Sharp interior and boundary regularity of the SMGTJ equation with either Dirichlet or Neumann boundary control

Triggiani, Roberto

doi:10.1007/978-3-030-46079-2_22

Abstract

An along‐isobath current in stratified waters leads to a bottom boundary layer. In models with no alongshore variation, cross‐isobath density transport in this bottom boundary layer reduce the velocity in the bottom boundary layer via thermal wind, and thus the bottom friction experienced by the current above the boundary layer—this is bottom‐boundary‐layer arrest. If, however, alongshore variation of the flow is allowed, the bottom boundary layer is baroclinically unstable. We show with high resolution numerical models that these instabilities reduce this arrest and allow bottom friction to decelerate the flow above the bottom boundary layer when the flow is in the Kelvin wave direction (so that the bottom Ekman transport is downwelling). Both the arrest of the bottom boundary layer and the release from this arrest are asymmetric; the friction experienced by flows in the direction of Kelvin‐wave propagation (downwave) is much greater than flows in the opposite direction. The strength of the near bottom currents, and thus the magnitude of bottom friction, is found to be governed by the destruction of potential vorticity near the bottom balanced by the offshore along‐isopycnal transport of this anomalous potential vorticity. A simple model of this process is created and used to quantify the magnitude of this effect and the resulting reduction of arrest of the bottom boundary layer.

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