Tidal Conversion by Subcritical Topography

Abstract

Analytical estimates of the rate at which energy is extracted from the barotropic tide at topography and converted into internal gravity waves are given. The ocean is idealized as an inviscid, vertically unbounded fluid on the f plane. The gravity waves are treated by linear theory and freely escape to z = ∞. Several topographies are investigated: a sinusoidal ripple, a set of Gaussian bumps, and an ensemble of “random topographies.” In the third case, topographic profiles are generated by randomly selecting the amplitudes of a Fourier superposition so that the power spectral density is similar to that of submarine topography. The authors' focus is the dependence of the conversion rate (watts per square meter of radiated power) on the amplitude of the topography, h0, and on a nondimensional parameter ϵ∗, defined as the ratio of the slope of an internal tidal ray to the maximum slope of the topography. If ϵ∗ ≪ 1, then Bell's theory indicates that the conversion is proportional to h20. The results ... Abstract Analytical estimates of the rate at which energy is extracted from the barotropic tide at topography and converted into internal gravity waves are given. The ocean is idealized as an inviscid, vertically unbounded fluid on the f plane. The gravity waves are treated by linear theory and freely escape to z = ∞. Several topographies are investigated: a sinusoidal ripple, a set of Gaussian bumps, and an ensemble of “random topographies.” In the third case, topographic profiles are generated by randomly selecting the amplitudes of a Fourier superposition so that the power spectral density is similar to that of submarine topography. The authors' focus is the dependence of the conversion rate (watts per square meter of radiated power) on the amplitude of the topography, h0, and on a nondimensional parameter ϵ∗, defined as the ratio of the slope of an internal tidal ray to the maximum slope of the topography. If ϵ∗ ≪ 1, then Bell's theory indicates that the conversion is proportional to h20. The results ...