Lagrangian velocity autocorrelation

It has been pointed out over the years that the simple exponential function of the form where / is travel time from the source, appears to approximate the Lagrangian velocity autocorrelation function R t) rather well (Neumann, 1978 Tennekes, 1979). If R(t) = exp(-l/r), then the mean square particle displacement is given by (Taylor, 1921)... 

It is of interest to compute the Lagrangian velocity autocorrelation resulting from trajectories generated by Eq. (10.4) ... 

The Lagrangian velocity autocorrelations can be used to evaluate several important quantities that characterize the fluctuating motion of solids,... 

The chaotic motion of the solids in gas fluidized beds necessitates the measurement of the fluctuating and mean velocities of the solids for thorough understanding of their dynamic behavior. The statistical information of the fluctuating velocity may be obtained from the Lagrangian autocorrelations. 

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