Wave turbulence theory has remained an active area of research since its inception in the early part of the last century. In the kinetic regime, the main objects of study are the wave kinetic equations. The breakthrough discovery of constant flux, time independent solutions by Zakharov in the late 1960's has allowed for the theories predictions to be verified both experimentally and computationally in a wide array of physical systems. However, there remain many open questions concerning the time dependent solutions of the wave kinetic equations. In this thesis, we aim to partially address this open area of the wave turbulence theory by providing numerical methods for the time dependent solutions of the isotropic 3-wave kinetic equations. The methods we develop herein are able to confirm previous analysis for time dependent solutions, specifically the behavior of the energy cascade of these solutions.
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Walton, Steven, "Numerical Methods for Wave Turbulence: Isotropic 3-Wave Kinetic Equations" (2023). Mathematics Theses and Dissertations. 19.