On the mixing properties of spherically symmetric helical coherent structures in turbulence

Abstract

A paradigmatic family of flow fields for localized, spherically symmetrical flow with maximal helicity—a model for helical coherent structures that are localized—is introduced. The Lagrangian mixing of the lowest order member of the family that is truly 3-D due to spiral arms is analyzed with linear theory, demonstrating that trajectory growth rates for the short, convective time scale are exponential and bounded by the extremal eigenvalues of the Jacobian. However, these rates show strong inhomogeneity and anisotropy associated with anomalous mixing. It was found for nonlinear Lagrangian mixing times that for this paradigm helical coherent structure, 22% of the trajectory pairs were bounded by the initial separation (non-mixing) and 78% mixed in various classifications of convective dispersal. All non-local studies of 10,000 Lagrangian trajectories could be categorized into five classes of growth (decay) patterns which exhibit the effects of localized, finite helicity/momentum associated with this class of velocity field. A scalar dispersion simulation confirms that the “patch” of fluid near the origin is slowly mixing—on the diffusive time scale—and is convected “unmixed” when the influence of molecular diffusion is still not pronounced (short times relative to Pe = 100 ).