On the energy transfer mechanisms in wave turbulence

Abstract: Weakly-nonlinear partial differential equations serve as fundamental tools for understanding turbulence, often referred to as weak or wave turbulence. While classical hydrodynamic turbulence demonstrates a sequential interaction of eddies of comparable size, where local interactions drive the energy cascade (Kolmogorov-Obukhov theory) within the inertial range, wave turbulence introduces an additional mechanism of energy transfer through resonant wave-wave interactions. However, the understanding for the efficiency of these resonant modes compared to local interactions is incomplete. Moreover, the role of resonant clusters has yet to be verified. This study explores various reduced mathematical models, inspired by physical systems, capturing 3-wave resonant interactions with alternative nonlinear terms. It illustrates how mode-to-mode energy transfer occurs within such resonant systems, alongside coexisting local transfers, for varying degrees of nonlinearity.