Correlations of vorticity and material line elements with strain in decaying turbulence

Abstract

Correlations of the vorticity and the passive material line element with strains in decaying turbulence are investigated. The mean principal rates of the strain and the growth rates of the vorticity and the material line element due to the nonlinear stretching are all found to be proportional to the square-root-mean enstrophy. The ratios of the principal rates are 4:1:−5. It is shown how these ratios help determining the values of free parameters in the phenomenological models of turbulence such as the Burgers vortex model proposed by Ashurst (private communication) and the Lundgren–Townsend vortex model by Pullin and Saffman [Phys. Fluids A 5, 126 (1993); 6, 3010 (1994)]. The mean growth rate of material line elements is slightly larger than the intermediate principal rate, but much less than the most positive one. Numerical results show that the material line element has nearly the same preferences in aligning with the principal directions of the strain corresponding to the mostly positive and the intermediate principal rates. The growth rate is approximately linearly correlated with the strain magnitude but almost uncorrelated with the vorticity magnitude. Conditional statistics and a simple model flow have been used to explain the above observations.