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Breaking in water wave models

Connections for Women: Dispersive and Stochastic PDE August 19, 2015 - August 21, 2015

August 20, 2015 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Vera Mikyoung Hur (University of Illinois at Urbana-Champaign)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • breaking - instability - discontinuity

  • water waves modelling

  • ocean waves

  • ill-posedness

  • non-linear PDE

  • dispersive PDE

  • shallow waves

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14328

Abstract

The surface of an ocean wave, after some time, may become vertical and accelerate infinitely rapidly; thereafter a portion of the surface overturns, projects forward and forms a jet of water. Think of the stunning Hokusai wave. The complexity of the governing equations of the water wave problem, however, prevents a detailed account of "breaking." Whitham in the 1970s conjectured that a model combining the water wave dispersion and a nonlinearity of the shallow water equations would capture the phenomenon. I will present its proof and use Whitham's model to illustrate the Benjamin-Feir instability of Stokes' periodic waves in water. I will discuss breaking, instabilities and ill-posedness for related, nonlinear dispersive equations.

Supplements No Notes/Supplements Uploaded
Video/Audio Files

14328

H.264 Video 14328.mp4 329 MB video/mp4 rtsp://videos.msri.org/data/000/024/026/original/14328.mp4 Download
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