Numerical computation of estuarine flows
Grubert, J.P. (1980). Numerical computation of estuarine flows. (Unpublished Doctoral thesis, The City University)
Abstract
A general system of one dimensional two-layer stratified flow equations is derived in terms of three dependent variables, discharge, level and density in each layer. Provision is made in these equations for bed slope, bed friction, wind friction, lateral discharges, interfacial mixing and quasi-laminar interfacial shear stress terms. These equations are solved using central implicit finite difference schemes with generalised algorithms so that any combination of subcritical and supercritical flows can be accommodated. In order that the computation can be made either in a single layer or a two-layer flow, the three lower layer equations are each split up into two halves, providing a four level fractional steps scheme. This flexibility in the computation is necessary when dealing with salt-wedge estuaries since the domain of the computation includes both single layer and two-layer flows.
An experimental programme was carried out to investigate the front conditions for a moving salt-wedge, and the conditions governing interfacial stability and mixing along salt-wedge interfaces. It was deduced theoretically that two distinct front types should exist in a salt-wedge estuary, namely wave front and St. Venant fronts. Experiments showed that although these front types exist, their flow conditions are different from that predicted by theory. Theory indicates that the onset of interfacial wave breaking can be expressed by a stability parameter which is a function of the interfacial densimetric Froude number and the interfacial Reynolds number. Experiments indicate that this parameter is independent of the flow Reynolds number upstream of a salt-wedge and can be scaled to give a stability parameter for prototype flows. The experiments also proved that mixing across a salt-wedge interface is a two-way process caused by the momentum exchange of turbulent flows, and that this rate of mixing is inversely proportional to the relative density.
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