Measurements of the isotropic transport equation for the mean energy dissipation rate in decaying grid turbulence indicate that the destruction term increases linearly with the Taylor microscale Reynolds number R-lambda whereas the skewness of the longitudinal velocity derivative is approximately independent of R-lambda. As a consequence, self-preservation based on the Taylor microscale lambda is strictly valid when R-lambda is constant during decay. The high wavenumber part of the vorticity spectrum scales approximately on the Kolmogorov microscale, thus excluding the possibility of a lambda-based similarity for all scales of motion except when R-lambda is constant.
Antonia, R. A., Zhou, T., Danaila, L., & Anselmet, F. (2002). Scaling of the mean energy dissipation rate equation in grid turbulence. Journal of Turbulence, 3, N/A. https://doi.org/10.1088/1468-5248/3/1/034