## AIMS Lab Seminar - Francis Poulin - Shallow Water Models: One Just Isn’t Enough

### Description

Speaker: Francis Poulin (University of Waterloo)

Title: Shallow Water Models: One Just Isn’t Enough

Abstract: The Shallow Water (SW) model is a simplified fluid dynamical model that has been very successful in describing some large-scale flows such as the Jet Stream in the atmosphere and the Gulf Stream in the oceans. While the model is very versatile, it has its limitations, and has been used for studies that are ill-suited to these restrictions. For example, many in the literature have used it to study shocks. Even though shocks naturally occur in this model, they violate one of its basic principles: the aspect ratio of shocks is not small and therefore they are non-hydrostatic. This is partly the motivation to consider other simplified models that can describe a wider range of motions. The Green-Naghdi SW model (GN) is a generalization to the SW model that allows for some non-hydrostatic effects to occur. This talk will review the basic assumptions of the SW model; present the derivation of the GN model; and discuss different effects that occur in GN. Some details about the difficulties of how to solve this model numerically will be discussed if time permits.