Energy spectra of certain randomly-stirred fluids
- 1 January 1979
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 19 (1), 419-422
- https://doi.org/10.1103/physreva.19.419
Abstract
The velocity correlations of an incompressible fluid governed by the Navier-Stokes equations are studied in steady states maintained by random-white-noise stirring forces with varying spatial correlations. The asymptotic properties of the long-wavelength fluctuations are deduced by field-renormalization-group techniques. The results of Forster, Nelson, and Stephen are recovered for the random-force spectra these authors discuss, and a Kolmogorov spectrum is obtained when the force correlations have equal strength at all wave numbers, that is, when the force correlations behave as in dimensions and . Although the derivation is valid to all orders in the anomalous dimension, it implicitly assumes that there is no crossover in operator dimensionality.
Keywords
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