Conversion of the Barotropic Tide

Using linear wave theory, the rate at which energy is converted into internal gravity waves by the interaction of the barotropic tide with topography in an ocean is calculated. Bell’s formula for the conversion rate is extended to the case of an ocean of finite depth H with weak two-dimensional topography h(x, y) and arbitrary buoyancy frequency N(z). Approximate solutions are computed using the WKB method, which reduce to the previous result for an ocean of infinite depth with constant stratification. The conversion rate for a finite-depth ocean can be substantially smaller than the infinite-ocean prediction when the length scale of the topography is of the same order as the horizontal wavelength of the internal tide. The conversion rate for two-dimensional Gaussian seamounts is calculated. Using observed statistics for the distribution of seamounts, the authors estimate 1/4 GW of conversion for a square of ocean floor of side 1000 km.