Internal tide generation from non-uniform barotropic body forcing

We model linear, inviscid, internal tides generated by the interaction of a barotropic tide with one-dimensional topography. Starting from body-forcing formulation hydrodynamic problem, we derive coupled-mode system (CMS) using local eigenfunction expansion stream function. For infinitesimal topography, solve this CMS analytically, recovering classical weak topography approximation (WTA) formula for barotropic-to-baroclinic energy conversion rate. arbitrary topographies, numerically. The enjoys faster convergence respect to existing modal solutions and can be applied in subcritical supercritical regimes both ridges shelf profiles. show that non-uniform affects baroclinic field locally over topographies large slopes study dependence radiated rate on criticality. non-radiating or weakly radiating are common regime. also assess region validity WTA commonly used Gaussian ridge compactly supported bump studied here first time. Finally, provide numerical evidence showing strongly regime, (respectively shelf) approaches value obtained knife-edge step)