Emergence and evolution of tripole vortices from net-circulation initial conditions
The emergence of coherent vortical structures is a hallmark of the evolution of two-dimensional turbulence. Two fundamental processes of this evolution have been identified in vortex merging and vortex axisymmetrization. The question of whether axisymmetrization is a universal process has recently been answered in the negative. In the linear approximation, vortices indeed become axisymmetric, due to shear-enhanced diffusion. In the case of nonlinear interactions, other outcomes are possible; in the present work, we discuss a situation in which the flow reorganizes into a tripolar vortex. By performing an extensive numerical study, spanning the parameter space, we pursue the questions of what dictates if the flow will become axisymmetric or will develop into a quasisteady tripolar vortex, and what are the stages and the time scales of the flow evolution. The initial condition in this study consists of a Gaussian monopole with a quadrupolar perturbation. The amplitude of the perturbation and the Reynolds number determine the evolution. A tripole emerges for sufficiently large amplitude of the perturbation, and we seek to find a critical amplitude that varies with Reynolds number. We make several physical observations derived from visualizing and postprocessing numerous flow simulations: looking at the decay of the perturbation with respect to viscous or shear diffusion time scales; applying mixing theory; obtaining the first few azimuthal modes of the vorticity field; and describing the long-time evolution.
©2007 American Institute of Physics (Received 13 April 2006; accepted 16 November 2006; published online 3 January 2007) Computing time provided by the Laboratory for Advanced Computation in the Mathematical Sciences (LCMS) of the University of Bristol (http://lacms.maths.bris.ac.uk/). Thanks to the PETSc team for prompt and always helpful tech support. L.A.B. thanks S. Le Dizès and E. Villermaux for discussions and correspondence. L.A.B.'s travel was possible thanks to a Nuffield Foundation Award.