Alignment of Vorticity and Scalar Gradient with Strain Rate in Simulated Navier-Stokes Turbulence

摘要

The alignment between vorticity and eigenvectors of the strain-r ate tensor in numerical solutions of Navier-Stokes turbulence is studied. Solutions for isotropic flow and homogeneous shear flow from pseudospectral calculations using 128(cubed) grid points have been examined. The propensity for vorticity alignment with a positive intermediate strain is a consequence of angular momentum conservation, as shown by a restricted Euler model of the coupling between strain and vorticity. Probability distributions for intermediate strain, conditioned on total strain, change from a symmetric triangular form at small strain to an asymmetric one for large strain. The most probable value of the asymmetric distribution gives strains in the ratios of 3:1 - 4. The evolution of the distribution from a symmetric to an asymmetric form as the strain magnitude increases is essentially the same in both flows, indicating a generic structure of intense turbulence. The alignment between the gradient of a passive scalar and eigenvectors of the strain-rate tensor for Prandtl numbers of 0.1, 0.2, 0.4, and 1.0 is studied. There is an increased probability for the scalar gradient to align in the most compressive strain direction, and the average gradient is larger when it is pointing in that direction.