Published: Nov. 5, 2013

Modulated Wavetrains in Dispersive Hydrodynamics

This talk will be followed by an informal lunch with APPM faculty and graduate students.



Mark Hoefer

Department of MathematicsNorth Carolina State University

Date and time: 

Tuesday, November 5, 2013 - 12:15pm


ECCR 257


Solitary waves and small amplitude dispersive radiation are important solution components of nonlinear wave problems.  A dispersive shock wave (DSW) represents the combination of solitary and dispersive waves into one coherent, expanding modulated wavetrain.  The generation of DSWs represents a universal mechanism to resolve hydrodynamic singularities in dispersive media.  Physical manifestations include undular bores on shallow water and in the atmosphere, nonlinear diffraction patterns in optics and ultracold atoms.  This talk will focus on the dispersive hydrodynamics associated with interfacial waves of viscous fluid conduits.  The derivation of an interfacial wave equation, modulation theory for DSWs, and experimental observations will be presented.  It will be argued that this system is particularly well-suited to the careful, laboratory study of universal dispersive hydrodynamics.