Abstract
Transverse dunes, which form under unidirectional winds and have fixed profile in the direction perpendicular to the wind, occur on all celestial objects of our solar system where dunes have been detected. Here we perform a numerical study of the average turbulent wind flow over a transverse dune by means of computational fluid dynamics simulations. We find that the length of the zone of recirculating flow at the dune lee — the separation bubble — displays a surprisingly strong dependence on the wind shear velocity, u*: it is nearly independent of u* for shear velocities within the range between 0.2 m/s and 0.8 m/s but increases linearly with u* for larger shear velocities. Our calculations show that transport in the direction opposite to dune migration within the separation bubble can be sustained if u* is larger than approximately 0.39 m/s, whereas a larger value of u* (about 0.49 m/s) is required to initiate this reverse transport.
Highlights
Transverse dunes, which form under unidirectional winds and have fixed profile in the direction perpendicular to the wind, occur on all celestial objects of our solar system where dunes have been detected
We write the Reynolds number as Re 5 U1Hrf/g, where H < 3.26 m for the transverse dune investigated here, while g < 1.78 3 1025 kg m21s21 is the dynamic viscosity of the air, and U1 is a characteristic value of the wind velocity — which is typically taken at a height of 1 m above the bed[24]
We have shown, for the first time, that the length of the separation streamline at the lee of the dune increases with u*, and that the separation streamline has an angle with the ground at the reattachment point which decreases with u*
Summary
Transverse dunes, which form under unidirectional winds and have fixed profile in the direction perpendicular to the wind, occur on all celestial objects of our solar system where dunes have been detected. We perform a numerical study of the average turbulent wind flow over a transverse dune by means of computational fluid dynamics simulations. In order to model dune morphodynamics, an analytical description of the average turbulent wind flow over the sand terrain is required. Such a model has been developed in Ref. 7 for computing the shear stress over a topography consisting of smooth hills, and has been further improved by many authors, in particular by Weng et al.[8]. The fit parameters for determining s(x) for different dune profiles are typically obtained from simulations performed with one single value of wind shear velocity regardless of the dune shape
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