Unified approach to weak turbulence (Q1060634)

Expansion methods from the dynamical theory of statistical mechanics were used to unify weak homogeneous turbulence formulations. The hierarchy of the associated wave-correlation functions are closed and the dynamical equations which statistically describe the nonlinear interaction of the different modes are derived. The nonlinearity is weak and the modes may have complex frequencies from the linearized problem describing either the stable or the unstable situation. Energy conservation is discussed for this model as well as other general properties. Resonant three-wave interaction and some other special cases are also discussed (like higher order wave-correlation functions as well as description of spatially inhomogeneous turbulence).