Tidal conversion at a very steep ridge

We obtain an analytic solution for the generation of internal gravity waves by tidal flow past a vertical barrier of height b in a uniformly stratified ocean of depth h\, >\, b and buoyancy frequency N. The radiated power (watts per metre of barrier) is 14 ₀ b² U² N 1- (f/) ²M (b/h), where ₀ is the mean density of seawater, U (t) the tidal velocity, and f the Coriolis frequency. The function M (b/h) increases monotonically with M (0) \, =\, 1, M (0. 92) \, =\, 2 and M (1) \, =\,. As b/h \, \, 1, M diverges logarithmically and consequently the radiated power grows as (h-b) /b. We also calculate the conversion in a realistically stratified ocean with strongly non-uniform buoyancy frequency, N (z). A rough approximation to the radiated power in this case is 14 ₀ b² U² N (b) 1- (f/) ² M (B/), where N (b) is the buoyancy frequency at the tip of the ridge and B is the height of the ridge in WKB coordinates. (The WKB coordinate is normalized so that the total depth of the ocean is. ) The approximation above is an over-estimate of the actual radiation by as much as 20% when B/ \, \, 0. 8. But the formula correctly indicates the strong dependence of conversion on stratification through the factor N (b).