TIME-DEPENDENT 2-LAYER HYDRAULIC EXCHANGE FLOWS

A theory is presented for time-dependent two-layer hydraulic flows thr ough straits. The theory is used to study exchange flows forced by a p eriodic barotropic (tidal) flow. For a given strait geometry the resul ting flow is a function of two nondimensional parameters, gamma = (g'H )T-1/2/L and q(b0) = u(b0)/(g'H)(1/2). Here g', H, L, T, and u(b0) are , respectively, the reduced gravity, strait depth and length scales, t he forcing period, and the barotropic velocity amplitude; gamma is a m easure of the dynamic length of the strait and q(b0) a measure of the forcing strength. Numerical solutions for both a pure contraction and an offset sill-narrows combination show that the exchange flow, averag ed over a tidal cycle, increases with qb0 for a fixed gamma. For fixed q(b0) the exchange increases with increasing gamma. The maximum excha nge is obtained in the quasi-steady limit gamma --> infinity. The mini mum exchange is found for gamma --> 0 and is equal to the unforced ste ady exchange. The usual concept of hydraulic control occurs only in th ese two limits of gamma. In the time-dependent regime complete informa tion on the strait geometry, not just at a finite number of control po ints, is required to determine the exchange. The model results are com pared to laboratory experiments for the pure contraction case. Good ag reement for both interface evolution and average exchange is found if account is made for the role of mixing, which acts to reduce the avera ge salt (density) transport. The relevance of these results to ocean s traits is discussed. It is shown that many typical straits lie in the region of parameter space where time dependence is important. Applicat ion to the Strait of Gibraltar helps explain the success of the unforc ed steady hydraulic theory.