Two-point-vortex evolution in an oscillatory shear flow with rotation
1 V. I. Il'ichev Pacific Oceanological Institute - 43, Baltiyskaya Street, Vladivostok, 690041, Russia
2 Far Eastern Federal University - 8, Sukhanova Street, Vladivostok, 690950, Russia
Received: 10 August 2014
Accepted: 25 September 2014
We concern ourselves with the bounded and unbounded quasi-periodic motions of two point vortices of unequal strengths unfolding in a two-dimensional incompressible inviscid fluid under the influence of an oscillatory shear flow with rotation and study in detail their impact on passive tracer transport. We deal with all the possible vortex sign combinations, thus considering general vortex motion along and against the rotation direction. All the sets of the vortex signs are shown to induce qualitatively divergent transport patterns. In general, if the vortices due to self-influence tend to move in the direction coinciding with the exterior rotation, then the induced transport will be less effective compared to the vortex motion aligned mainly against the rotation. Regions enduring effective stretching, and consequently prone to intense mixing are identified by means of finite-time Lyapunov exponents (FTLE). Looking into the local structure of the tracer field in the vicinity of the vortices, we show that varying external fields has almost no impact on the dynamics, inducing almost indistinguishable FTLE patterns. However, we establish that slightly further from the vortices the transport dynamics for both cases, bounded and unbounded, differs significantly, tending to rather elongated invariant manifolds in the unbounded motion case, and to round ones, enveloping stagnation zones with dominantly regular dynamics, otherwise. An exponential growth of the standard deviation of a tracer patch is established in the unbounded motion regime.
PACS: 47.32.C- – Vortex dynamics / 47.32.cb – Vortex interactions / 47.10.Df – Hamiltonian formulations
© EPLA, 2014