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et al., the Type 2 capillaries seen above the edge of the jump before turbulent collapse can be interpreted as shear instabilities, or “vortex waves”.

  1. Breaking in modulated wave trains (wave groups) occurs generally at lower wave steepnesses than in a uniform wave train. In a periodic group containing two waves (Figure 31) the onset of breaking occurred in a wave for which ak=0.32. Final overturning was at ak=0.38. There is no unique relation between the group velocity and the horizontal particle velocity at the onset of breaking.

  2. Contrary to earlier conclusions, the initial crest bulge in the experiments of Duncan et al. is not a crest instability, since it occurs at a lower wave steepness, but resembles more the instability that occurs in a wave group. However the final form of a breaking wave is remarkably invariant, whether it arises from a crest instability or from a wave group. To find a rational theory for the onset of breaking waves in a group is a main unsolved problem.


The author's work has been supported by the Office of Naval Research under Contracts N00014–91–1582 and N00014– 91–1–0008.


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