Three-Layer Circulations in Estuaries and Harbors

Abstract

A theory is developed for the three-layer circulation in an overmixed estuary (finite fresh-water influx) or harbor (zero fresh-water influx) accompanying a two-layer structure in the large body of water outside. A determinate act of algebraic equations is derived for the general case and the form of the equations shows that for zero fresh-water influx the discharge q1 from a harbor is proportional to the square root of the density difference between the two outside fluids. The problem is solved completely when there is a uniform depth H of the fluids inside and outside the harbor, when the fresh-water influx is zero, and when the two layers of fluid outside the harbor are of equal thicknesses. The solution shows that the outflowing layer of water has a thickness d=H/2 and a flux q1=HW(H?b0)1/2/8, where W is the width at the constriction and ?b0 the buoyancy difference between the two outside layers of water. A laboratory model reproduced the three-layer circulation of the theory. The outflowing fluid was quite turbulent and this made the observation of the layer thickness uncertain but it appeared to be close to the value d=H/2 of the theory.