title: Relation of the fourth-order statistical invariants of velocity gradient tensor in isotropic turbulence.
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.
authors.affiliation: LMP, Ecole Centrale de Pékin, Beihang University, Beijing 100191, China.
authors.forename: L
authors.initials: L
authors.lastname: Fang
authors.affiliation: LMP, Ecole Centrale de Pékin, Beihang University, Beijing 100191, China.
authors.forename: Y J
authors.initials: YJ
authors.lastname: Zhang
authors.affiliation: National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, School of Energy and Power Engineering, Beihang University, Beijing 100191, China.|Computer Science and Engineering Department, STFC Daresbury Laboratory, Warrington WA4 4AD, United Kingdom.
authors.forename: J
authors.initials: J
authors.lastname: Fang
authors.affiliation: LMFA, Ecole Centrale de Lyon, Université de Lyon, 69130 Ecully, France.
authors.forename: Y
authors.initials: Y
authors.lastname: Zhu