Models for Dispersive Fluid Flow

Abstract

This talk will focus on models for dispersive fluid flow in two and three dimensions which have arisen in various contexts. The models augment the Navier-Stokes model. One version is known in different contexts as the grade-two model of Rivlin and Ericksen and the Lagrangian Averaged Navier-Stokes (alpha) model. We will discuss derivations of models and some properties in applications. We will review what has been developed recently regarding the theoretical basis for the models and their (stable) numerical discretizations.  We will discuss a controversy regarding the sign of a coefficient in the grade-two model, and we will review the data and suggested resolutions.