Title: A Wave Theory of Waves

Speaker: Mark Hoefer, University of Colorado Boulder

Abstract: Hydrodynamic theories describe long wave propagation in a continuum, such as a fluid where the microscopic constituents are interacting fluid particles. When the constituents are interacting waves rather than particles, we arrive at a macroscopic wave theory of waves called dispersive hydrodynamics. A canonical example is the dispersive shock wave or DSW, which consists of an unsteady (expanding) collection of nonlinear oscillations terminating with zero amplitude (harmonic limit) at one end and zero wavenumber (soliton limit) at the other. Scale separation leads to the mathematical framework of nonlinear wave modulation theory, originally developed by G. B. Whitham in 1965. This talk will present a variety of developments and results in dispersive hydrodynamics utilizing Whitham modulation theory, numerical simulations, and experiment.

Zoom: https://northwestern.zoom.us/j/98867883380

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