The Structure of Energy Fluxes in Wave Turbulence

We calculate the net instantaneous power exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. In a first application to isotropic systems, we rederive the standard formula for the energy flux as a particular case for adjacent sets. We then exploit the new formalism to quantify nonlocal energy transfers in the example of surface capillary waves. These results establish a wave turbulence analog of the DIA formalism of Kraichnan (1959) for isotropic turbulence. A second application to nonisotropic wave systems expands the currently available set of tools to investigate magnitude and direction of the energy fluxes in these systems. We illustrate the use of the formalism by characterizing the energy pathways in the oceanic internal wavefield. Our proposed approach, unlike traditional approaches, is not limited to stationarity, scale-invariance and strict locality. In addition, our approach leads to: (i) an additional locality condition for wave turbulence spectra that was overlooked before; (ii) a number $w$ that quantifies the scale separation necessary for two sets of modes to be energetically disconnected - with potential important consequences in the interpretation of experiments of wave turbulence. The methodology presented here provides a general, simple and systematic approach to energy fluxes in wave turbulence