|Speaker :||Henrik Kalisch (University of Bergen, Norway)|
|Title :||Fully dispersive nonlinear model equations for hydroelastic waves|
|Time :||2018-02-09 (Fri) 16:20 - 17:20|
|Place :||Seminar Room 617, Institute of Mathematics (NTU Campus)|
In 1967, G. Whitham put forward a simple nonlinear nonlocal model
equation for the study of gravity waves at the free surface of an
inviscid fluid. The advantage of this equation was that it described
the propagation of small amplitude waves nearly perfectly, and in
addition was able to feature some nonlinear effects such as wave
steepening and peaking.
In this lecture we review Whitham's idea and present recent developments on formal asymptotics and on the mathematical proof of some of Whitham's conjectures. We then present some new models of Whitham type, in particular for capillary and hydro-elastic waves. The models are tested in the case of wave-sea-ice interaction and the response to a moving load on an ice sheet.