Resonances in an evolving hole in the swash zone

Abstract

Water oscillations observed in a 10-m diameter, 2-m deep hole excavated on the foreshore just above the low-tide line on an ocean beach are consistent with theory. When swashes first filled the initially circular hole on the rising tide, the dominant mode observed in the cross-shore velocity was consistent with a zero-order Bessel function solution (sloshing back and forth). As the tide rose and swash transported sediment, the hole diameter decreased, the water depth inside the hole remained approximately constant, and the frequency of the sloshing mode increased according to theory. About an hour after the swashes first reached the hole, it had evolved from a closed circle to a semi-circle, open to the ocean. When the hole was nearly semi-circular, the observed cross-shore velocity had two spectral peaks, one associated with the sloshing of a closed circle, the other associated with a quarter-wavelength mode in an open semi-circle, both consistent with theory. As the hole evolved further toward a fully semi-circular shape, the circular sloshing mode decreased, while the quarter-wavelength mode became dominant.