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Dynamic generation of capillary waves Hector D. Ceniceros and Thomas Y. Hou

Summary: Dynamic generation of capillary waves
Hector D. Ceniceros and Thomas Y. Hou
Applied Mathematics, California Institute of Technology, Pasadena, California 91125
~Received 28 April 1998; accepted 27 January 1999!
We investigate the dynamic generation of capillary waves in two­dimensional, inviscid, and
irrotational water waves with surface tension. It is well known that short capillary waves appear in
the forward front of steep water waves. Although various experimental and analytical studies have
contributed to the understanding of this physical phenomenon, the precise mechanism that generates
the dynamic formation of capillary waves is still not well understood. Using a numerically stable
and spectrally accurate boundary integral method, we perform a systematic study of the time
evolution of breaking waves in the presence of surface tension. We find that the capillary waves
originate near the crest in a neighborhood, where both the curvature and its derivative are maximum.
For fixed but small surface tension, the maximum of curvature increases in time and the interface
develops an oscillatory train of capillary waves in the forward front of the crest. Our numerical
experiments also show that, as time increases, the interface tends to a possible formation of trapped
bubbles through self­intersection. On the other hand, for a fixed time, as the surface tension
coefficient t is reduced, both the capillary wavelength and its amplitude decrease nonlinearly. The
interface solutions approach the t50 profile. At the onset of the capillaries, the derivative of the
convection is comparable to that of the gravity term in the dynamic boundary condition and the
surface tension becomes appreciable with respect to these two terms. We find that, based on the


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara
Hou, Thomas Yizhao - Applied and Computational Mathematics Department, California Institute of Technology


Collections: Mathematics