Viscous evolution of point vortex equilibria: The collinear state

Abstract

When point vortex equilibria of the 2D Euler equations are used as initial conditions for the corre- sponding Navier-Stokes equations (viscous), typically an interesting dynamical process unfolds at short and intermediate time scales, before the long time single peaked, self-similar Oseen vortex state dom- inates. In this paper, we describe the viscous evolution of a collinear three vortex structure that cor- responds to an inviscid point vortex fixed equilibrium. Using a multi-Gaussian 'core-growth' type of model, we show that the system immediately begins to rotate unsteadily, a mechanism we attribute to a 'viscously induced' instability. We then examine in detail the qualitative and quantitative evolution of the system as it evolves toward the long-time asymptotic Lamb-Oseen state, showing the sequence of topological bifurcations that occur both in a fixed reference frame, and in an appropriately chosen rotating reference frame. The evolution of passive particles in this viscously evolving flow is shown and interpreted in relation to these evolving streamline patterns.

arXiv comment17 pages, 15 figures

References in corpus (5)

• Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R^2
• Global stability of vortex solutions of the two-dimensional Navier-Stokes equation
• Long-time asymptotics of the Navier-Stokes and vorticity equations on R^3
• Interaction of vortices in viscous planar flows
• Generalized Helmholtz-Kirchhoff model for two dimensional distributed vortex motion

Cited by in corpus (4)

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