IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Curvature Singularities on the Surface of Water Waves

  • Oct. 11, 2012
  • 3:30 p.m.
  • LeConte 412


Boundary integral methods are naturally suited for tracking the motion of free surfaces in incompressible, inviscid flows. An important example is the propagation of waves on the surface of water, deep or shallow. Not only is the method naturally adaptive when fluid particles are tracked by following their motion, but also spectrally accurate numerical methods ensure high enough resolution that important mathematical behavior can be discerned. A pleasing viewpoint arises when the curvature of the surface location is considered as a complex-valued function of the complex-valued arclength. Pole singularities are found that move around the complex plane as the wave progresses. Of special interest is whether these singularities reach the real axis when the curvature singularity becomes physically real. We report on singularity behavior in general, but particularly when the water waves break.

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