Non-local gravity wave turbulence in presence of condensate

The k(-23/6) wave action spectrum with an inverse cascade is one of the fundamental Kolmogorov-Zakharov solutions for gravity wave turbulence, which is part of the citation for the Dirac Medal in 2003. Instead of confirming this solution, however, several existing simulations and experiments suggest a spectrum of k(-3) in set-ups corresponding to the inverse cascade. We provide a theoretical explanation for the latter, considering the condensate that naturally forms in finite domains of experiments/simulations. Our new theory hinges on: (1) derivation of a spectral diffusion equation when non-local interactions with the condensate become dominant, for the first time systematically formulated for quartet-interaction systems; and (2) careful analysis of the asymptotics of interaction coefficient with a remarkable cancellation of all leading-order terms.