Acceleration of a stratified current over a sloping bottom, driven by an alongshelf pressure gradient

Author Posting. © American Meteorological Society, 2005. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 35 (2005): 1305-1317, doi:10.1175/JPO2744.1.An idealized theoretical model is developed for the acceleration of a two-dimensional, stratified current over a uniformly sloping bottom, driven by an imposed alongshelf pressure gradient and taking into account the effects of buoyancy advection in the bottom boundary layer. Both downwelling and upwelling pressure gradients are considered. For a specified pressure gradient, the model response depends primarily on the Burger number S = Nα/f, where N is the initial buoyancy frequency, α is the bottom slope, and f is the Coriolis parameter. Without stratification (S = 0), buoyancy advection is absent, and the alongshelf flow accelerates until bottom stress balances the imposed pressure gradient. The e-folding time scale to reach this steady state is the friction time, h/r, where h is the water depth and r is a linear bottom friction coefficient. With stratification (S ≠ 0), buoyancy advection in the bottom boundary layer produces vertical shear, which prevents the bottom stress from becoming large enough to balance the imposed pressure gradient for many friction time scales. Thus, the alongshelf flow continues to accelerate, potentially producing large velocities. The acceleration increases rapidly with increasing S, such that even relatively weak stratification (S > 0.2) has a major impact. These results are supported by numerical model calculations.Funding was provided by the Division of Ocean Sciences of the National Science Foundation under Grant OCE-0241292. DCC also received some support from the Office of Naval Research under Grants N00014-00-1-0210 and N00014-02-1-0767