Modification of a turbulent spectrum through the injection of a monochronatic wave. Part 1. The evolution equation

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Abstract
Analysis of the influence of an injected monochromatic wave on a turbulent spectrum shows that the evolution equation of the ensemble average distribution function is significantly different from the classical diffusion equation in velocity space. The average turbulent collision operator involves the usual spatial and temporal autocorrelation of the stochastic field, together with the correlation of this field with its spatial gradient, and the velocity derivatives are complemented by spatial derivatives