AIM Seminar: Spectral diffusion in wave turbulence

Abstract: Classical concept in turbulence is an energy cascade from large to small scales leading to the famous Kolmogorov spectrum. In Wave Turbulence (WT), where the fundamental motions are random interacting waves rather than hydrodynamic vortices, an analogue to the Kolmogorov spectrum is a Kolmogorov-Zakharov spectrum describing stationary states with a constant energy flux from long to short wave modes. The Kolmogorov scenario relies on a locality property which assumes that the dominant nonlinear interaction occurs among scales (e.g. wave lengths) of similar sizes. This property is violated in some important WT systems, and one has to construct alternative theories describing interactions of widely separated scales. An important example here is the spectral diffusion describing evolution of WT when the dominant interactions are with an infrared end of the spectrum. In my talk, I will introduce the main ideas, mathematical descriptions and results for the WT systems arising in several well-known applications: water surface gravity waves, internal waves, planetary Rossby waves and MMT models.

Contact: Zaher Hani