Traveling waves in stratified water
Sam Walsh, CIMS
A wave propagating through water is said to be traveling provided that, if viewed in a frame of reference moving at some constant speed, the wave appears to be steady (i.e., independent of time). Traveling waves have been studied since at least the mid-19th century, yet many basic questions remain open in a number of physically significant regimes. For instance, stratified fluid, such as the ocean, where the density is not constant, have proven difficult to attack.
In this talk, we will present an existence theory for two-dimensional steady stratified waves in water, both with and without surface tension. We will also discuss some interesting features of these waves. For instance, it will be shown that under minimal regularity assumptions, the particle paths (in the steady frame) are actually real analytic. (Part of this work is joint with V. M. Hur.)