Abstract:
Since the 30's, turbulence theories have wrestled without much success with the problem of closure, replacing an infinite hierarchy of moment or cumulant equations with a finite set. Because of weak nonlinearity and separation of time scales, wave turbulence, the study of the long time statistical behavior of a sea of weakly nonlinear dispersive waves, has a natural asymptotic closure. All properties can be calculated in terms of a single (or set of) two point function (resp. functions) and it itself satisfies a single (or set of) closed equation (resp. equations) called the kinetic equation. The derivation of the closure depends on certain premises the validity of which I will discuss. There are surprises! I will also discuss the ranges of validity in wavenumber space for the finite flux Kolmogorov-Zakharov (KZ) solutions and indicate what happens outside of these ranges. For those unfamiliar with the derivation of the kinetic equation, the organizers have arranged a separate time for me to present this calculation in the simplest of contexts. |