Two-dimensional nonlinear dynamics of four driven vortices

Journal Article · Tue Mar 01 04:00:00 EST 1994 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.49.2062· OSTI ID:5213852

Guzdar, P N; Finn, J M; Rogalsky, A V; Drake, J F ^[1]

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1. Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States)

The interaction of four alternately driven counterrotating vortices in a two-dimensional box, with inpenetrable free-slip boundary conditions in the [ital x] direction and periodic boundary conditions in the [ital y] direction, has been studied numerically. For viscosity above a critical value the nonlinear state consists of four alternately counterrotating vortices. For a lower value of the viscosity the system evolves to a nonlinear steady state consisting of four vortices and shear flow generated by the peeling instability'' [Drake [ital et] [ital al]., Phys. Fluids B 4, 447 (1992)]. For a still lower viscosity the steady-state nonlinear state undergoes a Hopf bifurcation. The periodic state is caused by a secondary instability associated with vortex pairing. However, the vorticity of the shear flow, though periodic, has a definite sign. With a further decrease in the viscosity, a global bifurcation gives rise to a periodic state during which the vorticity of the shear flow changes sign. At even lower viscosity, there is a transition to a steady state, involving dominantly shear flow and a two-vortex state. Finally, this state undergoes a bifurcation to a temporally chaotic state, with the further decrease of viscosity. The results are compared to some recent experiments in fluids with driven vortices [P. Tabeling [ital et] [ital al]., J. Fluid Mech. 215, 511 (1990)].

• OSTI ID: 5213852
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 49:3; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
COMPUTERIZED SIMULATION
CONVECTION
ENERGY TRANSFER
FORCED CONVECTION
HEAT TRANSFER
INSTABILITY
MASS TRANSFER
NONLINEAR PROBLEMS
SIMULATION
STEADY-STATE CONDITIONS
TWO-DIMENSIONAL CALCULATIONS
VORTICES