We investigate the transport of mass and momentum between layers in idealized
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-scale exchange flow and
shear instabilities that form at the interface, parameterizing the effects of subgrid-scale turbulence. The closure scheme is based on an assumed steady, local balance of
turbulent production and dissipation in a density-stratified fluid.
The simulated flows are analysed using a two-layer decomposition and compared
with predictions from two-layer hydraulic theory. Inter-layer transport leads to a
systematic deviation of the simulated maximal exchange flows from predictions. Relative
to predictions, the observed flows exhibit lower Froude numbers, larger transports
and wider regions of subcritical flow in the contraction. To describe entrainment
and mixing between layers, the computed solutions are decomposed into a three-layer
structure, with two bounding 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 the overall
dynamics of the exchange. An example where bed friction leads to a submaximal
exchange is discussed. The external forcing required to sustain a net transport is
significantly less than predicted in the absence of bottom stresses.