Title:  Dispersive Hydrodynamics:  A Wave Theory of Waves

 

Abstract: Hydrodynamic theories describe long wave propagation in a continuum, such as a fluid where the microscopic constituents are fluid particles.  When the constituents are waves, we arrive at a macroscopic wave theory of waves called dispersive hydrodynamics. Starting from the inviscid Burgers' equation presented in introductory PDE courses and progressing through a variety of nonlinear dispersive wave models, including multidimensional and semi-discrete equations, this talk will provide a tour of dispersive hydrodynamics.  Nonlinear wave modulation theory, originally introduced by Whitham, will be used to mathematically analyze a variety of initial-boundary value wave problems, from dispersive wavebreaking to Mach reflection and a nonlinear radiation condition.  Along the way, theoretical results will be reflected through the lens of reality by examining some relatively simple fluid experiments.

 

Bio: Mark Hoefer is Professor and Chair of the Department of Applied Mathematics at the University of Colorado, Boulder, drawn back to the Rockies in 2014 after obtaining his PhD from the same department in 2006.  In between, he held postdoc positions at NIST and Columbia University before becoming an Assistant Professor in the Mathematics Department of North Carolina State University.  Mark's research encompasses the mathematics and physics, including experiments, of multiscale nonlinear waves.  He received the National Science Foundation's Career award in 2013 and the T. Brooke Benjamin Prize in Nonlinear Waves from SIAM in 2020.  In 2022, he was the principal organizer for a six-month research program on Dispersive Hydrodynamics at the Isaac Newton Institute in Cambridge, UK.