Title: Hydraulics and mixing in controlled exchange flows Authored by: Hogg, A.McC. Abstract:
Internal hydraulic theory is often used to describe idealised bi-directional exchange flow through a constricted channel. This approach is formally applicable to layered flows in which velocity and density axe represented by discontinuous functions that are constant within discrete layers. The layered structure of the hydraulic solution complicates its application to geophysical flows in which strong velocity gradients between layers may produce turbulent mixing which alters the two-layer structure. In this study we investigate mixing in exchange flows through a lateral contraction. The results fall into three distinct parts: a set of numerical simulations used to examine the effect of mixing upon exchange flux, a theoretical analysis of the mechanism of hydraulic control in stratified environments, and a laboratory model which is used to examine the physics of mixing processes in the flow.
First, numerical simulations of bi-directional density-driven exchange flows axe used to study the effect of turbulent mixing upon these flows. The numerical experiments are designed so that it is possible to specify the intensity of mixing. The simulated flows axe compared to two analytical solutions, first, the two-layer hydraulic solution which has no mixing, and second, a solution in which turbulent mixing dominates the flow. The simulations demonstrate that the two analytical solutions form the limits of a wide class of problems and that the flow regime in between the limiting solutions can be described by a single nondimensional parameter GrTA2, where GrT is a turbulent Grashof number, and A aspect ratio.
Hydraulic theory relies on the determination of flow conditions at points of hydraulic control, where long interfacial waves have zero phase speed. In the second stage we focus upon the propagation characteristics of the gravest vertical mode internal waves in exchange flows where mixing has produced a continuous stratification. Two approaches are used to determine the behaviour of the waves. In the first, waves axe mechanically excited at discrete locations within a numerically simulated bi-directional exchange flow and allowed to evolve under linear dynamics. A second approach, based on the stability theory of parallel viscous shear flows is used to interpret the direct excitation experiments. Two types of gravest mode solutions axe identified: vorticity modes and density modes. These modes are used to generalise the notion of hydraulic control in continuously stratified flows.
Thirdly, laboratory models of exchange flow through a contracting channel axe used to investigate the processes leading to mixing between two flowing layers. Shear-driven mixing is sensitive to changes in parameters such as the height of the water column and the density difference of the layers. Two regimes are found: the first where limited mixing is due to Holmboe instabilities, and the second where vigorous mixing is produced by Kelvin-Helmholtz billows.
Reference: Hogg, A.McC., 2002, Hydraulics and mixing in controlled exchange flows, PhD Thesis, University of Western Australia, Centre for Water Research Reference ED 1369 AH [Full Paper] [Library Catalogue] | 
