Simulation of non-hydrostatic, density-stratified flow in irregular domains

Abstract

A numerical model has been developed for simulating density-stratified flow in domains with irregular but simple topography. The model was designed for simulating strong interactions between internal gravity waves and topography, e.g. exchange flows in contracting channels, tidally or convectively driven flow over two-dimensional sills or waves propagating onto a shoaling bed. The model is based on the non-hydrostatic, Boussinesq equations of motion for a continuously stratified fluid in a rotating frame, subject to user-configurable boundary conditions. An orthogonal boundary fitting co-ordinate system is used for the numerical computations, which rely on a fourth-order compact differentiation scheme, a third-order explicit time stepping and a multi-grid based pressure projection algorithm. The numerical techniques are described and a suite of validation studies are presented. The validation studies include a pointwise comparison of numerical simulations with both analytical solutions and laboratory measurements of non-linear solitary wave propagation. Simulation results for flows lacking analytical or laboratory data are analysed a posteriori to demonstrate satisfaction of the potential energy balance. Computational results are compared with two-layer hydraulic predictions in the case of exchange flow through a contracting channel. Finally, a simulation of circulation driven by spatially non-uniform surface buoyancy flux in an irregular basin is discussed.