Agreement between dissipation estimates

When two or more shear probes, in close proximity, are used to collect simultaneous data, the rate of dissipation derived from the simultaneous data will not agree exactly. Even for nearly flawless measurements, there will be disagreement for purely statistical reasons. Measuring a turbulent shear is sampling a statistical process. The sample variance will differ from the population variance and this difference will reduce with increasing length of data in the sample. The sampling uncertainty is distributed lognormally with a variance of

[math]\displaystyle{ \sigma^2_{\ln\varepsilon} = \frac{5.5}{1 + \left(\hat{L}_f/4\right)^{7/9}}\ \ , \hat{L}_f \equiv \hat{L} V_f^{3/4} = \frac{L}{L_K} V_f^{3/4} }[/math]