Wave turbulence: A story far from over

Wave turbulence has had many successes, a natural asymptotic closure, the Kolmogorov-Zakharov (KZ) finite flux solutions, its universality and applications to ocean waves, magnetohydrodynamic waves, elastic waves. But there are also many open questions and challenges: The breakdown of the theory for KZ finite flux spectra at certain wavenumbers and the remedies; the failure of the closure and even the premises on which it is based when coherent structures become dominant such as in the MMT equation; the need for a second closure when the wave resonance curves foliate rather than fill wave vector space as for example happens in acoustic turbulence.

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