Structure function empirical constant

Short definition of Structure function empirical constant ([math]\displaystyle{ C_2 }[/math])
The empirical constant relating the longitudinal structure function [math]\displaystyle{ D_{LL} }[/math] to the dissipation rate ([math]\displaystyle{ \varepsilon }[/math])

This is the common definition for Structure function empirical constant, but other definitions maybe discussed within the wiki.

Dimensional analysis can be used to show that [math]\displaystyle{ D_{LL} }[/math] must satisfy the "two-thirds law", i.e., [math]\displaystyle{ D_{LL}(r,t) = C_2\varepsilon^{2/3}r^{2/3} }[/math] where [math]\displaystyle{ C_2 }[/math] is a universal constant.

The value of the constant is generally accepted to be [math]\displaystyle{ 2.1\pm 0.1 }[/math], based on the following studies:

1. Sauvageot (1992): Used Doppler radar measurements of turbulence in the atmosphere to obtain a value of [math]\displaystyle{ 2.0\pm 0.1 }[/math]
2. Saddoughi and Veeravalli (1994): Used measurements in a wind tunnel to obtain a value of [math]\displaystyle{ 2.1\pm 0.1 }[/math]
3. Sreenivasan (1995) : Compiled the results from experimental studies of both grid turbulence and shear flows to conclude that a value of 2.0 agreed best with the spectral inertial subrange equation