Turbulence spreading effects in the Landau-Ginzburg theory of Transport and Relaxation*

Gil and Sornette (1996) introduced a 2-field, bi-stable continuum model of avalanching, consisting of a bistable oder parameter(OP) and a control parameter(CP). For sub-critical bifurcation dynamics of OP and diffusive dynamics of CP it was demonstrated that avalanching and other SOC-like dynamics appear when diffusive relaxation of CP is faster than the instability growth rate of the OP and in the other limit of slow diffusion, avalanches comparable to the system size become dominant. A recent experiment (Inagaki et al (2013)) has reported bistable nature of turbulence. This makes this Landau-Ginzburg theory applicable to confinement problems, where the OP is turbulence intensity and CP is mean density. Turbulence spreading then naturally becomes an important concern. Hence Landau-Ginzburg theory à la Gil and Sornette is revisited with turbulence spreading. Novel findings including a quasi-periodic limit cycle state will be presented in detail in the meeting. Special attention will be focused on studies of the effective Prandtl Number dependence, which measures the relative strength of transport and spreading. We aim to understand how spreading modifies the avalanche distribution and spreading.