Date of Award
Master of Science in Oceanography
Melvin E. Stern
The interaction between a large isolated obstacle in a homogeneous rotating fluid and a small two-dimensional oscillatory current is considered, The problem is geophysically motivated by previous work concerning the dissipation of energy from forced flows by conversion into internal wave modes. It is hypothesized that if physical conditions permit rotational effects to dominate the flow, the interaction of the obstacle with the oscillatory current will result in the generation of trapped, resonant Rossby modes in the vicinity of the obstacle. Rossby waves are low frequency, depth-independent internal inertial oscillations, whose dynamics are governed by the conservation of potential vorticity in the rotating system.
Based on characteristics of flows dominated by rotation, an appropriate linear inviscid perturbation problem is formulated for the interaction. The physical behavior of the fluid permits the mathematical treatment to be two-dimensional. The mathematical problem is defined for a truncated cone obstacle, and application of the linearization and quasi-steady assumptions calls for the solution of a system of two linear partial differential equations.
Application of the proper boundary conditions leads to solutions for the flow patterns and to evaluation of the trapped Rossby wave eigenfrequencies. The flow is depth-independent. A Taylor column dominates the region above the obstacle, which is coupled to Rossby wave modes precessing around the obstacle. The Rossby wave eigenfrequencies depend on obstacle shape and on the rotation of the system.
Experimental work is designed to test the validity of the theory for the simplest Rossby wave mode. The construction of the rotating basin, and of the equipment which creates relative flow by oscillating the obstacle with respect to the fluid, is detailed.
Methods for achieving and measuring Rossby wave resonances experimentally are described, along with techniques for visualizing the flow. The resonance experiments employ the measurement of input current of the motor oscillating the obstacle to reflect the resonant response of the fluid. The equipment provides means for investigating the amplitude versus frequency spectrum of fluid response in finite steps. A suspension of fine aluminum particles in the fluid, whose orientations are sensitive to small shears in the interior, is used to visualize and to photograph the flow field.
Results of the resonance experiments constitute marginal proof of the linear inviscid theory. Resonances were observed in 36 of a total of 63 experiments. The positive results indicate agreement with theory to within 10 per cent. Negative results are attributable to inadequacies in the methods of frequency and current measurements. Some of the negative responses may also be due to exceeding the assumptions of the theory. Based on analysis of the results, improvements in the experimental method are suggested.
The flow visualization photographs confirmed the two-dimensional nature of the flow. The patterns also suggest experimental evidence for other specific f low characteristics derived in the theory.
Polgar, Tibor T., "Resonant Rossby Waves: Forced Flow in a Rotating Fluid Near an Obstacle" (1970). Open Access Master's Theses. Paper 2388.