Numerical Simulation of Strongly Stratified Flow Over a Three-Dimensional Hill

Abstract

A numerical study of stably stratified flow over a three-dimensional hill is presented. Large-eddy simulation is used here to examine in detail the laboratory experimental flows described in the landmark work of Hunt and Snyder about stratified flow over a hill. The flow is linearly stratified and U_∞/Nh is varied from 0.2 to 1.0. Here N and U_∞ are the buoyancy frequency and freestream velocity respectively, and h is the height of the hill. The Reynolds number based on the hill height is varied from 365 to 2968. The characteristic flow patterns at various values of U_∞/Nh have been obtained and they are in good agreement with earlier theoretical and experimental results. It is shown that the flow field cannot be predicted by Drazin's theory when recirculation exists at the leeside of the hill even at U_∞Nh ≪ 1. The wake structure agrees well with a two-dimensional wake assumption when U_∞/Nh ≪ 1 but lee waves start to influence the wake structure as U_∞/Nh increases. The dividing-streamline heights obtained in the simulation are in accordance with experimental results and Sheppard's formula. The energy loss along the dividing streamline due to friction/turbulence approximately offsets the energy gained from pressure field. When lee waves are present, linear theory always underestimates the amplitude and overestimates the wavelength of three-dimensional lee waves. The simulated variations of drag coefficients with the parameterK (=ND/π U_∞) are qualitatively consistent with experimental data and linear theory. Here D is the depth of the tank.