Time-Dependent Two-Layer Hydraulic Exchange Flows

Abstract

A theory is presented for time-dependent two-layer hydraulic flows through straits. The theory is used to study exchange flows forced by a periodic barotropic (tidal) flow. For a given strait geometry the resulting flow is a function of two nondimensional parameters, ? = (g?H)1/2T/L and qb0 = ub0/(g?H)1/2. Here g?, H, L, T, and ub0 are, respectively, the reduced gravity, strait depth and length scales, the forcing period, and the barotropic velocity amplitude; ? is a measure of the dynamic length of the strait and qb0 a measure of the forcing strength. Numerical solutions for both a pure contraction and an offset sill-narrows combination show that the exchange flow, averaged over a tidal cycle, increases with qb0 for a fixed ?. For fixed qb0 the exchange increases with increasing ?. The maximum exchange is obtained in the quasi-steady limit ??∞. The minimum exchange is found for ??0 and is equal to the unforced steady exchange. The usual concept of hydraulic control occurs only in these two limits of ?. In the time-dependent regime complete information on the strait geometry, not just at a finite number of control points, is required to determine the exchange. The model results are compared to laboratory experiments for the pure contraction case. Good agreement for both interface evolution and average exchange is found if account is made for the role of mixing, which acts to reduce the average salt (density) transport. The relevance of these results to ocean straits is discussed. It is shown that many typical straits lie in the region of parameter space where time dependence is important. Application to the Strait of Gibraltar helps explain the success of the unforced steady hydraulic theory.