TITLE:

Surface and Interfacial Waves, Shear, and Point-Vortices

DATE:

Friday, September 16th, 2016

TIME:

3:30 PM

LOCATION:

GMCS 324

SPEAKER:

Dr. Christopher Curtis. Assistant Professor, Department of Mathematics and Statistics. San Diego State University.

ABSTRACT:

The computation of surface and interfacial waves is a central

problem in fluid mechanics. In particular these problems appear

when we want to model sea-states or internal wave dynamics between

immiscible fluids. While much has been done, the effect of

vorticity on surface and internal wave propagation is still poorly

understood. To address this, we first look at shallow-water

propagation in density stratified fluids with piecewise linear

shear profiles. We show that by allowing for jumps in the shear

across the interface, relatively stronger nonlinear effects,

including dispersive shock waves, can be seen. Aside from

providing some insights into more complicated wave-current

systems, our approach can be generalized to any number of layers,

and thus the effects of more complicated shear profiles could be

studied.

Second, we study the problem of collections of irrotational point

vortices underneath a free fluid surface. We present a derivation

of a model and numerical scheme which allows for arbitrary numbers

of vortices in a shallow-water limit. While we are able to

recreate much of the classical results for how surface waves form

over two counter-propagating vortices, we go beyond this case and

look at several examples involving four vortices. We discuss a

wide range of unreported surface profiles and their associated

energetics. Again, our approach allows for any number of vortices

to be present, and this lets us provide some hint as to how

underwater eddies might generate free surface waves.

HOST:

Dr. Jose Castillo

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