Breakdown of self-similarity at the crests of large amplitude standing water waves

Details Breakdown of self-similarity at the crests of large amplitude standing water waves Breakdown of self-similarity at the crests of large amplitude standing water waves

2010-11-10

arxiv.org/abs/1011.2476v5

Phys. Rev. Lett, 107, 184501, 2011

Physics

Fluid Dynamics

4 pages, 5 figures. Final version accepted for publication

Scientific paper

10.1103/PhysRevLett.107.184501

We study the limiting behavior of large-amplitude standing waves on deep water using high-resolution numerical simulations in double and quadruple precision. While periodic traveling waves approach Stokes's sharply crested extreme wave in an asymptotically self-similar manner, we find that standing waves behave differently. Instead of sharpening to a corner or cusp as previously conjectured, the crest tip develops a variety of oscillatory structures. This causes the bifurcation curve that parametrizes these waves to fragment into disjoint branches corresponding to the different oscillation patterns that occur. In many cases, a vertical jet of fluid pushes these structures upward, leading to wave profiles commonly seen in wave tank experiments. Thus, we observe a rich array of dynamic behavior at small length scales in a regime previously thought to be self-similar.

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