Propagation of a finite-amplitude potential vorticity front along the wall of a stratified fluid
Stern, Melvin E.
Helfrich, Karl R.
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A similarity solution to the long-wave shallow-water equations is obtained for a density current (reduced gravity = g[prime prime or minute], Coriolis parameter = f) propagating alongshore (y = 0). The potential vorticity q = f/H1 is uniform in [minus sign][infty infinity] < x [less-than-or-eq, slant] xnose(t), 0 < y [less-than-or-eq, slant] L(x, t), and the nose of this advancing potential vorticity front displaces fluid of greater q = f/H0, which is located at L < y < [infty infinity]. If L0 = L([minus sign][infty infinity], t), the nose point with L(xnose(t), t) = 0 moves with velocity Unose = [surd radical]g[prime prime or minute]H0 [phi], where [phi] is a function of H1/H0, f2L20/g[prime prime or minute]H0. The assumptions made in the similarity theory are verified by an initial value solution of the complete reduced-gravity shallow-water equations. The latter also reveal the new effect of a Kelvin shock wave colliding with a potential vorticity front, as is confirmed by a laboratory experiment. Also confirmed is the expansion wave structure of the intrusion, but the observed values of Unose are only in qualitative agreement; the difference is attributed to the presence of small-scale (non-hydrostatic) turbulence in the laboratory experiment but not in the numerical solutions.
Author Posting. © Cambridge University Press, 2002. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 468 (2002): 179-204, doi:10.1017/S0022112002001520.
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