Dynamics of the von Karman vortex street
In chapter one, a complete linear-stability analysis of the von Karman vortex trail is given. The general initial-value problem is considered and it is shown that, even for the special spacing ratio, arbitrarily small initial data can become arbitrarily large in finite time. In chapter two, the propagation of signals on the vortex trail is treated. A variation of Kelvin's method of stationary phase is used to obtain theoretical wave speeds, which are then compared with Tritton's measurements of the velocity of signals on the vortex trail behind a cylinder. In chapter three, the nonlinear dynamics of the vortex trail is considered. Under periodic perturbations (the most unstable being of period two), the von Karman trail is shown to support a rich variety of solutions, e.g., unbounded and also quasi-periodic solutions. In the physical plane these solutions are related to the merging of vortices. Finally, a comparison between the theoretical results and recent experimental and numerical work on the evolution of the vortex trail behind bluff objects is made.
- Research Organization:
- Brown Univ., Providence, RI (USA)
- OSTI ID:
- 7159013
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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