Tidal generation of internal waves from a periodic array of steep ridges

Abstract

The generation of internal gravity waves by an oscillatory tidal flow over a periodic array of thin vertical walls is calculated analytically. For small values of the non-dimensional height $B=2\pi H\!N/L\omega$, the radiated power per wall is the same as for a single thin wall, and proportional to $B^2$, in agreement with the linear scaling. (Here $H$ is the wall height, $N$ the buoyancy frequency, $L$ the wall spacing, and $\omega$ the tidal frequency.) The radiated power is periodic in $B$ with period $2\pi$. It diverges logarithmically for $B=(1+2n)\pi$, and vanishes for $B=2n\pi$.