Instability of fluid vortices and generation of sheared flow

Abstract

A fluid equilibrium consisting of a periodic array of counter-rotating vortices is found to be unstable to the generation of one-dimensional sheared flow along the direction of periodicity. This instability is inviscid (exists for zero viscosity μ) or viscous (with growth rate γ∼μ3/4) depending on the elongation of the vortices. Nonlinearly, the instability goes through a vortex reconnection or ‘‘peeling’’ phase in which one of the vortices per period is destroyed, leading to a state with a chain of islands. Without a source, the flow evolves to pure one-dimensional shear flow, which decays because of viscosity on a much longer time scale. In the presence of a source driving the initial vortices, the flow evolves to an equilibrium having vortex flow plus shear flow and, for sufficiently high Reynolds number, having only one vortex per periodicity length rather than two, i.e., with islands.