains makingup a given concentration.

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responsible for the caprock erosion within the wake formedby the ebb flow. The shape and flow characteristics ofwakes downstream of cones of various angles are largelyself-similar [Calvert, 1967]. Calvert showed that the planviews of the wakes of both steep (60�) and shallow (20�) an-gle cones in fully turbulent flow are characterized by twofree shear layers that develop above the lower slopes of thecones, enclosing a separation bubble in which reverse flowand high values of turbulence parameters persist. Thus, itis probable that the turbulence intensity in the wakes of theyardangs is sufficient to break up the caprock such that thedeveloping whalebacks are subject to sustained abrasion bythe flow patterns over their backs.

5. Conclusions

[49] The existence of water-eroded landforms at Hills Flatsof similar form to aeolian yardangs is evidence of convergentevolution of form in response to geophysical forcing by afluid. The well-formed yardangs originated by extension ofgullies by tidal scour between promontories in the cliff linesuntil promontories are isolated. The body geometries aresemi-lemniscate and minimize hydraulic drag. The yardangsdecrease in size through time in a largely predictable fashion:the lengths being the least conservative dimension reducingthrough time more rapidly than height or width.[50] Importantly, for both air and water, the model casts

doubt on the simple role of the maximum of potential kineticenergy flux of suspended sediment in the two-dimensionalvertical as the controlling process for shaping the overhang-ing rock wall facing the dominant (ebb) flow. Instead,although a peak may occur in the vertical concentration pro-file, and despite the potential kinetic energy flux increasingaway from the bed, the sediment becomes finer with heightand the majority of these finer particles may not impact thesurface, so abrasion decreases. In addition, the distributionof total sediment flux, including the bed load component,will further be mediated by topographic forcing, and thisalso will influence the height of inverts. Turbulent ebb-flowseparation, symmetrical in plan view, occurs along andabove the distal flanks of the yardangs resulting in thedistinctive whaleback forms due to sustained abrasion overtheir backs. By analogy, the results of this investigation ofthe development of yardang-shaped bed forms in waterflows may aid interpretation of the formation mechanismsof aeolian yardangs more generally.

[51] Acknowledgments. Nick Lancaster is thanked for providingcopy of McCauley et al. [1977a]. Jon J. Williams (University of Plymouth)is thanked for the loan of the S4 current meter. Paul Bell (Proudman Ocean-ographic Laboratory) is thanked for pre-processing tide data, and DavidJones (POL) is thanked for the loan of the suspended sediment sampler.Jo Nield (University of Southampton) is thanked for Figure 2b. The editorand associate editor provided constructive guidance in the review process.The comments of Edward Anthony and four anonymous referees assistedgreatly in focusing the main arguments.

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