2019/10/24 by Sreethin Sreedharan K, K, Sreethin Sreedharan, Priyanka Shukla +1
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1910.12646
openalex publication_date 2019/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The restricted three-vortex problem is investigated with one of the point vortices fixed in the plane. The motion of the free vortex having zero circulation is explored from a rotating frame of reference within which the free vortex with non-zero circulation remains stationary. By using the basic dynamical system theory, it is shown that the vortex motion is always bounded and any configuration of vortices must go through at least one collinear state. The present analysis reveals that the inter-vortex distances in any non-fixed configuration of vortices are either periodic in time or aperiodic in time with vortices asymptotically converging to a collinear fixed configuration. The initial conditions required for different types of motion are explained in detail by exploiting the Hamiltonian structure of the problem.