Turbulence intensity pulse propagation with self-consistent nonlinear noise

Abstract

A model of turbulence intensity spreading with self-consistent nonlinear noise is derived systematically for the simple dynamical model of resistivity gradient driven turbulence. Local effective drive, thermal conduction damping, nonlinear coupling, and spatial scattering effects are included. As a consequence of nonlinear mode coupling processes (i.e., triad mode interactions), turbulence energy can be spatially scattered, leading to turbulence propagation and spreading. However, the range of any nonlinear mode interactions of the background with a test mode is restricted to within a few mode scale widths from the test mode rational surface. The speed of a turbulent spreading front is calculated. This front speed is effectively constant on macroscopic scales. We show that the effect of self-consistent nonlinear noise on the intensity front speed is modest, as a consequence of the ordering Δc<Lf, where Δc is the turbulence correlation length and Lf is the scale length of the front’s leading edge. The implications of these results for turbulence spreading models and the important differences between self-consistent mode coupling noise and ad hoc external noise are discussed. The broader implications of these results for turbulence front propagation are identified and explained.