Numerical simulations of dense clouds on steep slopes: Application to powder-snow avalanches

In this paper two-dimensional Direct Numerical Simulations (DNS) of dense clouds moving down steep slopes are presented for the first time. The results obtained are in good agreement with the overall characteristics – that is, the spatial growth rate and velocity variations – of clouds studied in the laboratory. Direct numerical simulations give, in addition to the overall flow structure, local density and velocity variations inside the cloud, not easily accessible in experiments. The validity of two-dimensional simulations as a first approach is justified by the dynamics of the flow and by comparison with experimental results. The interest of the results for powdersnow avalanches is discussed, concluding that two-dimensionality is acceptable and that large density differences need to be taken into account in future simulations. Introduction A powder-snow avalanche is a dense cloud of suspended snow particles moving down a steep slope. These flows can reach front velocities uf of 100 m s , and heights h of the order of 100 m. Measurements by intrusive probes are, therefore, very hazardous. In addition, powder-snow avalanches are rare events. Techniques such as georeferenced photography and radar now in use provide extremely valuable information concerning the avalanche dimensions, their shape and front velocities as well as velocities behind the front (Dufour and others, 2000, 2001). However, density or snow concentration measurements still rely on intrusive probes and are relatively uncertain. In parallel, laboratory experiments, simulating avalanches, were developed which gave useful information about the dynamics of these flows and the dependency of avalanche velocity and shape on slope angle. A review of laboratory experiments and the related theoretical models can be found in Hopfinger (1983) and Hutter (1996). The theoretical models show that entrainment of snow from the snow cover is an important aspect of avalanche motion (Hopfinger and Tochon-Danguy, 1977; Fukushima and Parker, 1990; Rastello and Hopfinger, in press). Generally, laboratory experiments are, unfortunately, limited to Boussinesq fluids of Boussinesq number %2−%1 %2 1. The principle similarity parameter is the densimetric Froude number provided the Reynolds number is sufficiently large for the flow to be fully turbulent (in free shear flows a continuous energy spectrum with a k− 5 3 spectral slope emerges when the flow Reynolds number is greater than 3 · 10). Commercial avalanche codes use depth averaged models and in some cases turbulence k-ε models for the powder cloud. Often these models are combined with a dense flow layer below the powder cloud and a transition layer in between (see e.g. Naaim and Gurer, 1998). In order to make progress in the understanding of the flow structure, more refined experiments are required (field studies and laboratory experiments). Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) are alternative approaches. These give access to all the flow quantities desired and would be of particular interest for the study of the interaction of an avalanche with structures for instance. Unfortunately, the complex structure of avalanches make such numerical simulations still difficult. For this reason only Boussinesq gravity currents on horizontal boundary have been simulated at present (Necker and others, 2002). Here we present the first DNS of dense clouds motion on slopes. These simulations are, at present, two-dimensional and for %2−%1 %2 1 ; the relevance of 2D simulations which allow to reach high Reynolds numbers, is supported by the dynamics of avalanches discussed below. Before refining the simulations by going to a 3D code, it is of interest to study first such first order effects as snow entrainment and large %2−%1 %2 . Ultimately, DNS and LES can serve as bench mark tests for averaged models used in practice.