Numerical simulation of vortices with axial velocity deficits

Abstract

Axial velocity deficit is a source of instability in vortices that may otherwise be stable. Temporal large-eddy simulation is performed to study the response of vortices with axial velocity deficits to random and controlled disturbances at high Reynolds numbers. The q vortex [Batchelor, J. Fluid Mech. 20, 321 (1964)] is used as a model of such vortices. When the vortex is linearly unstable, the disturbances grow and result in the appearance of large-scale helical sheets of vorticity. Later, these large-scale helical structures break up into small-scale filaments. Associated with the formation of the large-scale structures is a redistribution of both angular and axial momentum between the core and the surroundings. The redistribution weakens the axial velocity deficit in the core while strengthens the rigid-body-like rotation of the core. The emerging mean velocity profiles drive the vortex core to a stable configuration. The vortex eventually returns to a laminar state, with an insignificant decay in the tangential velocity, but with a much weakened axial velocity deficit. A direct numerical simulation obtained at a lower Reynolds number confirms the above conclusions.