Structure function empirical constant
From Atomix
| Short definition of Structure function empirical constant ([math]\displaystyle{ C_2 }[/math]) |
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| 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:
- Sauvageot (1992)[1]: Used Doppler radar measurements of turbulence in the atmosphere to obtain a value of [math]\displaystyle{ 2.0\pm 0.1 }[/math]
- Saddoughi and Veeravalli (1994)[2]: Used measurements in a wind tunnel to obtain a value of [math]\displaystyle{ 2.1\pm 0.1 }[/math]
- Sreenivasan (1995) [3]: 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
Notes
- ↑ H. Sauvageot. 1992. Radar Meteorology. Artech House. doi:{{{doi}}}
- ↑ K. R. Sreenivasan. 1994. Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech.. doi:https://doi.org/10.1017/S0022112094001370
- ↑ K. R. Sreenivasan. 1995. On the universality of the Kolmogorov constant. Phys. Fluids. doi:10.1063/1.868656
