Analysis and Applied Mathematics Seminar
Ming Chen
University of Pittsburgh
Existence of large-amplitude steady stratified water waves
Abstract: We consider 2D steady water waves with heterogeneous density. The presence
of stratification allows for a wide variety of traveling waves, including
fronts, so-called generalized solitary waves with ripples in the far
field, and even fronts with ripples! Among these many possible wave
patterns, we prove that for any smooth choice of upstream velocity and
monotone streamline density function, there always exists a continuous
curve of solitary waves with large amplitude, which are even and
decreasing monotonically on either side of a central crest. As one moves
along this curve, the horizontal fluid velocity comes arbitrarily close to
the wave speed.
We will also discuss a number of results characterizing the qualitative
features of solitary stratified waves. In part, these include bounds on
the Froude number from above and below that are new even for constant
density flow; an a priori bound on the velocity field and lower bound on
the pressure; a proof of the nonexistence of monotone bores for stratified
surface waves; and a theorem ensuring that all supercritical solitary
waves of elevation have an axis of even symmetry. This is a joint work
with Samuel Walsh and Miles Wheeler.
Monday October 24, 2016 at 4:00 PM in SEO 636