The universal nature of zero-crossing time and velocity scales in turbulent shear flows

Recent studies have shown that the turbulence production process in shear flows is not entirely random, but rather quasiperiodic in nature. Since the large eddies play a decisive role in these processes in all shear flows, it is instructive to see if they bear any common characteristics. The possible universal distributions¹ of time and velocity scales (T, u_p) in the low-frequency component of the turbulent signals–defined, respectivley, as the interval between successive zero crossings and the intervening absolute peak value of the longitudinal velocity signal–have been explored in a number of flows. These include the self-preserving regions of a turbulent boundary layer, plane jet, circular jet, and plane mixing layer and the initial mixing regions of a plane jet and circular jet. Both T and u_p distributions show universal trends: T distributions agree well with the log normal distribution except in their extreme excursions, whereas up distributions are intermediate between log normal and Gaussian distributions.