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

Abstract

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.

Exchange between a freshwater embayment and a large lake through a long, shallow channel

“…It is only at the end of the flood period (1T/12 to 3T/12), when the thickness of the surface layeras defined here-vanishes, that this control is lost. The southern end has G 2 values close to 1 but still subcritical during most of the tidal cycle, which is the result of bottom friction, as suggested by Winters and Seim (2000) for flows through smooth contractions. Only in the flood-ebb (3T/12 to 4T/12) and ebb-flood (9T/12 to 11T/12) transitions at the southernmost end of the channel and within LO (beyond the northern end of the channel) does the flow reach critical conditions.…”

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

“…This third layer is created by mixing at the interface [14]. The simulations also show higherorder dynamics not captured by the theory, e.g.…”

Estuarine Overmixing

“…In real estuaries, it is not necessarily clear how this could occur. Generally, there will be some mixing in the vicinity of a constriction if the flow is hydraulically controlled (see, e.g., Winters and Seim 2000;Farmer and Armi 1999;MacDonald and Geyer 2004), but it is not clear what the magnitude of the mixing is at the actual critical point. Bottom drag may also play a role in the bottom layer, even when the upper layer is essentially inviscid.…”