Linear response theory of turbulence

Abstract

This article presents a review on the extension of the idea of linear response theory (LRT) that is well known in the statistical mechanics of systems near thermal equilibrium state, so as to be applied to the statistics in turbulence. The idea has been applied to the statistics in the inertial subrange of turbulence in an unbounded fluid domain. Recently, the idea was extended to one-point statistics in the inertial sublayer of a wall bounded turbulence. A similarity between the energy flux, from large to small scales, in homogeneous isotropic turbulence and momentum transfer in the wall-normal direction in wall bounded turbulence plays a key role in the extension. This article presents also a discussion on further extension of the scope of LRT to the statistics of single-particle diffusion in turbulence.