Abstract
Turbulent fluctuations are treated using a stationary distribution functionw st for an order parameter fieldΨ representing a fluid. Naive scale invariance ofw st yields thek −5/3 spectral law in three dimensions andk −3 in two dimensions. The noise parameter of the stationary distribution is connected with energy flow or enstrophy conservation, respectively. In order to include fluctuations of the local energy dissipation a grand distribution function is introduced.
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Grossmann, S. Scaling properties of fluctuations in stationary turbulence. Z Physik B 22, 401–406 (1975). https://doi.org/10.1007/BF01312813
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DOI: https://doi.org/10.1007/BF01312813