The role of dissipation and mixing in exchange flow through a contracting channel

We investigate the transport of mass and momentum between layers in idealiz ed exchange flow through a contracting channel. Lock-exchange initial value problems are run to approximately steady state using a three-dimensional, non-hydrostatic numerical model. The numerical model resolves the large-sca le exchange flow and shear instabilities that form at the interface, parame terizing the effects of subgrid-scale turbulence. The closure scheme is bas ed on an assumed steady, local balance of turbulent production and dissipat ion in a density-stratified fluid. The simulated flows are analysed using a two-layer decomposition and compar ed with predictions from two-layer hydraulic theory. Inter-layer transport leads to a systematic deviation of the simulated maximal exchange flows fro m predictions. Relative to predictions, the observed flows exhibit lower Fr oude numbers, larger transports and wider regions of subcritical flow in th e contraction. To describe entrainment and mixing between layers, the compu ted solutions are decomposed into a three-layer structure, with two boundin g layers separated by an interfacial layer of finite thickness and variable properties. Both bounding layers lose fluid to the interfacial layer which carries a significant fraction of the horizontal transport. Entrainment is greatest from the faster moving layer, occurring preferentially downstream of the contraction. Bottom friction exerts a drag on the lower layer, fundamentally altering th e overall dynamics of the exchange. An example where bed friction leads to a submaximal exchange is discussed. The external forcing required to sustai n a net transport is significantly less than predicted in the absence of bo ttom stresses.