Large Eddy Simulation of Turbulent Flow Over a Hill Using a Canopy Stress Model

Abstract

Mathematical modelling of a turbulent flow over hilly terrains is an important topic in both mesoscale weather prediction and boundary layer meteorology. In comparison to the classical terrain-following coordinate approach, the immersed boundary technique on a Cartesian grid simplifies the implementation of the boundary condition on the surface of the hill, and this approach also mitigates discretization errors which would occur due to the terrain-following coordinate transformation. In the present research, we have extended a canopy stress model to formulate the boundary condition on the surface of a hill and considered the large eddy simulation method to predict the interaction between the near-surface coherent structures and a smooth hill. In addition to the canopy stress model, the turbulent stress has also been varied dynamically as the surface is approached, where the canopy stress model is derived based on the experimental observation that the drag coefficient becomes independent of the Reynolds number (Re) when Re is sufficiently large. The proposed model has been tested by simulating a neutrally stratified atmospheric boundary layer over a periodic array of smooth hills. The agreement among the results of the present simulation, a dynamically similar experiment, and an equivalent numerical model suggests the potential benefits of the proposed method of simulating turbulent flow over hilly terrains.