Abstract
Although direct and inverse energy cascades in wave spectra have been the subject of numerous efforts in recent years, few actual computations have been presented. In this study, we give explicit estimates for the energy fluxes associated with direct and inverse cascades. A critical frequency fc is determined at which there is no net flux. That is, the direct energy cascade, consisting of energy fluxes cascading from low to high frequencies, is balanced by the corresponding inverse cascade, consisting of energy fluxes from high to low frequencies. We show numerically that the existence of fc is related to self-similarity.
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