Physics of turbulence spreading and explicit nonlocality

In this paper, we systematically derive a model for turbulence spreading from the basic kinetic equation. The model contains explicit nonlocal nonlinear diffusion and nonlocal growth. When the nonlocality scale parameter delta(b) (banana width) vanishes, this model reduces to the usual turbulence spreading model. We elucidate the mechanisms of nonlinear saturation and nonlocal growth. Results show that nonlocal effects, especially the nonlocal growth, thicken the turbulence spreading front and increase the speed of front propagation. More turbulence intensity penetrates the stable region when delta(b) increases. The penetration depth Delta(p) is proportional to delta(b)/L-T, therefore the fraction of turbulence in the unstable region scales as 1 - delta (b*). The transport scales the same way.

Automated summary

In this paper, a model for turbulence spreading is derived from the basic kinetic equation, containing explicit nonlocal nonlinear diffusion and growth. The mechanisms of nonlinear saturation and nonlocal growth are elucidated, showing that nonlocal effects increase the thickness of the turbulence spreading front and speed up front propagation. A higher nonlocal scale parameter leads to more turbulence penetrating the stable region, with the penetration depth being proportional to the scale parameter.