Physics of Turbulence Spreading and Explicit Nonlocality

Turbulence can spread from the linear unstable region into the stable or weakly unstable region. Thus, turbulence spreading can introduce more turbulence than expected from the linear stability, therefore breaks the scenario of local turbulence. From a simplified gyro-phase and bounce-phase averaged kinetic equation, using the 2-point correlation function, 2-point quasilinear approximation and Green’s function, we systematically derived an explicitly nonlocal model for turbulence spreading. Explicit nonlocality means that the evolution of quantities at r are explicitly affected by other positions, as characterized by the Green’s function convolution. The Green’s function comes from the inverting of potential vorticity to electric potential, and has the kernel width of several δ_b (banana orbit width). Our model recovers the usual spreading model when δ_b is small. Results show that the nonlocal effects, especially the nonlocal growth, thicken the spreading front and speed up front propagating. Penetration into the stable region Δ_p linearly grows with δ_b. Convolution reduces the growth rate in the unstable region, thus decreases the saturation level of turbulence, and lead to a simple linear relation I/l_r*²=1 - δ_b for the total turbulence intensity in the unstable region.