Hydraulic control of two-layer flow in “quadratic”-type channels

Abstract

Previous treatments of two-layer exchange flow in a rectangular channel have been extended to consider the effects of channel geometry upon the hydraulics of such flows. Attention has been focussed on exchange flows in “quadratic” channels, defined as flow cross-sections having a single width maximum w0 at the surface and a single depth maximum D (not necessarily located at the centre of the channel cross section). The analysis shows that the effects of channel cross sectional geometry can be quantified satisfactorily in terms of a shape parameter ξ representing the ratio of the cross-sectional area of the channel to that of the equivalent rectangular channel having the same values of w0 and D. Specifically, the analysis shows that suitable definitions of the Froude numbers of the two fluid layers in terms of the shape parameter ξ enables the familiar general criticality condition G² = 1 to be formulated for the composite Froude number. Furthermore, the application of the so-called functional approach to this type of channel problem is demonstrated to show excellent quantitative consistency with the results of the hydraulic model for two reference examples (the horizontal constriction and the sill) already studied intensively for rectangular channels. Finally, an analysis is presented to show the effects upon the exchange flow of changes in ξ in the along-channel direction.

Keywords:

• Exchange flows
• stratified flows
• channel
• hydraulic control
• estuaries