Long waves on the continental shelf: an experiment to separate trapped and leaky modes

Abstract

Random fluctuations in sea level, ζ, in the frequency range 0·1-60 cycles per hour were measured along the coast near Oceanside, California, where the coastline and bottom contours are fairly straight and parallel for 30 km. The two-dimensional covariance $R(\eta, \tau) = \langle \zeta (y,t) \zeta (y + \eta, t+ \tau) \rangle$ was computed for points separated by various distances η along the coast. The Fourier transform $S(f,n) = \int \int R(\eta, \tau)exp [2\pi i (n \eta + f \tau)]d \eta d \tau$ gives the contribution towards the ‘energy’ $\langle \zeta ^2 \rangle$ per unit temporal frequency f per unit spacial frequency (long-shore component) n. It is found that most of the energy is confined to a few narrow bands in (f, n) space, and these observed bands correspond very closely to the gravest trapped modes (or edge waves) computed for the actual depth profile. The bands are 0·02 cycles per km wide, which equals the theoretical resolution of the 30 km array. Very roughly S(f,n) ≈ S(f, -n), corresponding to equal partition of energy between waves travelling up and down the coast. Theory predicts ‘Coriolis splitting’ between the lines f± (n) corresponding to these oppositely travelling waves, but this effect is below the limit of detection. The principal conclusion is that most of the low-frequency wave energy is trapped.