H theorems in statistical fluid dynamics

Citation:
Carnevale, GF, Frisch U, Salmon R.  1981.  H theorems in statistical fluid dynamics. Journal of Physics a-Mathematical and General. 14:1701-1718.

Abstract:

It is demonstrated that the second-order Markovian closures frequently used in turbulence theory imply an H theorem for inviscid flow with an ultraviolet spectral cut-off. That is, from the inviscid closure equations, it follows that a certain functional of the energy spectrum (namely entropy) increases monotonically in time to a maximum value at absolute equilibrium. This is shown explicitly for isotropic homogeneous flow in dimensions d>or=2, and then a generalised theorem which covers a wide class of systems of current interest is presented. It is shown that the H theorem for closure can be derived from a Gibbs-type H theorem for the exact non-dissipative dynamics.

Notes:

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Website

DOI:

10.1088/0305-4470/14/7/026