Direct simulation of plane-symmetric deep-water gravity waves shows a strongly nonlinear regime with omega^-4 and k^-4 spectra, shock fronts, and -7/2 steepness tails, with no weak-turbulence spectrum detected.
Strong wave turbulence in strongly local large $N$ theories
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abstract
We study wave turbulence in systems with two special properties: a large number of fields (large $N$) and a nonlinear interaction that is strongly local in momentum space. The first property allows us to find the kinetic equation at all interaction strengths -- both weak and strong, at leading order in $1/N$. The second allows us to turn the kinetic equation -- an integral equation -- into a differential equation. We find stationary solutions for the occupation number as a function of wave number, valid at all scales. As expected, on the weak coupling end the solutions asymptote to Kolmogorov-Zakharov scaling. On the strong coupling end, they asymptote to either the widely conjectured generalized Phillips spectrum (also known as critical balance), or a Kolmogorov-like scaling exponent.
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Effects of strong turbulence for water waves
Direct simulation of plane-symmetric deep-water gravity waves shows a strongly nonlinear regime with omega^-4 and k^-4 spectra, shock fronts, and -7/2 steepness tails, with no weak-turbulence spectrum detected.