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Nonlinear interactions and turbulence of capillary surface waves
The dynamics of the waves propagating on a water surface is often
influenced by nonlinear effects. The complex and disordered patterns of
gravity waves seen on a choppy sea are indeed interpreted as a
statistical dynamic equilibrium of waves in interaction. Using among
some others the hypothesis of weak non linearity (small deformation of
the free-surface), the wave turbulence theory describes analytically
these states. When the surface tension is the main restoring mechanism,
the surface waves are called capillary waves and their wavelengths are
of scale of the centimeter or smaller. Nonlinear interactions and
turbulence of capillary waves are reported, but a major difference with
the large scale gravity waves consists in the significant viscous
dissipation in the propagation of capillary waves. In this seminar,
based on the analysis of several experimental works, we show that the
dissipation has important consequences on the nonlinear dynamics of
capillary waves. First, by increasing the width of the dispersion
relation, the contribution of non-resonant interactions is enhanced.
Then, large enough wave amplitudes are required for the nonlinear
effects to overcome the dissipation. Consequently, the turbulent states
of capillary waves correspond to strongly nonlinear regimes, beyond the
wave turbulence theory.