Critical conditions and composite Froude numbers for layered flow with transverse variations in velocity

Abstract

A condition is derived for the hydraulic criticality of a 2-layer flow with transverse variations in both layer velocities and thicknesses. The condition can be expressed in terms of a generalized composite Froude number. The derivation can be extended in order to obtain a critical condition for an N-layer system. The results apply to inviscid flows subject to the usual hydraulic approximation of gradual variations along the channel and is restricted to flows in which the velocity remains single-signed within any given layer. For an intermediate layer with a partial segment of sluggish flow, the long-wave dynamics of the overlying and underlying layers become decoupled.

Hydraulic Criticality of the Exchange Flow through the Strait of Gibraltar

“…The long-wave speeds can be calculated from Eq. (2.7) of Pratt et al (1999) and can be shown to depend on the three Froude numbers as well as the value of r and the dimensionless depth ratios d 1 5 H 1 /H and d 2 5 H 2 /H, where…”

“…This complication can be dealt with when the layer thicknesses, but not the velocity, are allowed to vary across the strait. The procedure, described by Baines (1995), has been used to investigate the threelayer hydraulics of the Bab al Mandab (Pratt et al 1999). When the layer depths and velocities vary, the criticality of the flow can be determined by a criterion developed by Pratt (2008).…”

“…The procedure, described by Baines (1995), has been used to investigate the threelayer hydraulics of the Bab al Mandab (Pratt et al 1999). When the layer depths and velocities vary, the criticality of the flow can be determined by a criterion developed by Pratt (2008). The procedure can be applied to an arbitrary number of layers, and we will do so for twoand three-layer representations of the flow through the Strait of Gibraltar.…”

“…We have investigated the hydraulic behavior of the exchange flow through the Strait of Gibraltar using the recent hydraulic criterion developed by Pratt (2008). The continuous vertical stratification has been approximated first by a two-layer system and then by a threelayer system and cross-strait variations in velocity and layer thickness are accounted for.…”

“…The purpose of this paper is to assess the criticality of the exchange flow for both the two-and three-layer cases, including these crossstrait variations. To this end, the recent hydraulic criterion model developed by Pratt (2008) for an arbitrary number of layers, allowing for cross-channel variations in both thickness and velocity, has been adapted to the Strait of Gibraltar. The new criterion determines the hydraulic criticality of the flow as a whole across any section, and thereby removes any ambiguity that arises when the flow varies from being locally subcritical to supercritical across a section.…”