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Waves Seminar Series

Wednesday, September 6,  2006, 3:00 pm
Cullimore 611
New Jersey Institute of Technology

The eddy viscosity for nonlinear waves over a turbulent surface

André Nachbin

Instituto Nacional de Matemática Pura e Aplicada

Rio de Janeiro, Brazil

Abstract

In recent years we have been studying the effective (asymptotic) behavior for pulse shaped waves propagating over a highly disordered (turbulent) surface. These waves range from linear (hyperbolic) travelling pulses, to weakly dispersive Airy-like waves, all the way to solitary waves. In all cases we are able to capture the apparent viscosity due to the interaction of these waves with the disordered, turbulent surface. In particular for the (nonlinear) viscous shallow water model, we obtain a scale dependent eddy viscosity without any closure hypothesis whatsoever. We will present an overview of the asymptotic analysis for these wave solutions and illustrate theoretical results through numerical experiments.