An approximate calculation of the Lagrangian auto-correlation coefficient for stationary homogeneous turbulence

Abstract

An approximate relation between the Lagrangian auto-correlation coefficient of the velocity of a fluid particle and the Eulerian velocity correlation in a field of stationary homogeneous turbulence has been pro-posed by Corrsin). The relation is used here to derive an integro-differential equation for the Lagrangian auto-correlation, and to calculate it for a particular form of the Eulerian correlation. It is found that the time scale of the Lagrangian auto-correlation is O•4 L_p/(µ²)^1/2, where L_p is the longitudinal integral scale of the turbulence and (µ²)^1/2 is the root-mean-square component of velocity. It is also found that the Lagrangian auto-correlation decreases algebraically for large times. It is pointed out that the method is not expected to apply to non-stationary turbulence as generated by a grid in a wind tunnel.

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