Affiliation:
1. P.N. Lebedev Physical Institute of the Russian Academy of Sciences
2. P.N. Lebedev Physical Institute of the Russian Academy of Sciences; National Research University Higher School of Economics
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).
Funder
Russian Science Foundation
Publisher
P.P. Shirshov Institute of Oceanology, RAS
Reference7 articles.
1. Il’yn A.S., Sirota V.A., and Zybin K.P. Statistical properties of the T-exponential of isotropically distributed random matrices. J. Stat. Phys., 2016, Vol. 7, p. 709.
2. Kolmogorov A.N. Rasseyanie energii pri lokalno isotropnoy turbulentnosti. Dokladi Akademii nauk SSSR, 1941, Vol. 32, No. 1, pp. 19–21.
3. Kopyev A.V. and Zybin K.P. Exact result for mixed triple two-point correlations of velocity and velocity gradients in isotropic turbulence. Journal of Turbulence, 2018, Vol. 19, No. 9,
4. pp. 717–730.
5. Kazantsev A.P. Enhancement of a magnetic field by a conducting fluid. Sov Phys JETP, 1968, Vol. 26, pp. 1031.