Coloquio de Matemáticas Aplicadas

Ocean swell plays an important role in the transport of energy across the ocean, yet its evolution is not well understood. In the late 1960s, the nonlinear Schrödinger (NLS) equation was derived as a simplified model for the propagation of ocean swell over large distances. More recently, a number of generalizations of the NLS equation based on a simple dissipation assumption have been proposed. We will begin by introducing these models and their properties. Next, we will show that they accurately model wave evolution in the laboratory setting. Finally, we will test the efficacy of the NLS equation and four of its generalizations in modeling ocean swell by comparing results from numerical simulations with the classic Snodgrass et al. swell measurements. We show that dissipative models perform significantly better than conservative ones and are overall reasonable models for swell amplitudes, indicating dissipation is an important physical effect in ocean swell evolution. We also show that the nonlinear models did not out-perform their linearizations, indicating linear models may be sufficient in modeling ocean swell evolution over large distances.

Imparte

Prof. John Carter

College of Science and Engineering

University of Seattle, EUA