On Internal Waves Propagating Across a Geostrophic Front

AbstractReflection and transmission of normally-incident internal waves propagating across a geostrophic front, like the Kuroshio or Gulf Stream, are investigated using a modified linear internal-wave equation. A transformation from depth to buoyancy coordinates converts the equation to a canonical partial differential equation, sharing properties with conventional internal-wave theory in the absence of a front. The equation type is determined by a parameter Δ, which is a function of horizontal and vertical gradients of buoyancy, the intrinsic frequency of the wave and the effective inertial frequency, which incorporates the horizontal shear of background geostrophic flow. In the northern hemisphere, positive vorticity of the front may produce Δ≤0, i.e., a “forbidden zone”, in which wave solutions are not permitted. Thus, Δ=0 is a virtual boundary that causes wave reflection and refraction, although waves may tunnel through forbidden zones that are weak or narrow. The slope of the surface and bottom bound...