2004 Flow Structures Over Dunes

www.elsevier.com/locate/geomorph

Geomorphology 59 (2004) 149–164

Numerical modelling of flow structures over idealized transverse

aeolian dunes of varying geometry

Daniel R. Parsonsa,*, Ian J. Walkerb, Giles F.S. Wiggsc

aSchool of Earth Sciences, University of Leeds, Woodhouse Lane, Leeds LS2 9JJT, UKbDepartment of Geography, University of Victoria, P.O. Box 3050, Station CSC, Victoria, British Columbia, Canada V8W3P5

cDepartment of Geography, University of Sheffield, Western Bank, Sheffield S10 2TN, UK

Accepted 16 July 2003

Abstract

A Computational Fluid Dynamics (CFD) model (PHOENICSk 3.5) previously validated for wind tunnel measurements is

used to simulate the streamwise and vertical velocity flow fields over idealized transverse dunes of varying height (h) and stoss

slope basal length (L). The model accurately reproduced patterns of: flow deceleration at the dune toe; stoss flow acceleration;

vertical lift in the crest region; lee-side flow separation, re-attachment and reversal; and flow recovery distance. Results indicate

that the flow field over transverse dunes is particularly sensitive to changes in dune height, with an increase in height resulting

in flow deceleration at the toe, streamwise acceleration and vertical lift at the crest, and an increase in the extent of, and strength

of reversed flows within, the lee-side separation cell. In general, the length of the separation zone varied from 3 to 15 h from the

crest and increased over taller, steeper dunes. Similarly, the flow recovery distance ranged from 45 to >75 h and was more

sensitive to changes in dune height. For the range of dune shapes investigated in this study, the differing effects of height and

stoss slope length raise questions regarding the applicability of dune aspect ratio as a parameter for explaining airflow over

transverse dunes. Evidence is also provided to support existing research on: streamline curvature and the maintenance of sand

transport in the toe region; vertical lift in the crest region and its effect on grainfall delivery; relations between the turbulent

shear layer and downward forcing of flow re-attachment; and extended flow recovery distances beyond the separation cell. Field

validation is required to test these findings in natural settings. Future applications of the model will characterize turbulence and

shear stress fields, examine the effects of more complex isolated dune forms and investigate flow over multiple dunes.

D 2003 Elsevier B.V. All rights reserved.

Keywords: Aeolian; Dunes; Computational Fluid Dynamics (CFD); Flow acceleration; Flow separation; Flow reversal; Flow recovery; Aspect

ratio

1. Introduction

The role of secondary flow structures in the mor-

phology, dynamics and spacing of desert sand dunes

0169-555X/$ - see front matter D 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.geomorph.2003.09.012

* Corresponding author. Tel.: +44-113-343-6624; fax: +44-113-

343-5259.

E-mail address: [email protected] (D.R. Parsons).

has been the focus of much recent research (McKenna

Neuman et al., 1997, 2000; Wiggs, 2001; Walker and

Nickling, 2002) and has been complimentary to sim-

ilar investigations of bedforms in fluvial environments

(e.g., Nelson et al., 1993; Bennett and Best, 1995).

Building upon earlier work over low-angled hills

(e.g., Jackson and Hunt, 1975; Bowen and Lindley,

1977; Bradley, 1980; Britter et al., 1981; Zeman and

D.R. Parsons et al. / Geomorphology 59 (2004) 149–164150

Jensen, 1987; Raithby et al., 1987), this recent re-

search has greatly improved our understanding of

dune form–flow interactions (stoss flow acceleration,

crestal separation, lee re-circulation, re-attachment,

etc.). This progress has been achieved with field

studies of windward flow dynamics (Lancaster et al.,

1996; Frank and Kocurek, 1996a; Wiggs et al., 1996;

McKenna Neuman et al., 2000) and lee-side flow

separation and recovery (Frank and Kocurek, 1996b;

Walker and Nickling, 2002, in press (a,b)). However,

while field and laboratory studies have succeeded in

providing some imprecise relationships between dune

aspect ratio and flow acceleration (e.g., Lancaster,

1994) and have provided detailed empirical relation-

ships characterizing the flow field over transverse

dunes and related these to dune height and lee-side

flow re-attachment and recovery (e.g., Frank and

Kocurek, 1996b; Walker and Nickling, in press (a)),

questions remain as to the presence and the sensitivity

of these secondary flow structures to changes in dune

geometry.

Progress in this regard is hampered by paucity of

additional field and laboratory studies to validate such

relationships and by the relatively small number of

dune geometries investigated. In particular, the com-

plex turbulent structure in the lee side of dunes has

generally precluded the measurement of flow structure

in this region, largely because of limitations in instru-

mentation (Nickling and McKenna Neuman, 1999;

McKenna Neuman, 2002). Mathematical modelling of

airflow over dunes has provided additional data for

the investigation of secondary flow regimes, but

studies to date have also suffered from an inability

to simulate the highly turbulent flow in the lee of

dunes (e.g., Walmsley et al., 1982; Raithby et al.,

1987; Stam, 1997). For example, Stam (1997) applied

an analytical flow model based on Jackson and Hunt’s

(1975) boundary layer model, which is unable to

solve the reverse flow lee-side eddy. This limits the

calculation of flow structures to low angle dunes

where lee-side eddies are not present. Stam (1997)

notes that numerical techniques are required success-

fully to simulate flows over a greater range of dune

forms.

Numerical flow models have been widely applied

in engineering disciplines for many years. In the last

few years, there has been a proliferation of the use of

Computational Fluid Dynamics (CFD) in the fields of

geomorphology and hydrology (see Bates and Lane,

1998). These models provide spatially rich data on

flow field properties that facilitate considerable in-

sight and understanding of the distribution of complex

flow processes. Indeed, these models can provide

details of the flow field that are often difficult to

measure and offer controlled conditions in which

certain aspects of the experimental set up can be

varied rapidly. This paper applies a CFD model to

flow over idealized transverse aeolian dunes and

describes the sensitivity of different elements of the

flow field to variations in geomorphic parameters. The

model used is capable of simulating the highly turbu-

lent reverse flow vortex in the lee of the dune and so is

able to provide an acceptable solution of the down-

wind distance to flow re-attachment given variations

in dune height, windward slope length and, thus,

aspect ratio.

2. Methods

2.1. Numerical model

This paper employs a numerical model based upon

the PHOENICSk 3.5 code, which is one of several

commercially available CFD programs. The model

solves the elliptic form of the Reynolds-averaged

Navier–Stokes equations in two dimensions with a

finite volume method: a cuboidal grid in a Cartesian

frame. The form of the dune was represented within

the model using a relatively new ‘cut-cell’ porosity

treatment, where the intersections of the inserted

geometry with the grid lines are determined and the

areas and volumes of partially blocked cells are

calculated to a high degree of accuracy (Spalding

and Zhang, 1996; Yang et al., 1997a,b). The equation

formulation is modified to account for the local non-

orthogonal intersection of the dune with the grid cells,

resulting in significantly enhanced predictions of near-

surface flow dynamics.

The hybrid-upwind interpolation scheme (Peclet

number = 2) applied in the model is only first order

accurate and can suffer from numerical diffusion

when flow is highly skewed relative to the grid.

Nevertheless, it is more stable than higher-order

schemes, and investigations analogous to this present

one have indicated that errors due to the interpolation

Fig. 1. Simulated incoming plane bed velocity profile.

D.R. Parsons et al. / Geomorphology 59 (2004) 149–164 151

scheme are not likely to be significant (e.g., Waterson,

1994). The pressure and momentum equations were

coupled through the SIMPLEST algorithm (a varia-

tion of SIMPLE; Pantaankar and Spalding, 1972)

where pressure and velocity fields were iteratively

calculated until continuity errors in mass and momen-

tum were adequately small (residuals were < 0.01%

of inlet flux). Turbulence closure was achieved

through application of a two-equation k–e model,

modified by renormalisation group theory (Yakhot et

al., 1992). This turbulence model is recommended for

simulating flows with significant mean strain and

shear. For example, it has been shown to perform

better in the prediction of sheared and re-circulating

flows over backward facing steps (e.g., Bradbrook et

al., 1998).

2.2. Model application and assessment

The model was initially applied to the experimental

set-up of Walker and Nickling (in press (a)) (see

Parsons et al., in press, for full details). Mass flux

values were specified for each grid cell in the up-

stream inflow, providing an incoming velocity profile

for the model. In order to simulate upwind effects of

the dune (e.g., pressure stagnation and flow deceler-

ation), this profile had to be specified far enough

upstream of the dune. A modelled inflow profile was

specified that implicitly produced the measured plane

bed boundary layer (with a free stream velocity of 13

m s� 1) at the point of dune intersection (see Walker

and Nickling, in press (a)). This inflow profile was

used in all the experiments in this paper (Fig. 1). At

the outlet profile, a zero pressure boundary condition

was applied, and, thus, calculated pressure values for

all cells in the domain were defined relative to this.

The length of the simulation domain was 960 cm and

flow depth was 76 cm, with the dune toe positioned at

500 cm into the domain, matching the conditions and

dimensions of the wind tunnel simulation of Walker

and Nickling (in press (a)). In the cell at the fluid–

solid interface, it was necessary to prescribe condi-

tions for the velocity and turbulence parameters. For

this purpose, the universal ‘Law of the Wall’ was

applied in the interface cells. In this experiment,

smooth wall conditions were applied, matching the

roughness experimental set-up of Walker and Nick-

ling (in press (a)).

Full verification and validation of the numerical

model to these experimental conditions and the flow

measurements obtained was demonstrated and dis-

cussed by Parsons et al. (in press). Validation was

based on 415 predicted points within the model

domain, which coincided with the locations of meas-

urements taken in the wind tunnel experiment. Al-

though excellent agreement between the measured

and predicted velocities was established, with corre-

lation coefficients for streamwise and vertical velocity

components of 0.97 and 0.83, respectively (Table 1;

Fig. 2), there are significant zones of disagreement,

particularly for the lower velocities (Fig. 2). Parsons et

al. (in press) identified that the majority of these

points are from the lee separation zone where, due

to design limitations, the measuring probe (a TSIRIFA 300 constant temperature hot-film anemometer)

applied in the wind tunnel experiment (Walker and

Nickling, in press (a)) was unable to resolve the

highly turbulent and negative velocities within this

region. Thus, although the validation process identi-

fied some notable differences between the measured

and modelled results, they are primarily due to the

limitations of the measuring instrument rather than

that of the numerical model. In regions where the

instrument is known to perform well, the match is

very good. Indeed, the removal of validation points in

the lee re-circulation zone improves the relationships

Table 1

Linear regression results between predicted and measured variables

for all validation points (n= 415) and for all points excluding those

within the dune lee separation zone (212)

Variable b Coefficient Correlation

coefficient

Streamwise velocity

(all points)

1.41 0.98

Vertical velocity

(all points)

1.03 0.83

Streamwise velocity

(excluding separation zone)

1.29 0.95

Vertical velocity

(excluding separation zone)

1.03 0.88

Table 2

Geometric properties of Experiments 1–9

Experiment

number

Dune

height

(h)

Stoss

base

length

(L)

Stoss

angle

Aspect

ratio

(h/L)

Lee

base

length

Lee

slope

angle

1 8.00 56.00 8.13 0.143 12.80 32.0

2 8.00 112.00 4.09 0.071 12.80 32.0

3 8.00 28.00 15.95 0.286 12.80 32.0

4 8.00 84.00 5.44 0.095 12.80 32.0

5 8.00 42.00 10.78 0.190 12.80 32.0

6 4.00 56.00 4.09 0.071 6.40 32.0

7 16.00 56.00 15.95 0.286 25.61 32.0

8 6.00 56.00 6.12 0.107 9.60 32.0

9 12.00 56.00 12.10 0.214 19.20 32.0


(Table 1), with a considerable increase in the vertical

velocity correlation, and although there is slight

decline in the streamwise velocity correlation, there

is a significant movement of the regression line

towards that of equality. Furthermore, qualitative

assessment of the predicted flow patterns and the

indications given by flow streamers (see Walker and

Nickling, in press (a)) confirm the presence and the

extent of the separation zone, which is successfully

simulated by the numerical model.

The model is able to simulate areas of flow

stagnation at the toe, acceleration up the stoss slope

Fig. 2. Comparison of modelled to measured velocities (a) streamwise (U)

(2002) (Experiment 1 in Table 2).

and flow reversal in the lee, which closely match

measurements obtained in the wind tunnel. The model

is therefore deemed able to provide a realistic and

complete 2D picture of the flow structure over ideal-

ized dune forms, providing prediction fields that are

spatially much richer than results produced by current

wind tunnel experiments and field studies. The use of

numerical modelling allows rapid alteration the ge-

ometry of the dune under controlled conditions, per-

mitting analysis of the interactive effect of dune form

on the flow field.

and (b) vertical (V) for the wind tunnel data of Walker and Nickling

orphology 59 (2004) 149–164 153

2.3. Experiments

Based on the successful verification and validation

of the model (Parsons et al., in press), it was deemed

appropriate to use the model to test the effect of

simple dune geometry variations on streamwise and

vertical velocity flow fields. In particular, certain

elements of the flow field were investigated including:

� velocity profiles at the dune toe, dune crest and at

three dune heights downstream of the crest;� streamwise and vertical velocity profiles at 1 cm

above the dune toe, crest and three dune heights

downstream of the crest;

D.R. Parsons et al. / Geom

Fig. 3. Isovel contour plots of streamwise velocity (U, m s� 1) calculated for

in Table 2).

� lee-side separation zone length; and� lee-side distance to flow recovery.

Simulated velocity profiles and the streamwise

velocities near the bed are of interest for predicting

the effects of dune aspect ratio on stoss flow acceler-

ation and the strength of flow within the separation

cell, particularly for examining the implications for

sediment transport. Vertical velocities provide insight

on the presence of streamwise curvature effects (i.e.,

flow stabilization) as well as the occurrence and

magnitude of vertical lift or downdrafts over different

dune forms. The last two parameters were of partic-

ular interest due to the ability of the model to predict

five different dune geometry scenarios (Experiments 1, 2, 5, 6 and 7


separated and reversed flow in the highly turbulent

lee-side eddy. The lee-side separation zone length was

determined from the location where the simulated

near-surface streamwise velocity at 1 cm changed

from negative (upstream) to positive (downstream)

in orientation. Distance to flow recovery in the lee

was determined as the point at which the simulated

near-surface streamwise velocity at 1 cm above the

surface was within 99% of its unperturbed upwind

value. This point was not necessarily the point where

the full boundary layer had recovered; nevertheless, it

does provide an indication of flow recovery. A fixed

1-cm distance from the surface was applied in each

experiment as the uniform grid resolution used in the

modelling precluded the variable setting this near-

surface distance.

Details of the differing dune geometries that were

used in the model runs are shown in Table 2. All units

are in centimetres and degrees, allowing testing and

comparisons with simulated experiment of the wind

tunnel data of Walker and Nickling (in press (a)).

3. Results

The model output for streamwise velocity (U, m

s� 1) is shown as isovel contour plots in Fig. 3. The

results shown here correspond to Experiments 1, 2, 5,

6 and 7 in Table 2 and cover a range of dune height,

stoss length and aspect ratios simulated in this inves-

tigation. Flow separation length and distance to flow

recovery results are summarized in Table 3.

Table 3

Distances from dune crest to flow re-attachment and flow recovery

over each of the experimental dune geometries

Experiment

number

Length to flow

re-attachment, cm

(x/h) from crest

Length to flow

recovery, cm

(x/h) from crest

1 73 (9.13) 558 (69.75)

2 59 (7.34) 526 (65.75)

3 96 (12.00) 594 (74.25)

4 65 (8.13) 544 (68.00)

5 82 (10.25) 568 (71.00)

6 13 (3.25) 306 (76.50)

7 234 (14.63) 724 (45.25)

8 34 (5.67) 424 (70.67)

9 148 (12.33) 624 (52.00)

In each experiment, it is clear that the intrusion of

the dune into the simulated boundary layer has a large

effect on flow structure. In each case, the model

predicts flow deceleration immediately upwind of the

dune followed by windward slope acceleration to a

maximum velocity at the crest. These results corre-

spond to findings in previous investigations (e.g.,

Jackson and Hunt, 1975; Bowen and Lindley, 1977;

Lancaster et al., 1996; McKenna Neuman et al., 1997;

Walker and Nickling, 2002; Wiggs, 1993; Wiggs et al.,

1996). In the lee of the dunes, the simulations shown in

Fig. 3 show large disturbances in streamwise velocity

with flow re-attachment occurring within approxi-

mately 3–15 dune heights and flow recovery occur-

ring several tens of dune heights downwind (Table 3).

The dune in Experiment 7 was steep-sided, and, here,

near-bed flow recovery occurs just within the bound-

aries of the simulation. Another interesting observation

is the convergence in the upper (faster) isovels of the

flow field, which corresponds to a zone or ‘jet’ of

accelerated, overshot flow extending from the crest

above the flow separation cell (Walker and Nickling,

2002). This effect is observable for Experiments 1, 2

and 5 where dune height (h) has been maintained and

is less apparent for Experiments 6 and 7.

Fig. 4 shows the vertical velocity field (V, m s� 1)

for the same group of experiments. For each experi-

ment, a zone of positive V exists on the upper stoss

increasing toward a maximum at the crest. This relates

to the topographic (upward) forcing of the dune on

near-surface streamlines. Small pockets of positive V

are also evident on the mid-lee slope indicating

vertical lift in this region.

A zone of strong downward flow delineated by the

� 0.8 m s� 1 isovel exists in the lee extending above

the flow separation region from the base of the lee

slope to beyond the flow re-attachment point. This

zone of downward flow can be seen to shift further

downstream with increases in dune height (Fig. 4) and

appears to vary with the size of the lee-side separation

cell. Indeed, this zone of downdraft aligns closely

above the point of flow re-attachment as was mea-

sured in Walker and Nickling’s (in press (a)) study.

Interestingly, the height of this zone extends to ap-

proximately 5 h for all runs (with the exception of the

steep dune in Experiment 7). These observations

confirm that dune height (and not necessarily aspect

ratio) plays an important role in perturbing the pres-

Fig. 4. Isovel contour plots of vertical velocity (V, m s� 1) calculated for five different dune geometry scenarios (Experiments 1, 2, 5, 6 and 7 in

Table 2).


sure filed over the dune and influencing the vertical

velocity distributions and flow re-attachment (Walker

and Nickling, in press (a)).

The sensitivity of flow patterns to changing dune

geometry are highlighted in more detail in Figs. 5 and

6 and in Figs. 7–12. Full velocity profiles at the dune

toe, crest and lee with changing dune stoss slope

length and changing dune height are provided in Figs.

5 and 6, respectively. Figs. 7–10 identify changes in

the near-bed velocity components with changes in the

dune stoss length and the dune height. The variability

of separation re-attachment length and distance to

flow recovery with changing dune geometry are

detailed in Figs. 11 and 12.

Figs. 6 and 7 indicate that both deceleration at the

toe and acceleration at the crest are sensitive to

changes in dune height while maintaining dune stoss

slope length (i.e., as dune stoss angle increases). Both

figures indicate that increasing dune height appears to

have a greater impact on acceleration at the crest than

on deceleration at the toe. Furthermore, near-bed flow

velocities at the toe decelerate almost linearly with

increasing dune height as near-bed acceleration at the

crest follows a power function (Fig. 7). Streamwise

velocity in the lee of the dune decreases rapidly with

increasing dune height, before becoming negative as

the separated lee-side eddy reverses flow at the foot

of the lee slope (Figs. 6 and 7). The magnitude of the

Fig. 5. Velocity profiles at the dune toe, crest and lee for changing dune stoss slope lengths (Experiments 1, 6, 7, 8 and 9 in Table 2).


lee-side sheltering effect near the bed increases dra-

matically with dune height for the range of dune sizes

simulated here (Fig. 7). When the flow is reversed,

increasing dune height has the effect of increasing the

velocity of near-surface reversed flow at 3 h down-

stream of the crest in the separation cell, although this

increase appears rather minor.

The effect of changing stoss slope basal length (L)

while maintaining dune height is shown in Figs. 5 and

8. Increasing stoss slope length appears to have a

negligible impact upon streamwise velocities at the

crest, although minor effects are clear for velocities at

the toe and in the lee (i.e., near-bed lee-side velocities

become less negative). Such results are expected given

that stoss slope angle is less sensitive to a change in

stoss slope length than a change in dune. A steepening

of this windward angle leads to both an increase in

flow acceleration at the dune crest and flow deceler-

ation in the upwind toe region due to increased

streamline compression and flow stagnation effects

respectively (Wiggs et al., 1996).

Figs. 9 and 10 are similar to Figs. 7 and 8, except

that they focus on vertical velocity at the crest, toe and

lee side of each of the experimental dune geometries.

Dune height is shown to have a significant impact on

vertical velocity in the crestal regions of the dunes due

to topographic forcing and a small, but significant,

effect on vertical velocities at the toe (Fig. 9). This

increase in V in the toe region with increasing dune

height provides some support for the streamline cur-

vature model of Wiggs et al. (1996). Sediment trans-

port is maintained through this toe region, despite a

reduction in time-averaged streamwise flow velocity,

as a consequence of concave streamline curvature

resulting in increased turbulence intensity and Rey-

nolds stresses (Wiggs et al., 1996). The small increase

in vertical velocity with increasing dune height shown

in these experiments (Fig. 9) corresponds to an

Fig. 6. Velocity profiles at the dune toe, crest and lee for changing dune heights (Experiments 1, 6, 7, 8 and 9 in Table 2).

Fig. 7. Streamwise velocity as a function of dune height.


Fig. 8. Streamwise velocity as a function of dune stoss slope length.


increase in streamline angle from 2.5j to 8.0j in the

toe region.

As expected, dune height appears to have only a

small effect on vertical velocities close to the surface

in the lee (at 3 h downstream of the crest) (Fig. 9). At

low dune heights (4 and 6 cm), the negative vertical

velocities indicate that downward flow occurs closer

to the form as flow reattaches (Fig. 4). At dune heights

above 8 cm, there is no evidence of a vertical velocity

component in the flow structure, with the zone of

Fig. 9. Vertical velocity as a f

negative vertical velocity shifting downstream. This is

attributed to re-attachment lengths being much greater

at higher dune heights (Fig. 11) than the measurement

point 3 h downstream of the crest, and, hence, near-

surface flow at 3 h is dominated by the reversed

streamwise component in larger dunes.

Fig. 10 shows that vertical velocities decline rap-

idly with increasing stoss length. It appears that

changes in stoss slope length have a greater impact

on vertical velocities at the crest than on streamwise

unction of dune height.

Fig. 10. Vertical velocity as a function of dune stoss slope length.


velocities (Fig. 8). This is expected given that changes

in stoss slope length have an immediate impact on

streamline angles at the dune crest. In addition, shorter

stoss slope lengths result in steeper windward slopes,

and, hence, higher vertical velocities at the crest (Fig.

10). This appears to have a lesser effect at the dune toe

where V decreases only slightly with increasing stoss

slope length. Similar to Fig. 9, the results in Fig. 10

suggest that vertical velocity at the bed in the separa-

tion cell is independent of dune geometry.

Fig. 11. Separation zone length (cm) as

The length of the flow separation zone with

changing dune aspect ratio is shown in Fig. 11.

In general, flow re-attaches within 3–15 dune

heights downwind (Table 3), which fits within

previously documented estimates of 4–10 h (Frank

and Kocurek, 1996b; Walker and Nickling, 2002).

These data confirm Walker and Nickling’s (2002)

suggestion that an increase in dune height (i.e., an

increase in aspect ratio) causes a corresponding

increase in the extent of the lee-side separation cell

a function of dune aspect ratio.


(i.e., flow re-attachment occurs further downwind

from the dune crest). The wide range in values

from 3 < x/h < 15 (i.e., 3–15 dune heights down-

wind from the crest) indicates the sensitivity of the

structure of the lee-side eddy to this geometrical

parameter. The data also show that a similar, though

less steep, relation occurs if dune height is main-

tained at a constant but stoss slope length is

decreased (i.e., also an increase in aspect ratio).

The different gradients of the relations evident in

Fig. 11 for changing dune height and changing

stoss length indicate that the length of the separa-

tion zone is more sensitive to the former.

Similarly, Fig. 12 shows the effect of dune aspect

ratio on the downwind distance to flow recovery in

the lee side of the dune. In general, streamwise

velocities at the surface do not recover to 99% of

upwind values until approximately 52–77 dune

heights downwind. However, even at these distances,

only the near-surface velocity values have recovered,

with the full boundary layer profile often still recov-

ering. Although actual recovery distances increase

with aspect ratio, interestingly, the shortest height

normalised recovery distances occur over the tallest

dunes with the steepest stoss slope angles (Experi-

ments 7 and 9, Table 3). These flow recovery lengths

exceed Lancaster’s (1988) estimate of 10–15 h and

Walker and Nickling’s (in press (b)) estimate of 25–

30 h, and they are closer to distances of 30–50 h for

Fig. 12. Distance to flow recovery (cm)

flow over a backward-facing step and sub-aqueous

dunes (Bradshaw and Wong, 1972; McLean and

Smith, 1986, respectively). The relationship shown

(Fig. 12) for increasing dune height in the aspect ratio

demonstrates a power function increase in recovery

distance. Similarly, a decrease in stoss slope length

(resulting in an increase in the aspect ratio) increases

recovery distance in a linear relation that is less steep

than that for changing dune height (Fig. 12).

The results in Figs. 11 and 12 are interesting in that

while variations in dune height and stoss slope length

both influence the aspect ratio of the dune, they have

differing impacts on the downwind distance to flow

recovery and the separation zone length. In both

cases, the airflow structure is more sensitive to

changes in dune height than changes in stoss slope

length.

4. Discussion

To date, logistical and instrumentation limitations

have prevented effective characterization of flow field

response over transverse dunes of varying geometry.

Only recently have CFD models become available

and validated for use in simulating the flow field over

isolated transverse dunes (see Parsons et al., in press).

It is clear from this simulation and other previous

wind tunnel and field studies that variations in stream-

as a function of dune aspect ratio.


wise and vertical velocities over transverse dunes are

the outcome of the intrusion of the dune into the

atmospheric boundary layer. The result is a perturba-

tion in the near-surface pressure field resulting in

fluid momentum changes that, in turn, cause second-

ary flow effects such as: flow stagnation and decel-

eration at the upwind toe; streamline compression,

flow acceleration and vertical lift up the windward

slope; and, in the lee, flow separation, streamline

expansion, flow re-attachment and reversal, a zone

of downward vertical flow and a lengthy flow recov-

ery distance. These secondary flow effects are shown

in this study to vary significantly with dune geome-

try—namely dune height, stoss basal length and, thus,

aspect ratio.

4.1. Streamwise velocity distribution

The CFD model used in this study reliably predicts

streamwise flow deceleration immediately upwind of

the dune followed by windward slope acceleration to

a maximum velocity at the crest. At the dune toe,

velocities increase only slightly with stoss slope

length (i.e., for less steep dunes) and decrease only

slightly with increases in dune height for the range of

forms investigated. This is likely the result of a

reduced stagnation effect imposed on the flow by

dune with lesser aspect ratios (i.e., less steep dunes)

(Wiggs et al., 1996). Toward the crest, flow acceler-

ation is more sensitive to increases in dune height than

to stoss slope length. This is primarily due to stoss

slope angle being more sensitive to changes in dune

height than basal length and thus dune height exerting

a greater perturbation on the windward flow field,

which results in enhanced streamline convergence

and, hence, flow acceleration over taller dunes.

The model also characterizes lee-side streamwise

velocity variations very effectively (Parsons et al., in

press). Reversed near-surface velocities inside the

separation zone increase slightly (i.e., become less

negative) with increasing stoss slope length (Figs. 5

and 8) but are highly sensitive to changes in dune

height (Figs. 6 and 7). This difference is highlighted

through comparison of the lee profiles in Figs. 5 and

6. Taller dunes having a larger lee-side separation

cell and stronger reversed flow near the surface can

be explained for two main reasons. First, stoss flow

is accelerated more toward, and overshot faster from,

the crest of taller, steeper dunes. Second, the lee-side

velocity gradient in the separation zone is steeper,

and as a result, momentum exchange and resultant

recycling of fluid mass back toward the dune is

greater (Walker and Nickling, in press (a)). There-

fore, for the range of dune forms investigated in

this study, taller dunes with greater aspect ratios (i.e.,

h/L>0.14) have larger lee-side flow separation

regions (Fig. 11) and stronger near-surface reversed

flows (Figs. 5 and 6).

Dune height also has a greater effect than stoss

slope length on streamwise flow velocity recovery

distance (Fig. 12). Interestingly, the shortest normal-

ised recovery distances occur over the tallest dunes

with the steepest stoss slope angles (Experiments 7

and 9, Table 3) while longer distances (up to 76.5 h)

are required for shorter dunes. This is mainly due to

the effects normalising for height (Table 3) and Fig.

12 demonstrates the effect of h and L and, thus, aspect

ratio on the actual recovery distances. The power law

function with increases in dune height shows that

recovery distance increases begin to diminish with

larger heights (Experiments 1 and 9). This may relate

to enhanced turbulent momentum exchange and dis-

sipation in the larger flow separation region in the lee

of steeper obstacles, thereby reducing the distance for

boundary layer recovery. It may also be due to

increases in negative vertical velocity magnitudes in

the lee forcing higher streamwise velocity towards the

surface and producing recovery sooner. This will be

explored further in a related paper.

4.2. Vertical velocity distribution

This study shows that vertical velocity variations

on the windward face are most affected by dune

height and stoss slope length (i.e., increasing stoss

slope angle), especially at the crest. This confirms

the widely held view that dunes with steeper wind-

ward slopes experience greater topographic forcing,

streamline convergence and flow acceleration toward

the crest (Lancaster, 1985; Tsoar, 1985; Wiggs,

1993; Lancaster et al., 1996). It is shown here that

as dune height increases, flow is overshot with

greater vertical velocity (upward lift) from the crest

(Figs. 3 and 9).

In terms of sand transport at the dune toe, the

decrease in streamwise velocity (and hence sand


transport) with increasing dune height (Fig. 7) may be

offset by an increase in streamline angle (controlled

by stoss slope length) and a rise in vertical velocity

(Figs. 9 and 10). This, in turn, may result in higher

turbulence intensities, Reynolds stresses and vertical

lift in the toe region that might be sufficient to

maintain sand transport in this region, which supports

recent wind tunnel and field studies by McKenna

Neuman et al. (2000) and Walker and Nickling (in

press (a,b)) and the streamline curvature model of

Wiggs et al. (1996).

In the lee, near-surface vertical velocities are only

slightly sensitive to changes in dune height for the

range of forms simulated. The effect is greatest for

shorter dunes (i.e., h < 8 cm) where the 1-cm mea-

surement height 3 h downstream of the crest at in the

dune lee shows greater downward velocity as it is

closer to the upper boundary of the smaller separation

cell (Figs. 4 and 10). This may also reflect a small

pocket of vertical lift (i.e., positive V) evident over

the mid lee slope for most runs (Fig. 4). This occurs

due to a steep favourable (negative) pressure gradient

that causes slower lee flow to rise toward the faster

flow in the shear layer bounding the separation cell

(Walker and Nickling, in press (a)). This phenomenon

is found in flow over roofs (Ginger and Letchford,

1993) and over low-angle fluvial dunes (Best and

Kostaschuk, 2002). Walker and Nickling (in press (a))

suggest that this effect (combined with slope effects

and impact from fallout grains, though slight) is able

to reduce transport thresholds in the lee slope region.

They also indicated that vertical updrafts in the upper

lee enhance modified suspension of grains into the lee

to distances well beyond typical saltation trajectories

(cf. Nickling et al., 2002). This reinforces the thought

that saltation is not likely the dominant mechanism

for sediment delivery into the lee and that secondary

lee-side airflow patterns have a significant effect on

dune sedimentary dynamics (Walker and Nickling, in

press (a)).

The flow field simulation (Fig. 4) shows that

beyond the lift region immediately leeward of the

crest, flow becomes downward (i.e., vertical velocities

become negative) beyond the lee slope. The progres-

sive shift from stoss-upward to lee-downward motion

reflects a wave-like, dune-generated perturbation in

the flow field and confirms measured patterns over

sub-aqueous dunes (Best and Kostaschuk, 2002) and

over an idealized aeolian form (Walker and Nickling,

in press (a)). This wave-like influence of dune form

on vertical velocity extends to a height of approxi-

mately 3–5 h and the shift to downward flow trans-

lates further downwind over the lee-slope as dune

height increases (Fig. 4). In general, the extent of the

downward flow zone appears to be relatively inde-

pendent of stoss slope length and, hence, aspect ratio.

It extends from the crest (for shorter dunes) to tens of

dune heights downwind (e.g., >14 h for the taller dune

in Experiment 7) and the flow re-attachment point is

found near the downwind edge of the faster core of is

zone. Though this paper does not characterize turbu-

lence, this finding corroborates Walker and Nickling’s

(in press (a)) claim that downward flow from a

turbulent shear zone (their zone ‘G’) overlying the

separation region drives flow re-attachment at the

surface. This study also shows that, like the separation

cell, the extent of this zone is more dependent on dune

height and not necessarily explained the aspect ratio

alone. Therefore, the influence of dune form on

vertical velocity plays an important role in sediment

delivery into the lee via grainfall in separated airflows

(Nickling et al., 2002) as well as in determining the

point of flow re-attachment, boundary layer recovery

and subsequent saltation development distance (Walk-

er and Nickling, in press (a,b)).

5. Conclusion

Analysis of CFD-derived flow structures over

idealized transverse dunes has shown the potential

to quickly and reliably test relations between dune

geometry and wind flow structure. Data confirm that

the flow field over transverse dunes is particularly

sensitive to changes in dune height, with an increase

in height resulting in flow deceleration at the toe,

acceleration at the crest and an increase in the size of

the lee-side separation zone. Evidence is provided to

support the streamline curvature model of Wiggs et al.

(1996) that explains the maintenance of sand transport

in the toe region of the dune despite declining stream-

wise velocities. This study also confirms patterns of

vertical lift in the crest region and downward flow

beyond the lee slope documented by Walker and

Nickling (in press (a)), which respectively have influ-

ence on lee-side sediment delivery via grainfall (Nick-


ling et al., 2002) and flow re-attachment, boundary

layer recovery and the re-development of saltation at

distances tens of dune heights downwind of the dune

(Walker and Nickling, in press (b)). The structure of

lee-side airflow has been shown to be very sensitive to

changes in dune height (h) and stoss slope basal

length (L). The length of the lee-side separation zone

varied from approximately 3–15 h downwind, in-

creasing with height or shorter stoss slope lengths.

Similarly, the downwind distance to flow recovery

ranged from 45 to >75 dune heights downwind with

changes in dune height.

The differing effects of height and stoss slope

length in these experiments raises questions regarding

the applicability of dune aspect ratio as a parameter

for explaining airflow over transverse dunes. Though

changes in either L or h can produce the same aspect

ratio (h/L), this study shows that dune height has a

greater effect on streamwise flow perturbations (e.g.,

flow deceleration at the dune toe, flow acceleration at

the dune crest, reversed lee-side surface flow) and on

lee-side flow structure (e.g., separation cell length,

flow recovery distance). In general, steeper (and not

longer) dunes of the same aspect ratio have a greater

effect on the flow field, particularly in the lee, for the

range of dune shapes investigated in this study. This is

because the important factor is the size of the dune in

relation to the boundary layer rather than the actual

shape of the dune, which is described by the aspect

ratio.

Further experimentation using CFD for calculating

airflow over transverse dunes is planned and extended

analyses will include shear stress development and

turbulent momentum exchange on simple triangular

dune profiles before extending experimentation to

more complex and realistic dune geometries consist-

ing of concave–convex-shaped windward slopes and

multi-dune geometries.

Acknowledgements

This work was undertaken while Daniel Parsons

was in receipt of a NERC studentship GR16/99/FS/2

with additional financial support from the British

Geomorphological Research Group to attend the

International Conference on Aeolian Research 5 at

Lubbock, TX.

References

Bates, P.D., Lane, S.N. (Eds.), 1998. High Resolution Flow Mod-

elling. Hydrological Processes 12, 1129–1396 (Special issue).

Bennett, S.J., Best, J.L., 1995. Mean flow and turbulence structure

over fixed, two-dimensional dunes: implications for sediment

transport and bedform stability. Sedimentology 42, 491–513.

Best, J.L., Kostaschuk, R.A., 2002. An experimental study of

turbulent flow over a low-angle dune. Journal of Geophysical

Research 107, 3135–3154.

Bowen, A.J., Lindley, D., 1977. A wind tunnel investigation of the

wind speed and turbulence characteristics close to the ground

over various escarpment shapes. Boundary - Layer Meteorology

12, 259–271.

Bradbrook, K.F., Biron, P., Lane, S.N., Richards, K.S., Roy, A.G.,

1998. Investigation of controls on secondary circulation and

mixing processes in a simple confluence geometry using a

three-dimensional numerical model. Hydrological Processes

12, 1371–1396.

Bradley, F., 1980. An experimental study of the profiles of wind

speed, shearing stress and turbulence at the crest of a large

hill. Quarterly Journal of the Royal Meteorological Society

106, 101.

Bradshaw, P.,Wong, F.Y.F., 1972. The reattachment and relaxation of

a turbulent shear layer. Journal of Fluid Mechanics 52, 113–135.

Britter, R.E., Hunt, J.C.R., Richards, K.J., 1981. Analysis and wind

tunnel studies of speed up, roughness effects and turbulence

over a two-dimensional hill. Quarterly Journal of the Royal

Meteorological Society 107, 91–110.

Frank, A., Kocurek, G., 1996a. Airflow up the stoss slope of sand

dunes: limitations of current understanding. Geomorphology 17,

47–54.

Frank, A., Kocurek, G., 1996b. Toward a model of airflow on the

lee side of aeolian dunes. Sedimentology 43, 451–458.

Ginger, J.D., Letchford, C.W., 1993. Characteristics of large pres-

sures in regions of flow separation. Journal of Wind Engineering

and Industrial Aerodynamics 49, 301–310.

Jackson, P.S., Hunt, J.C.R., 1975. Turbulent wind flow over a low

hill. Quarterly Journal of the Royal Meteorological Society 101,

929–955.

Lancaster, N., 1985. Variations in wind velocity and sand transport

rates on the windward flanks of desert sand dunes. Sedimentol-

ogy 32, 581–593.

Lancaster, N., 1988. Controls of aeolian dune size and spacing.

Geology 16, 972–975.

Lancaster, N., 1994. Dune morphology and dynamics. In: Abra-

hams, A.D., Parsons, A.J. (Eds.), Geomorphology of Desert

Environments. Chapman & Hall, London, pp. 474–505.

Lancaster, N., Nickling, W.G., McKenna Neuman, C., Wyatt, V.E.,

1996. Sediment flux and airflow on the stoss slope of a barchan

dune. Geomorphology 17, 55–62.

McKenna Neuman, C., 2002. The role of instrumentation in aeolian

research: recent advances and future challenges. Joint Meeting

of the International Conference on Aeolian Research (ICAR5)

and The Global Change and Terrestrial Ecosystem–Soil Erosion

Network (GCTE-SEN), Texas Tech University, Lubbock, Texas,

22–25 July 2002.


McKenna Neuman, C., Lancaster, N., Nickling, W.G., 1997. Rela-

tions between dune morphology, air flow, and sediment flux on

reversing dunes, Silver Peak, Nevada. Sedimentology 44,

1103–1113.

McKenna Neuman, C., Lancaster, N., Nickling, W.G., 2000. The

effect of unsteady winds on sediment transport on the stoss

slope of a transverse dune, Silver Peak, NV, USA. Sedimentol-

ogy 47, 211–226.

McLean, S.R., Smith, J.D., 1986. A model for flow over two-

dimensional bed forms. Journal of Hydraulic Engineering 112,

300–317.

Nelson, J.M., McLean, S.R., Wolfe, S.R., 1993. Mean flow and

turbulence fields over two-dimensional bedforms. Water Re-

sources Research 29, 3935–3953.

Nickling, W.G., McKenna Neuman, C., 1999. Recent investigations

of airflow and sediment transport over desert dunes. In: Goudie,

A.S., Livingstone, I., Stokes, S. (Eds.), Aeolian Environments,

Sediments and Landforms. Wiley, Chichester, pp. 15–47.

Nickling, W.G., McKenna Neuman, C., Lancaster, N., 2002. Grain-

fall processes in the lee of transverse dunes, Silver Peak, Neva-

da. Sedimentology 49, 191–209.

Pantaankar, S.V., Spalding, D.B., 1972. A calculation procedure for

heat, mass and momentum transport in three-dimensional para-

bolic flows. International Journal of Heat and Mass Transfer 15,

1782–1799.

Parsons, D.R., Wiggs, G.F.S., Walker, I.J., Garvey, B.G., in press.

Time-averaged numerical modelling of airflow over an idealised

transverse dune.

Raithby, G.D., Stubley, G.D., Taylor, P.A., 1987. The Askervein

hill Project: a finite control volume prediction of three dimen-

sional flow over the hill. Boundary - Layer Meteorology 39,

247–267.

Spalding, D.B., Zhang, Q., 1996. ASAP—simulating flows with a

Cartesian mesh. Proceedings of the PHOENICS User Confer-

ence, Tokyo, 1996.

Stam, J.M.T., 1997. On the modelling of two-dimensional aeolian

dunes. Sedimentology 44, 127–141.

Tsoar, H., 1985. Profile analysis of sand dunes and their steady state

significance. Geografiska Annaler 67A, 47–59.

Walker, I.J., Nickling, W.G., 2002. Dynamics of secondary airflow

and sediment transport over and in the lee of transverse dunes.

Progress in Physical Geography 26, 47–75.

Walker, I.J., Nickling, W.G., in press (a). Mean flow and turbulence

characteristics of simulated airflow over isolated and closely

spaced transverse dunes. Sedimentology.

Walker, I.J., Nickling, W.G., in press (b). Simulation and measure-

ment of surface shear stress over isolated and closely spaced

transverse dunes. Earth Surface Processes and Landforms.

Walmsley, J.L., Salmon, J.R., Taylor, P.A., 1982. On the application

of a model of boundary-layer flow over low hills to real terrain.

Boundary - Layer Meteorology 23, 17–46.

Waterson, N.P., 1994. Validation of convection discretisation

schemes. VKI Dip Rep. 1994-33. Von Karmen Institute for

Fluid Dynamics, Rhode-Saint-Genese, Belgium, pp. 1–177.

Wiggs, G.F.S., 1993. Desert dune dynamics and evaluation of

wind velocity: an integrated approach. In: Pye, K. (Ed.), The

Dynmics and Environmental Context of Aeolian Sedimentary

Systems. Geological Society Special Publication, vol. 72,

pp. 37–46.

Wiggs, G.F.S., 2001. Desert dune processes and dynamics. Progress

in Physical Geography 25, 53–79.

Wiggs, G.F.S., Livingstone, I., Warren, A., 1996. The role of

streamline curvature in sand dune dynamics: evidence from field

and wind tunnel measurements. Geomorphology 17, 29–46.

Yakhot, V., Orszag, S.A., Thangam, S., Gatshi, T.B., Speziale, C.G.,

1992. Development of a turbulence model for shear flow by a

double expansion technique. Physics of Fluids. A, Fluid Dy-

namics 4, 1510–1520.

Yang, G., Causon, D.M., Ingram, D.M., 1997a. Calculation of 3-D

compressible flows around moving bodies. 21st International

Symposium on Shock Waves, Australia, July 20–25.

Yang, G., Causon, D.M., Ingram, D.M., Saunders, R., Batten, P.,

1997b. A Cartesian cut-cell method for compressible problems:

Part A. Static-body problems; Part B. Moving-body problems.

Aero Journal of the Royal Aeronautical Society, 47–65.

Zeman, O., Jensen, N.O., 1987. Modification of turbulence charac-

teristics in flow over hills. Quarterly Journal of the Royal Mete-

orological Society 113, 55–80.

Documents

2004 Flow Structures Over Dunes