Structure functions and breakdown criteria for wave turbulence

We study the structure functions of wave turbulence at small separations. We show that the criteria for breakdown obtained previously by examining the uniform validity of the asymptotic closure govern how close wave turbulence stays to joint Gaussianity. A new result in the case of small separations in that the system behavior is organized by a special point in the (α,β) plane where α and β are the homogeneity parameters for the linear and nonlinear coupling coefficients. Finally, we explore how modifications of the breakdown criteria are necessary because of the strengths of non-local long-wave-short-wave interactions.