Selection of dune shapes and velocities Part 2: A two-dimensional modelling

By Bruno Andreotti, P. Claudin, S. Douady. 2002

193 citations recorded by the source corpus.

Abstract:We present in this paper a simplification of the dune model proposed by Sauermann et al. which keeps the basic mechanisms but allows analytical and parametric studies. Two kinds of purely propagative two dimensional solutions are exhibited: dunes and domes. The latter, by contrast to the former, do not present a slip face. Their shape and velocity can be predicted as a function of their size. We recover that dune profiles are not scale invariant (small dunes are flatter than the large ones), and that the inverse of the velocity grows almost linearly with the dune size. We furthermore get the existence of a critical mass below which no dune solution exists. It rises the problem of dune nucleation: how can dunes appear if any bump below this minimal mass gets eroded and disappears? The linear stability analysis of a flat sand bed shows that it is unstable at large wavelengths: dune can in fact nucleate from a small sand mass if the proto-dune is sufficiently long.

Subfields: Atmospheric Science, Earth-Surface Processes

View Paper: https://www.semanticscholar.org/paper/51b1397643b96f5c103e13b79dac6fb9a8d037ef

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Citations in the corpus

On aeolian transport: Grain-scale interactions, dynamical mechanisms and scaling laws (2011, background): “…understanding and the quantitative description of sand transport by wind is a major issue discussed in the aeolian community (Sarre, 1987; Pye and Tsoar, 1990; Anderson et al., 1991; McEwan and Willetts, 1993, 2000; Andreotti et al., 2002a; Nickling and McKenna Neuman, 2009; Zheng, 2009).”
The physics of wind-blown sand and dust (2012, background): “Indeed, the turbulent nature of the flow over the dune leads to nonlinear hydrodynamic effects in the shear stress perturbation (Stam 1997, van Boxel et al 1999, Kroy et al 2002, Andreotti et al 2002a, Fourrière et al 2010).”
A two-species model of aeolian sand transport (2004, methodology): “Since the air is not involved in the ejection process, the ejection velocity should scale on √ gd which can be interpreted as the velocity necessary to escape from the potential trapping at the surface of the sand bed (Quartier et al. 2000; Andreotti et al. 2002a).”
Bed load transport in turbulent flow at the grain scale: Experiments and modeling (2010, background): “It can be noted that this equation has the same form as that proposed by Andreotti et al. [2002], but with a different saturation length.”