Tide-topography interactions in a stratified shelf sea II. Bottom trapped internal tides and baroclinic residual currents

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Abstract
The generation of topographically bounded internal tides and baroclinic residual currents is discussed for a linearly stratified fluid in the limit of small-amplitude topography and weak damping. It is shown that quasi-nonlinear advection by the barotropic tide generates a residual and higher harmonics, besides the ever present fundamental driving frequency in the internal motions. At all frequencies the along-isobath currents and the cross-isobath circulation are bottom intensified, the intensification being a function of the internal Rossby deformation radius. For a step topography the weak cross-isobath residual circulation has a characteristic three-cell structure with a down-slope bottom current at the position of the steepest slope, which is also the center of the along-isobath residual jet. In contrast to barotropic currents in the quasi-nonlinear regime, the baroclinic currents are exponentially bounded to the topography, rather than extending over a finite interval, in which the e-folding distance is the internal deformation radius.