Mixed Triple Two-Point Correlations of Velocity and Velocity Gradients in Homogeneous Isotropic Turbulence

Abstract

On the basis of Kolmogorov’s 4/5 law (Kolmogorov, 1941; Landau, Lifschitz 1975) analytical relations for triple two-point correlations of velocity and velocity gradients in homogeneous isotropic incompressible turbulence are derived (Kopyev, Zybin, 2018). The corresponding correlation tensor can be expressed in terms of the dissipation rate, the second-order correlation function for the longitudinal velocity increment, and the new scalar function of distance between the points. However, some components of the tensor do not depend on the new function. The derived analytical results are in agreement with the data obtained from direct numerical simulations. The function can be well approximated in the inertial range by a constant value that depends on the dissipation only. The application of the obtained correlators in the turbulent transport theory is discussed (Il’yn, Sirota, Zybin, 2016; Kazantsev, 1968). The study was performed in Central Aerohydrodynamic Institute (TsAGI) with the funding of Russian Science Foundation (project No. 17-11-01271).