Penetrating outflows and the dam-breaking problem
Abstract:A new analytical method for computing the speed at which the nose of a rotating intrusion advances along a straight coast is proposed. The nonlinear model includes two active layers; the width of the basin in which the intrusion advances is taken to be finite. Friction is assumed to be small but the motions near the leading edge are not constrained to be quasi-geostrophic.
In contrast to previous models (Stern et al., 1982; Kubokawa and Hanawa, 1984a, b) which rely on the assumption that the current head behaves like a long wave and the flow is hydrostatic, the propagation rate is computed by taking into account the flow forces behind and ahead of the nose without assuming a hydrostatic pressure near the head. Specifically, it is argued that the integrated sum of the momentum flux and pressure forces ahead of the leading edge must balance the flow force behind the head. This balance provides a relationship which enables one to compute the desired advancement rate; it leads to a set of five algebraic equations with five unknowns which can be solved analytically.
It is found that, in an ambient ocean with a finite depth, steady propagation rates are possible only when the intrusion is taking place in an oceanic channel with a (predicted) finite width. The steady advancement rate varies from 0.811 (g′D)1/2 to 0.824 (g′D)1/2 (where g′ is the "reduced gravity" and D is the upstream depth of the intrusion near the wall).
The above results illustrate that the presence of rotation makes the dynamics richer. In contrast to the family of solutions found here, there is only one steadily propagating solution (which conserves both energy and momentum) in the absence of rotation; it corresponds to a propagation rate of √2(g′D)1/2/2. For an infinitely deep and infinitely broad ocean the new results do not yield a steady propagation rate. Possible application of this theory to various oceanic situations is mentioned.
Document Type: Research Article
Publication date: 1987-08-01
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