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Free-surface flow past oscillating singularities at resonant frequency

Published online by Cambridge University Press:  20 April 2006

G. Dagan  and
T. Miloh
G. Dagan
Affiliation:
School of Engineering, Tel-Aviv University, Israel
T. Miloh
Affiliation:
School of Engineering, Tel-Aviv University, Israel
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Abstract

This paper analyses the problem of a flow past an oscillating body moving with constant velocity, below and parallel to a free surface. Special attention is given to frequencies of oscillation in the neighbourhood of the critical frequency ωc= 0.25 g/U, where the classical linearized solution yields infinitely large wave amplitude. As a result both the lift and drag forces acting on the oscillating body at the resonant frequency are singular. It is demonstrated in the paper how this resonance is elimi- nated by considering higher-order free-surface effects, in particular the interaction between the first- and third-order terms. The resulting generalized solution yields finite wave amplitudes at the resonant frequency which are O(ε½) and O(εlogε) for 2 and 3 dimensions respectively. Here 6 is a measure of the singularity strength. It is also shown that inclusion of third-order terms causes a shift in the wavenumber and group velocity which eliminates the singularity in the lift and drag expressions at the resonant frequency. These results are illustrated by computing the lift and drag experienced by a submerged oscillating horizontal doublet in a uniform flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 120 , July 1982 , pp. 139 - 154
Copyright
© 1982 Cambridge University Press

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