Spiral structures in turbulent flow

Abstract

Spiral structures are natural candidates for the role of the ‘generic structures’ of turbulent flow, because they are the eventual outcome of Kelvin-Helmholtz instability, an all-pervasive phenomenon associated with nearly all shear flows at very high Reynolds number. Such structures were proposed by Lundgren (1982) in a model of the fine structure of turbulence in which axial stretching of rolled-up spiral vortices played an essential role. This model could be viewed as a natural development of Townsend’s (1951) model of the dissipative structures of turbulence in terms of a random distribution of vortex sheets and/or tubes, each such structure being subjected to the local rate of strain (assumed uniform and constant) associated with all other vortex structures (see Batchelor 1982, § is known that compressive strain (with two positive principle rates of strain) is more likely in isotropic turbulence than extensive strain, so that sheets form with higher probability than tubes. However these are immediately subject to the Kelvin-Helmholtz instability which may be impeded, but not entirely suppressed, by the stretching process.