Computation of gravity currents in estuaries

TLDR: In this article, the two-layer model is applied to the Rotterdam Waterway, where a salt water and a fresh water layer are assumed to be present, either with or without mixing between them.

Abstract: A great deal of literature has been devoted to gravity currents in estuaries. However, more or less detailed theoretical models of these phenomena are scarce. This is partly due to the fact that the equations have been difficult to solve if they describe the situation with some generality. This difficulty is surmounted by the use of digital computers. A more fundamental drawback is the lack of knowledge concerning the physical processes of turbulent flow in a stratified fluid. This precludes a detailed two- or three-dimensional description of the flow-pattern. Some schematical models exist which give an overall picture of the flow, still taking variations in space (along the estuary) and time (with the tide) into account. One of these is the two-layer model that is the subject of the present study. It is found that a great part of the information required for engineering applications can be obtained from it. A salt water and a fresh water layer are assumed to be present, either with or without mixing between them. Although flow in most estuaries is not strictly stratified, the two-layer schematization can be useful. This follows from an investigation of the approximations involved in the derivation of the equations. Empirically, the same fact is demonstrated by applying the two-layer model to the partly mixed Rotterdam Waterway. Knowledge of the turbulent flow processes, though in a less detailed form, is still required for a two-layer model, mainly to describe turbulent friction and mixing at the interface, as well as convection through it. If the interface is assumed to be impermeable, only the turbulent friction remains as an empirical parameter. Although the dynamical processes are reproduced less well in this case, the applicability is found to be superior, due to the small number of empirical parameters. Too little is yet known concerning the exchange of salt and water between the layers to permit a more detailed reproduction by means of the model with mixing. The latter therefore will be applied only if information on the salinity is required. The two-layer models result in mean velocities in each layer, and for the case with mixing also in mean densities. These parameters can be applied to define a family of velocity and density profiles. Combined with a crude model of the turbulent structure, this turns out to give reasonably realistic profiles. Therefore as an extension of the two-layer model an estimate of the velocity (and density) profiles can be given. The theory is verified by means of the 1956 measurements in the Rotterdam Waterway. A satisfactory correspondence is found, especially for the case without mixing. An estimate of the interfacial frictional coefficient as a function of the global conditions is obtained by hindcasting a number of flume tests. Although the present study is concerned mainly with estuaries, the two-layer model can be applied to several other cases of stratified flow, notably those concerned with thermal stratification. Such applications, however, require specific descriptions of empirical quantities, like mixing, friction, radiation.