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STEADY MOTION AROUND A SYMMETRICAL OBSTACLE MOVING ALONG THE AXIS OF A ROTATING LIQUID

Robert R. LongJohns Hopkins University

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Abstract

An investigation by G. I. Taylor, of the steady motion of an obstacle along the axis of a rotating fluid, is extended in this paper. It is shown that Taylor's particular solution is just one of an infinity of functions comprising the general solution.

The theory is applied to motions in a rotating cylinder of fluid. A critical Rossby number is derived, below which the flow around the obstacle is wave-like. When the Rossby number is greater than the critical value, the flow consists only of a local perturbation that dies out rapidly on both sides of the obstacle. Various other critical numbers exist, below which additional modes of oscillation become dynamically possible.

An experiment was designed to test the theoretical results of this paper. An obstacle was moved along the axis of a long cylinder of rotating water. The resulting flow patterns were observed visually and photographically. The three-dimensional wave motions which occurred in the experiment were unquestionably the same as those in the theoretical solution.

Abstract

An investigation by G. I. Taylor, of the steady motion of an obstacle along the axis of a rotating fluid, is extended in this paper. It is shown that Taylor's particular solution is just one of an infinity of functions comprising the general solution.

The theory is applied to motions in a rotating cylinder of fluid. A critical Rossby number is derived, below which the flow around the obstacle is wave-like. When the Rossby number is greater than the critical value, the flow consists only of a local perturbation that dies out rapidly on both sides of the obstacle. Various other critical numbers exist, below which additional modes of oscillation become dynamically possible.

An experiment was designed to test the theoretical results of this paper. An obstacle was moved along the axis of a long cylinder of rotating water. The resulting flow patterns were observed visually and photographically. The three-dimensional wave motions which occurred in the experiment were unquestionably the same as those in the theoretical solution.

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