Pattern Formation in the Nearshore

Abstract

The sandy shores of ocean beaches deform under the continual action of waves and currents into a rich set of patterns and morphologies with scales from centimeters to kilometers. Since the bathymetry acts as a boundary condition to the progressing waves and those waves also slowly modify the bathymetry, an important feedback loop exists. It appears to be this feedback that causes observed nearshore morphologies, rather than the sand simply responding to a pattern of forcing imposed by the fluids. Because interactions between the fluid and sediment are inherently nonlinear, they can be complicated to study. For weak nonlinearities, perturbation techniques are available, or the system may be modeled numerically in a series of small time steps. However, as the time scales of interest extend, small errors in forward stepping models grow exponentially and other approaches are needed. Self organization models study the phenomenology that is derived from very simple feedback loops, felt to represent the essence of the nearshore system and implemented by sets of rules. Top down modeling examines long time series of field data to extract empirically the basic physics required to explain the observed phenomenology. Merging the results of these approaches will facilitate progress.