Exact result for mixed triple two-point correlations of velocity and velocity gradients in isotropic turbulence

摘要

On the grounds of Kolmogorov's 4/5 law analytical relations for triple two-point correlations of velocity and velocity gradients in homogeneous isotropic incompressible turbulence are derived. The corresponding correlation tensor can be expressed in terms of dissipation epsilon, the second-order longitudinal velocity structure function and one more scalar function of distance between the points. However, some components of the tensor do not depend on. 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 epsilon only. The application of the obtained correlators in the turbulent transport theory is discussed.