Exact expression of Lagrangian velocity autocorrelation function in isotropic homogeneous turbulence

Abstract

In the steady, incompressible, isotropic and homogeneous turbulent flow with a joint Gaussian distribution for the velocity field, the exact expression of Lagrangian velocity autocorrelation function in the entire range of the time difference is analytically given in this paper. By this expression, the time dependences of the mean square values of the Lagrangian displacement, the Lagrangian integral time scales and their ratios to the relevant Eulerian scales are given for model spectra. In addition, comparisons between the magnitudes of the Lagrangian and Eulerian velocity autocorrelation functions are performed with the model spectra.

Time Dependence of Eulerian Velocity Correlation Tensor Spectrum in Isotropic Homogeneous Turbulence

“…On the other hand, a dimension analysis and a scaling theory are very useful, but without an actual example, they give only an estimation. So, by using the exact expression of Lagrangian velocity autocorrelation function, which was given in the previous paper [4,5], the conditions, under which its Fourier frequency component becomes inversely proportional to a square value of the frequency, are numerically studied with some model spectra, and the numerical results obtained here support that a temporal damping factor is a function of ε 1 / 3 *; 2 / 3 *. In addition, the physical interpretation of the result is proposed.…”

“…Lagrangian velocity autocorrelation function (V(i) · V(0)) u in a steady, incompressible, isotropic, homogeneous turbulent flow with a joint Gaussian distribution for the velocity field is exactly given by [4,5]:…”