TRR 181 Seminar "Explicit nonlinear waves of fluid models on extended domains and unbounded growth with backscatter"

The TRR 181 seminar is held byArtur Prugger (University of Bremen, PhD in M2) on November 7, 11 am at Universität Hamburg, Bundesstr. 53, room 22/23.

Abstract

Large scale motions in geophysical flow models are often characterised by linear waves, which are obtained by linearising the equations. But there are also explicit solutions of the fully nonlinear equations, which often characterise Rossby waves, since they are in geostrophic balance.

In this talk I will introduce the idea behind these explicit nonlinear waves and show their occurrence in different fluid models in extended domains. We have discovered a surprising plethora of explicit solutions, extending known solutions scattered in the literature. As an application, we especially focus on a rotating shallow water model with simplified backscatter. In this case one finds not only geostrophic explicit solutions, but also ageostrophic ones. Moreover, here energy accumulates in selected scales due to the backscatter terms and causes exponentially and unboundedly growing ageostrophic nonlinear waves. This also relates to instability of coexisting stationary waves and is an instance of the role of nonlinear waves in energy transfer and illustrates their role in preventing energy equidistribution for general data.