Estimation of nonlinear transfer functions for fully developed turbulence

A statistical method for modeling the linear and quadratically nonlinear relationship between fluctuations monitored at two points in space or time in a turbulent medium is presented. This relationship is described with the aid of linear and quadratic transfer functions and the concept of coherency is extended to quantify the goodness of the quadratic model. A unique feature of the approach described in this paper is that it is valid for non-Gaussian “input” and “output” signals. The validity of the approach is demonstrated with simulation data. The method is applied to experimental data taken in the turbulent edge plasma of the TEXT tokamak. The results indicate a three wave process with energy transfer to large scale fluctuations. The estimation of transfer functions is a first step in quantitatively measuring coupling coefficients and the energy transfer.