As the major direct contributor of desertification, wind erosion has always been considered as a typical and interesting issue in the environmental fields, since it plays an important role during the formation of sand dunes and ripples. According to Bagnold's research [1], the sand particle motion mainly consists of three modes: saltation, suspension and creep. Different models has been developed to simulate the particle behavior and the deformation of a dune in the turbulent boundary-layer (TBL) flow. Our goal is to develop a numerical method to compute the time evolution of dunes or ripples subjected to aeolian erosion.

In our team, numerical methods have already been developed to simulate the saltation and the transport of solid particles in boundary layers [2].The fluid flow is taken into account through large eddy simulations (LES) using the code ARPS [3]. This approach allows the computation of the instantaneous evolution of large turbulent structures able to produce sweeping events responsible for scalar state far from the average field. To take into account the solid particles, a Lagrangian stochastic model is coupled with the LES. The solid particles are tracked in a Lagrangian way. Different models have been introduced to take into account the interaction of the particles with the soil, especially the aerodynamic entrainment, the rebound and the splash effects. Those particles/soil interaction will be used to model the deformation of sand dune or ripple.

However, the LES approach, based on finite differences on structured grids, is not able to simulate moving complex terrains. Therefore, the first goal of the present work is to modify the numerical approach to simulate turbulent flow on moving and deformed surface.

An immersed boundary method (IBM) proposed by Lunquist [4], has been introduced in ARPS to facilitate the LES simulation with moving terrain. It is direct forcing approach and the boundary conditions are directly imposed on the immersed surface.

Two canonical simulation cases including experimental data are chosen to verify the accuracy of the immersed boundary method. A turbulent flow over a sinusoidal dune performed by Lopes [5] and a Gaussian dune performed by Simoëns [6].

The immersed boundary method has been successfully developed and implemented in ARPS. Good agreement between experimental data and simulated results demonstrates the ability of improved solver to simulate TBL flow with moving deformed terrain.

References

[1] Tsoar, H. (1994). Bagnold, RA 1941: The physics of blown sand and desert dunes. London: Methuen. Progress in physical geography, 18(1), 91-96.

[2] Vinkovic, I., Aguirre, C., Ayrault, M., & Simoëns, S. (2006). Large-eddy Simulation of the Dispersion of Solid Particles in a Turbulent Boundary Layer. Boundary-Layer Meteorology, 121(2), 283-311.

[3] Xue, M., Droegemeier, K. K., Wong, V., Shapiro, A., Brewster, K., Carr, F., Weber D., Liu Y., & Wang, D. (2001). The Advanced Regional Prediction System (ARPS)-A multi-scale nonhydrostatic atmospheric simulation and prediction tool. Part II: Model physics and applications. Meteorology and atmospheric physics, 76(1), 143-165.

[4] Lundquist, K. A., Chow, F. K., & Lundquist, J. K. (2010). An immersed boundary method for the weather research and forecasting model. Monthly Weather Review, 138(3), 796-817.

[5] Lopes, A. M. G., Oliveira, L. A., Ferreira, A. D., & Pinto, J. P. (2013). Numerical simulation of sand dune erosion. Environmental fluid mechanics, 13(2), 145-168.

[6] Simoëns, S., Saleh, A., Leribault, C., Belhmadi, M., Zegadi, R., Allag, F., Vignon J. M., & Huang, G. (2015). Influence of Gaussian hill on concentration of solid particles in suspension inside turbulent boudary layer. Procedia IUTAM, 17, 110.