Energetics of tidally generated internal waves for nonuniform stratification

The generation of internal waves from barotropic tides can be quantified in terms of the conversion rates. These have often been obtained by applying the WKB approximation, which yields an expression for the conversion rates which is proportional to the seabed buoyancy frequency N_B. For small values of N_B or strong variations of the buoyancy profile N(z), this gives unreliable results. Using homogenization theory it is here shown that the conversion rate instead depends on the value of N(z) averaged over a vertical region at the bottom of the same magnitude as the vertical length-scale of the internal wave, which for the lowest modes is of the same order as the entire ocean depth. This gives a substantially larger conversion rate.