Departmental Colloquium
Catherine Sulem
University of Toronto
Interaction between internal and surface waves in a two layers fluid
Abstract: We consider a situation in which a fluid is composed of two essentially immiscible layers
separated by a sharp interface such as a thermocline or a pycnocline of differential salinity.
Internal waves of various types are commonly generated in the world's oceans, and large
amplitude, long wavelength nonlinear waves can be produced in the interface and propagate
over large distances. In some physically realistic instances, the visible signature of internal
waves on the surface of the ocean is a band of roughness which propagates at the same
velocity as the internal wave. Several of the earliest observations are the most striking,
consisting of long brightly shining strips of many kilometers in extent, visible through the
effect of the reflection at an oblique angle of the setting sun, and photographed from the
Space Shuttle. I will discuss the asymptotic analysis of the coupling between the interface and the free surface of a two layers fluid in a scaling regime chosen to capture these observations, in
which the internal mode is treated as a long wavelength nonlinear internal wave, while the
surface mode is smaller and taken in a modulational regime.
This talk is based on joint work with Walter Craig and Philippe Guyenne.
This is the opening lecture for the Midwest PDE Seminar at UIC (November 13-14, 2010).
Friday November 12, 2010 at 3:00 PM in SEO 636