Boundedness of the velocity derivative skewness in various turbulent flows

The variation of S, the velocity derivative skewness, with the Taylor microscale Reynolds number Re_λ is examined for different turbulent flows by considering the locally isotropic form of the transport equation for the mean energy dissipation rate ⋷_iso. In each flow, the equation can be expressed in the form S + 2G/Re_λ = C/Re_λ, where G is a non-dimensional rate of destruction of ⋷_iso and C is a flow-dependent constant. Since 2G/Re_λ is found to be very nearly constant for Re_λ ≥ 70, S should approach a universal constant when Re_λ is sufficiently large, but the way this constant is approached is flow dependent. For example, the approach is slow in grid turbulence and rapid along the axis of a round jet. For all the flows considered, the approach is reasonably well supported by experimental and numerical data. The constancy of S at large Re_λ has obvious ramifications for small-scale turbulence research since it violates the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82-85) but is consistent with the original similarity hypothesis (Kolmogorov, Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299-303).