The PVC technique – a method to estimate the dissipation length scale in turbulent flows

A time-averaged length scale can be defined by a pair of successive turbulent-velocity derivatives, i.e. [dnu(x)/ dxn]′/ [dn+1u(x)/ dxn+1]′. The length scale associated with the zeroth- and the first-order derivatives, u′/u′x, is the Taylor microscale. In isotropic turbulence, this scale is the average length between zero crossings of the velocity signal. The average length between zero crossings of the first velocity derivative, i.e. u′x/u′xx, can be reliably obtained by using the peak-valley-counting (PVC) technique. We have found that the most probable scale, rather than the average, equals the wavelength at the peak of the dissipation spectrum in a plane mixing layer (Zohar & Ho 1996). In this study, we experimentally investigate the generality of applying the PVC technique to estimate the dissipation scale in three basic turbulent shear flows: a flat-plate boundary layer, a wake behind a two-dimensional cylinder and a plane mixing layer. We also analytically explore the quantitative relationships among this length scale and the Kolmogorov and Taylor microscales.