Length scales microscales, velocity

Like the velocity spatial correlation function discussed in Section 2.1, the scalar spatial correlation function provides length-scale information about the underlying scalar field. For a homogeneous, isotropic scalar field, the spatial correlation function will depend only on r = r, i.e., R,p(r, t). The scalar integral scale L and the scalar Taylor microscale >-,p can then be computed based on the normalized scalar spatial correlation function fp, defined by... 

Earlier it was stated that the structure of a turbulent velocity field may be presented in terms of two parameters—the scale and the intensity of turbulence. The intensity was defined as the square root of the turbulent kinetic energy, which essentially gives a root-mean-square velocity fluctuation U. Three length scales were defined the integral scale /q, which characterizes the large eddies the Taylor microscale X, which is obtained from the rate of strain and the Kolmogorov microscale 1, which typifies the smallest dissipative eddies. These length scales and the intensity can be combined to form not one, but three turbulent Reynolds numbers Ri = U lo/v, Rx. = U X/v, and / k = U ly/v. From the relationship between Iq, X, and /k previously derived it is found that / ... 

Li and Olsen [14] were the first to perform such calculations. They calculated spatial correlations from ensembles of instantaneous velocities fields for flows in square microchannels and defined turbulent length scales in the streamwise and transverse directimis as the distance it takes normalized spatial correlations of streamwise velocity correlations to drop to 0.5. These correlation lengths in the streamwise and transverse directions were called Lxuu and Lyu , respectively. A comparison of these microchaimel correlation lengths normalized by microchannel width, W, and correlation lengths for macroscale chaimels [15] are shown in Table 1. Excellent agreement was observed between the microscale... 

On the other hand, the turbulent velocity fluctuations RMS v affect microscale processes, again variously estimated at 100 to 200 microns or less, on down to possibly the mixing length or possibly on down to the scale of molecular reaction. 

Given these two parameters three unique length, velocity, and time scales can be formed from dimensional analysis, i.e., the Kolmogorov microscales ... 

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