Chapter 13: A reaction network approach to the theory of acoustic wave turbulence

This post is based on my paper  Let us consider the acoustic wave turbulence kinetic equation $latex    \partial_tf \ = \ Q[f] $ where $latex   Q[f]$ is the collision term, describing pure resonant three-wave interactions. The equation is a three-wave kinetic one, in which the collision operator is of the form $latex   … Continue reading Chapter 13: A reaction network approach to the theory of acoustic wave turbulence

Chapter 12: On the energy cascade of acoustic wave turbulence: Beyond Kolmogorov-Zakharov solutions

In weak turbulence theory, the Kolmogorov-Zakharov spectra is a class of time-independent solutions to the kinetic wave equations. In this paper, we construct a new class of time-dependent solutions to those kinetic equations. These solutions exhibit the interesting property that the energy is cascaded from small wavenumbers to large wavenumbers. We can prove that starting … Continue reading Chapter 12: On the energy cascade of acoustic wave turbulence: Beyond Kolmogorov-Zakharov solutions