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