Maximal two-layer exchange through a contraction with barotropic net flow

Abstract

The gravitational exchange of two fluids with different densities between reservoirs connected by a channel of constant depth and slowly varying breadth is analysed as a problem of internal hydraulics. It is shown that maximal two-way exchange with a net barotropic flow requires the presence of two controls, one at the narrrowest section and a second or ‘virtual’ control lying to one side of the narrowest section. The two controls are connected by a subcritical region, but are separated from subcritical conditions in the reservoirs by supercritical flow and stationary internal bores. Solutions are found for maximal exchange without a net barotropic component, in which case the problem is similar to that first examined by Stommel & Farmer (1953). The Stommel & Farmer analysis is shown to be a rather special limiting example of submaximal exchange, not generally applicable to natural flows. The addition of a net barotropic flow yields a range of different flow types, including maximal exchange, one-layer baroclinic flow, one-layer barotropic flow, submaximal flow governed by a reservoir condition and two-layer unidirectional flow. The maximal-exchange solution is integrated for periodic barotropic flow.

The influence of tidal range on the exchange between San Diego Bay and the ocean

“…While tidal range appears to play an important role in the exchange at the mouth of San Diego Bay, other factors that may also influence the exchange include topography [Ozsoy, 1977;Signell and Butman, 1992], longshore currents or wind [Fischer et al, 1979], stratification [Armi and Farmer, 1986], and coriolus [Kapolnai et al, 1996]. In general, these mechanisms will alter the exchange by changing the exchange regions of the ebb and flood tides.…”

Hydraulics and mixing in controlled exchange flows

“…First, in the absence of mixing, viscosity, and friction, internal hydraulic theory [Wood, 1970;Armi, 1986;Armi and Farmer, 1986;Lawrence, 1990;Dalziel, 1991] can be used to predict the velocities and depths of two distinct layers. Alternatively, if the exchange flow is dominated by turbulent mixing, we can find a solution where velocity is limited by turbulent eddy viscosity, and transport of mass is due to a combination of advection and turbulent diffusion [Cotmack et al, 1974;Offricer, 1976 Internal hydraulic theory is based on a simple balance between inertial and buoyancy forces.…”

Blockage of saline intrusions in restricted, two-layer exchange flows across a submerged sill obstruction

“…In the studies of the bi-directional channel flows, the internal hydraulic modelling solutions are usually limited to maximal or sub-maximal exchange flows [1,4,24]. Therefore, an essential consideration in the internal hydraulic analysis of two-layer flows has been to determine the location(s) of sections of internal control (G 2 = 1).…”

“…1). According to Armi and Farmer [1], for this maximal exchange-flow case, the two controls are connected by an internally sub-critical branch (i.e. G 2 \ 1), and separated from the upstream and downstream channel parts by super-critical branches (i.e.…”

“…G 2 \ 1), and separated from the upstream and downstream channel parts by super-critical branches (i.e. G 2 [ 1). However, with a comparatively large net-barotropic flow component in the surface layer, the second control can also be located in the fresh water source side (i.e.…”