On the fine-scale structure of turbulence

Abstract Recent experimental measurements of the energy spectrum of turbulence at very large wave-numbers have shown that the motion represented by these wave-number components is determined by the kinematic viscosity and the total turbulent energy dissipation, although the range of wave-numbers responsible for the bulk of the viscous dissipation is far from the condition of absolute equilibrium postulated in the theory of local similarity. To account for this anomaly and for the observed spatial inhomogeneity of the motion, it is suggested that the motion is essentially a random distribution of vortex sheets and lines, in which the vorticity distribution is effectively stationary in time, due to balance between the opposing effects of vorticity diffusion by molecular viscosity, and vorticity production and convection by the turbulent shear. The spectrum functions due to stationary vorticity distributions in two types of shear field, viz. plane shear and axial extension, have been computed and compared with experiment. A better fit is obtained for plane shear, which produces a vortex sheet, than for axial extension, which leads to a vortex line, and there is some experimental evidence that conditions suitable for the production of vortex sheets are more common than for production of vortex lines. Finally, the implications of the validity of this hypothesis are considered in relation to the applicability of the Heisenberg form for the turbulent energy transfer.