Collapse of the turbulent dissipative range on Kolmogorov scales

It is pointed out that the collapse of the turbulent dissipative range on Kolmogorov scales does not require either of the two major assumptions in Kolmogorov's [“The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk USSR 30, 299 (1941)] similarity hypothesis, i.e., Rλ, the Taylor microscale Reynolds number, is very large and local isotropy is satisfied. In particular, the Kolmogorov velocity and length scales are shown to be the appropriate normalization scales when the large-scale terms in the transport equations for the second-order statistics can be neglected. Evidence for this scaling is discussed critically on the basis of the available data. It is also shown that this scaling breaks down when Rλ becomes too small, typically below 20.