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Relation of the fourth-order statistical invariants of velocity gradient tensor in isotropic turbulence
L Fang1, Y J Zhang1, J Fang2,3
1LMP, Ecole Centrale de Pékin, Beihang University, Beijing 100191, China.
Abstract:
We show by direct numerical simulations (DNSs) that in different types of isotropic turbulence, the fourth-order statistical invariants have approximately a linear relation, which can be represented by a straight line in the phase plane, passing two extreme states: the Gaussian state and the restricted Euler state. Also, each DNS case corresponds to an equilibrium region that is roughly Reynolds-dependent. In addition, both the time reversal and the compressibility effect lead to nonequilibrium transition processes in this phase plane. This observation adds a new restriction on the mean-field theory.
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