Spatial and spectral evolution of turbulence spectra

We present a general formulation of a theory of spreading of turbulence based on nonlinear mode couplings, which is inherently linked to spectral evolution. We present a derivation from simple two-field perspective based upon a gradien diffusion hypothesis, justified by a two scale direct interaction approximation (TSDIA) for weak turbulence. The complexity and anisotropy of spatial and spectral dynamics, however, limits our analysis to examination of different classes of triad interactions. We demonstrate that radially extended eddys, are the most effective structures in promoting spreading of turbulence. Thus, spectral evolution that tends towards such eddies, facilitate spatial spreading. We also show that, in a two field model, due to their respective spectral tendencies, internal energy spreads faster than kinetic energy.