In classical WKB theory the only way wave energy density, as a surrogate for wave action density, can increase or decrease along a ray is as a result of the ray focusing or widening. This occurs when the group velocity is divergent. There are particular regions, however, where the wave can resonantly exchange action with another wave mode with approximately the same wavenumbers; a situation known as Landau–Zener transition, mode conversion, linear (adiabatic) resonance, etc. This effect invalidates locally the underlying assumption of WKB theory that no scattering of energy occurs between WKB wave modes. In this paper this effect is investigated theoretically for free long baroclinic Rossby waves in a two-layer planetary geostrophic model of the ocean with a purely zonal topography, here taken as a Gaussian ridge. The waves are excited along the east coast by an unspecified wavemaker at a fixed frequency ω. In the computation considered, mode conversion is found to occur principally near the ridge’s top and on the eastern flank. The predictions of mode conversion theory are tested against the results of direct numerical simulations. This shows excellent agreement, both for the locations of mode conversion points, and for the amplitude of the transmitted and converted WKB wave modes.