The hydraulics of two flowing layers with different densities

Abstract

This is a theoretical and experimental study of the basic hydraulics of two flowing layers. Unlike single-layer flows, two-layer flows respond quite differently to bottom depth as opposed to width variations. Bottom-depth changes affect the lower layer directly and the upper layer only indirectly. Changes in width can affect both layers. In fact for flows through a contraction control two distinct flow configurations are possible; which one actually occurs depends on the requirements of matching a downstream flow. Two-layer flows can pass through internally critical conditions at other than the narrowest section. When the two layers are flowing in the same direction, the result is a strong coupling between the two layers in the neighbourhood of the control. For contractions a particularly simple flow then exists upstream in which there is no longer any significant interfacial dynamics; downstream in the divergent section the flow remains internally supercritical, causing one of the layers to be rapidly accelerated with a resulting instability at the interface. A brief discussion of internal hydraulic jumps based upon the energy equations as opposed to the more traditional momentum equations is included. Previous uniqueness problems are thereby avoided.

Hydrography and high‐temperature heat flux of the Rainbow hydrothermal site (36°14′N, Mid‐Atlantic Ridge)

“…In the full-depth hydrographic profiles the Medi'terranean water tongue is apparent as a layer of nearly constant salinity in the approximate 02 (potential temperature referenced to 2000 dbar) range of 8ø-10øC (see Figure 4) In the case of an inviscid steady two-dimensional flow along a channel of slowly varying geometry a horizontally asymmetric density distribution (i.e., differing reservoir conditions) implies that the flow is (hydraulically) controlled [Armi, 1986]. Pratt [1986] The simple one-and-a-half layer reduced gravity model with zero upstream potential vorticity introduced by Whitehead et al [1974] is considered adequate for this purpose, mainly because it is the simplest model of rotating hydraulics, which has been tested in similar contexts [Whitehead, 1997].…”

Tidal asymmetry in an estuarine pycnocline: Depth and thickness

“…Inviscid hydraulic control theory was expanded to two layers by Armi [1986] and Farmer and Armi [1986].…”

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.…”

“…-+ It can be shown that only two of (4), (5), and (6) are independent [Armi, 1986]. A flow is said to be maximal if it has both a virtual control and a topographic control [Armi and Farmer, 1987].…”