Abstract
A model is presented for the fluctuating flow through a strait of nonuniform depth connecting two semi-infinite oceans.
An analytical solution is found. The solution is applied to several depth profiles to study the effect of the topography on the volume flux through the strait. A nondimensional number σ = (∂h/∂x)fW/2ωh is found to determine the importance of the topography of the strait, where f, ω, W, L and h are the Coriolis parameter, fluctuating frequency, and the width, length and depth of the strait, respectively. If σ < 0.6, the effect of the variation of strait depth is negligible; if σ increases, the effect of the depth variation is to shorten the length of the strait, thus allowing more flux through the strait; at the value of about σ = π/2, the strait is almost invisible to the open oceans as far as the flux is concerned.
The mechanism of the geostrophic control of the flux through the strait is studied. A model of energy balance clearly shows that the flux is limited by the amount of the energy which the two outgoing Kelvin waves can carry: the flux through the strait can not be greater than the flux at the geostrophic-control limit, otherwise it will generate in the open oceans such big Kelvin waves that they would carry away more energy than the strait system can receive from the incoming Kelvin waves.
