Vortical structures generated by a localized forcing

Korabel, Vasily N. (2005) Vortical structures generated by a localized forcing. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

Vortex structures (monopoles, dipoles, quadrupoles) as well as more complex structures (vortex streets) are fundamental elements of geophysical turbulence. Because they can effectively transport momentum, heat, salt and biochemical products, they play an essential role in ocean dynamics. Organized vortex structures are a well-known feature of quasi-two-dimensional flows where motion in one direction is suppressed due to one of the following physical mechanisms: background rotation of the system, density stratification or geometrical restrictions such as for the flows in thin layers or soap films. -- Vortex dipoles are formed in a viscous fluid when a force is applied locally to some volume of fluid. If the force acts impulsively, a translating vortex dipole is generated. If the force starts at t = 0 and then acts continuously a starting jet with a dipole at its front is generated. Solutions for unsteady viscous flows generated by the action of continuous or impulsive localized forces are obtained in Oseen approximation. The solutions are compared with direct numerical simulations of vortex dipoles as well as with laboratory experiments. The comparison shows good quantitative agreement in both cases. -- A physical problem where the localized force acting continuously on fluid is placed in a uniform stream is equivalent to a problem of a fixed body in a uniform stream, while the couple of forces acting in opposite direction are equivalent to the problem of self-propelled body moving at constant velocity through a fluid. The solutions for the two-dimensional far-field wake are obtained in both cases. At a certain Reynolds number, wakes become unstable and form vortex streets. New series of high-resolution 2D numerical simulations is performed to study the characteristics of the wakes including the shedding frequency for a wide range of control parameters such as translational velocity, magnitude and spatial extent of a localized force. The results of numerical experiments of unsteady wake flow show existence of a great variety of flow regimes and are in good qualitative agreement with laboratory experiments.

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