Lagrangian integral time scale

The Lagrangian integral time scale Jl can be considered as a measure of the time during which a fluid particle persists, in the mean, in a motion in a given direction. In Section VIU we will discuss Ti, quantitatively. Where unambiguous, 71 will be denoted simply by T. 

Another quantity of interest is the Lagrangian integral time scale. 

The definition of X incorporates the fact that the Lagrangian integral time scale is of the order of Zilw,. The statistical theory of turbulent diffusion outlined in the beginning of Section VIII,B can be used to estimate the functional dependence of g as... 

Next, it is of interest to compute the Lagrangian integral time scale of the process [recall Eq. (8.6)] ... 

In terms of the Lagrangian integral time scale, Eq. (99), we find... 

The Lagrangian integral time scale of the process is defined by ... 

Computations of the Lagrangian integral time scale for different experiments yielded values in the range of 0.4 to 0.8 seconds for different compartments. These time scales are not strongly dependent on gas superficial velocity or column diameter. This implies that the Lagrangian fluctuating velocity is statistically independent of itself beyond about 0.6 seconds i in this interval the particle moves from one eddy (correlated region of flow) to another. 

The spatial and temporal inhomogeneities in the turbulence are of such scales that a particle released anywhere in the fluid will, over an interval At, behave as though it were in a fleld of stationary, homogeneous turbulence. In other words, the integration time step At should be much larger than the Lagrangian time scale of the turbulence. 

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