Theory of turbulence spreading by penetrative convection and mode coupling

The intensity of inhomogenous turbulence may spread via avalanches or non-local mode couplings. These two processes are related and while mode coupling provides a mechanism for spreading, avalanches also, evolve the turbulence profile separately. Avalanches are the result of accumulation of density gradient in time at a slower time scale, resulting in intermittent, ``convective'' transport. It is essential to incorporate this effect to understand profile evolution and thus ``penetrative convection,'' which necessarily implies spreading. Here we consider a model that incorporates the effects of zonal flows, zonal ``density'' and fluctuation-fluctuation mode couplings as well as linear growth, non-linear damping and linear group propagation. We use an EDQNM type analysis of simple drift-wave turbulence within the Hasegawa-Wakatani model, to compute the effect of mode coupling between different $k_y$ modes. We observe it is predominantly the internal energy [i.e. $|\widetilde{n}|^2$], that is nonlinearly affected by these processes, whereas kinetic energy [i.e. $| \nabla \widetilde{\Phi}|^2$] simply follows due to linear coupling. Features, which distinguish between spreading by mode coupling and by penetrative convection will be elucidated and discussed.