Publicación: DYNAMICS AND BIFURCATION OF PASSIVE TRACERS ADVECTED BY A RING OF POINT VORTICES ON A SPHERE
Fecha
2020
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JOURNAL OF MATHEMATICAL PHYSICS
Resumen
WE CONSIDER THE DYNAMICS OF A PASSIVE TRACER, ADVECTED BY THE PRESENCE OF A LATITUDINAL RING OF IDENTICAL POINT VORTICES. THE CORRESPONDING INSTANTANEOUS MOTION IS MODELED BY A ONE DEGREE OF FREEDOM HAMILTONIAN SYSTEM. SUCH A DYNAMICS PRESENTS A RICH VARIETY OF BEHAVIORS WITH RESPECT TO THE NUMBER OF VORTICES, N, AND THE RING?S CO-LATITUDE, ?O?OR, EQUIVALENTLY, ITS VERTICAL POSITION QO = COS??O. WE CARRY OUT A COMPLETE DESCRIPTION OF THE GLOBAL PHASE PORTRAIT FOR THE CASES N = 2, 3, 4 BY DETERMINING EQUILIBRIUM POINTS, THEIR STABILITY, AND BIFURCATIONS WITH RESPECT TO THE PARAMETER ?O, AND BY CHARACTERIZING THE SEPARATRIX SKELETON. MOREOVER, FOR N ? 5, WE PROVE THE EXISTENCE OF A VALUE OF BIFURCATION ?ON SUCH THAT WHEN ?O = ?ON (?O = ? ? ?ON, RESPECTIVELY) THE SOUTH (NORTH, RESPECTIVELY) POLE BECOMES A N-BIFURCATION POINT, I.E., A SYMMETRIC WEB OF N CENTERS AND N SADDLES BIFURCATES FROM THE CORRESPONDING POLE.
