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

Abstract

ABSTRACTOn 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 ε, 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 ε only. The application of the obtained correlators in the turbulent transport theory is discussed.