Technique for the experimental estimation of nonlinear energy transfer in fully developed turbulence

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Abstract
A new procedure for calculating the nonlinear energy transfer and linear growth/damping rate of fully developed turbulence is derived. It avoids the unphysically large damping rates typically obtained using the predecessor method of Ritz [Ch. P. Ritz, E. J. Powers, and R. D. Bengtson, Phys. Fluids B 1, 153 (1989)]. It enforces stationarity of the turbulence to reduce the effects of noise and fluctuations not described by the basic governing equation, and includes the fourth‐order moment to avoid the closure approximation. The new procedure has been implemented and tested on simulated, fully developed two‐dimensional (2‐D) turbulence data from a 2‐D trapped‐particle fluid code, and has been shown to give excellent reconstructions of the input growth rate and nonlinear coupling coefficients with good noise rejection. However, in the experimentally important case where only a one‐dimensional (1‐D) averaged representation of the underlying 2‐D turbulence is available, this technique does not, in general, give acceptable results. A new 1‐D algorithm has thus been developed for analysis of 1‐D measurements of intrinsically 2‐D turbulence. This new 1‐D algorithm includes the nonresonant wave numbers in calculating the bispectra, and generally gives useful results when the width of the radial wave number spectrum is comparable to or less than that of the poloidal spectrum.