Spatiotemporal evolution of asymmetries in turbulent trailing vortices

The outward propagation of asymmetries introduced to originally axisymmetric turbulent flows is investigated numerically and semi-analytically, where three-dimensional (3D) Batchelor vortices at high Reynolds numbers and with arbitrary swirl numbers are explored as test cases. It is well established that disturbances (asymmetries) added to a two-dimensional axisymmetric flow propagate radially outward, in order to re-axisymmetrize the vortex, but they cease to travel at a critical distance, known as the stagnation radius (Montgomery and Kallenbach, Q. J . R. Meteorol. Soc. , vol. 123, 1997, pp. 435–465). We utilize direct numerical simulations (DNS) and an inviscid model developed by linearizing the momentum and vorticity transport equations around the base (unperturbed) flow in helical coordinates to demonstrate that, in contrast with two-dimensional cases, 3D vortices enable the unbounded radial propagation of asymmetries. We further apply the Wenzel-Kramers-Brillouin (WKB) analysis to the linear model, which treats perturbations as compact wavepackets, to transform the partial differential equations of the linear model to a few ordinary differential equations. However it has been shown in the climate science community that the WKB approach ubiquitously predicts stagnation radii and heights for disturbances introduced to 3D cyclone-like vortices, here, we are able to identify a narrow range of parameters, for which the WKB analysis also supports an unrestrained, outward propagation for disturbances. Finally, the mechanisms governing the momentum transport at different times and locations, thereby promoting the outward advection of perturbations, are elucidated using the the linear rapid distortion theory (RDT) and numerical simulations. RDT is a powerful means for the study of vortex-turbulence interactions based on the separation of the flow into a steady, background field and a turbulent perturbation velocity field, which is initially homogeneous and isotropic. Since the DNS of the full Navier-Stokes equations rapidly stabilizes to a laminar, high-swirl-number configuration, the DNS of the linearized transport equations and the nonlinear governing equations without base-flow interactions are also carried out, in order to uncover the primary mechanisms for the growth and radial propagation of perturbations as well as the nonlinear processes causing growth arrest at fixed swirl numbers.