The interaction of surface and internal tides with boundary currents

Barotropic (surface) and baroclinic (internal) tidal motions are known to be prevalent in major boundary currents. The variable bottom topography and the sheared mean flow influence the propagation properties of such motions. Hence, the trapping and scattering properties of the continental margin are affected by boundary currents. In turn, the baroclinic tides affect the dynamic stability of boundary currents. With no mean current, several classes of coastally trapped waves are admissible: (1) external and internal Kelvin waves at all frequencies; (2) topographic Rossby waves at sub-inertial frequencies; and (3) inertial gravity edge waves at super-inertial frequencies. A sheared mean current causes dynamic effects in the dispersion relation for coastal trapped waves. Also, free Poincaré waves (at super-inertial frequencies) and Rossby waves (at sub-inertial frequencies) may be incident upon the continental margin. Their reflection properties are affected by the sheared mean boundary current as well as the variable bottom topography. A two-layered model is considered, with a mean geostrophic flow prescribed in the vicinity of the continental margin.The continental margin is assumed to be zonally oriented and uniform and of infinite length. Both the water depth and the interface depth are taken to be continuous and monotonically decreasing in the shoreward direction. Length scales are provided by the basic state: the width of the continental margin, the barotropic and baroclinic radii of deformation, and the widths of the upper and lower layer boundary currents. As an archetypical example of monochromatic frequency waves, tidal motions are considered. With density stratification, internal tides can be generated from external tides through partial reflection of an incident external plane wave from variable bottom topography or through resonant interaction of an external Kelvin wave with an inertial gravity edge wave. Examination of the alteration of these generation processes by boundary currents is the objective of the present analysis. Thus, stable, linearized waves are of primary interest. The spatial structure of the wave potential, which is largely determined by the potential vorticity of the mean flow, is investigated as a function of non-dimensional wave frequency, alongshore wave number, and the mean flow Rossby number. Then attention is restricted to super-inertial frequencies, and two related problems are considered: coastal wave trapping and scatt