Wave propagation along freely propagating surface gravity current fronts

Abstract

This work deals with the propagation and evolution of disturbances which move along freely p opagating two-dimensional gravity current fronts. Examples of evolving perturbations on fronts are displayed in real-aperture radar images of gravity currents in the coastal zone. The theory of Cooper et al. (2001), which is based upon the ray tube formulation of Whitham (1974), is employed t simulate disturbances of the sort seen in this imagery and in the larger body of literature. Initial a omalies in both shape and velocity are introduced and allowed to evolve, and several types of new and interesting behaviors emerge. Shape perturbations of the form x = a sech δy evolve into two anomalies, which separate in time as they propagate in opposite directions along the front. When the value of a is increased, the disturbances, which propagate along the gravity current, can break, forming breaking frontal waves (BFWs). These manifest themselves as sharp angular features to either side of the main bulge. Two types of velocity disturbances are employed. The first has the form U = U 0 (1 + a sech δy), and evolves to preserve a single frontal bulge that increases in amplitude and width as it propagates. Here again, large values of â result in BFWs. In this case, they replicate the general behavior present in the imagery. The second type of velocity perturbation used is U = U 0 (1 + â cos δy). The smallest values of a generate no BFWs, but yield fronts which oscillate in space and time. Larger values produce a string of BFWs which are qualitatively similar tc the cusp-and-trough morphology observed so frequently in nature. The largest values of a allow the gravity current to form a string of large, bulbous structures which intersect one another as they propagate forward and spread laterally. And finally, we make an effort to correlate the results of the simulations with the shapes seen in radar and visible imagery in the literature.