Abstract
AbstractIn this article, the effect shelflike topography has on the stability of a jet that flows along the smooth shelf is addressed. The linear stability problem is solved to determine for which nondimensional parameters a shelf can either destabilize or stabilize a jet. These calculations reveal an intricate dependence of growth rate on topography. In particular, the authors determine that retrograde topography (with the shallow water on the left) always stabilizes the jet (in relation to the flat-bottom equivalent), whereas prograde topography (with the shallow water on the right) can either stabilize or destabilize the jet depending on the particular values of the Rossby number and topographic parameters. For Rossby numbers of order 1 and larger, prograde topography is strictly stabilizing. For small Rossby numbers, small-amplitude topography destabilizes whereas large topography stabilizes. The nonlinear evolution of these instabilities is explored to confirm the predictions from the linear theory and, also, to illustrate how stabilization is directly related to fluid transport across the shelf.
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