Numerical Simulation of Stably Stratified Flow Over Hills.

The aim of the work described in this thesis is the development and application of a method to simulate computationally flows such as those investigated by Castro and Snyder [17], specifically flow over three-dimensional hills at high Reynolds and moderate to low obstacle Froude number. For hills elongated in the span wise direction, this flow regime is characterized by breaking lee waves and accelerated flow near the lower surface downstream of the obstacle. Simulations were performed by discretizing the three-dimensional Reynolds-averaged Navier-Stokes equations, and solving these numerically by a finite volume method. Buoyancy was modelled using the Boussinesq approximation, and modified k-e models employed for turbulence closure. The results obtained are found to be in reasonably good agreement with experimental flow visualizations. Critical Froude numbers for wave breaking are also found to be in reasonable agreement. Further, comparison is made with the nonlinear hydrostatic theory of Smith [101]; agreement is found to be fair, although the theory postulates a flow configuration differing from those observed in simulations. Also investigated were the effects of modifications to the turbulence model, Reynolds number, small departures from linear stratification, of wall, symmetry, and wave-permeable boundary conditions, and of the size of the computational domain. The last of these was found to affect the transient development of the flow, but to have only a weak effect on the steady state converged to, pending the arrival of reflected internal waves. Grid independence of the solution was investigated, and found to be satisfactory. One subsequent grid dependence test, however, yielded more equivocal results