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Continual skipping on water

Published online by Cambridge University Press:  12 January 2011


I. J. HEWITT
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2 Canada
N. J. BALMFORTH
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2 Canada
J. N. McELWAINE
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
Corresponding
E-mail address:

Abstract

Experiments are conducted to study the planing and skipping of a rectangular paddle on the surface of a shallow stream. The paddle is allowed to move freely up and down by attaching it to a pivoted arm. A steady planing state, in which the lift force from the water balances the weight on the paddle, is found to be stable for small stream velocities but to become unstable above a certain threshold velocity which depends upon the weight and the angle of attack. Above this threshold, the paddle oscillates in the water and can take off into a continual bouncing, or skipping, motion, with a well-defined amplitude and frequency. The transition is sometimes bistable so that both a steady planing state and a regular skipping state are possible for the same experimental parameters. Shallow-water theory is used to construct simple models that explain the qualitative features of the planing and skipping states in the experiments. It is found that a simple parameterisation of the lift force on the paddle proportional to the depth of entry is not sufficient to explain the observations, and it is concluded that the rise of water ahead of the paddle, in particular the way this varies over time, is responsible for causing the planing state to become unstable and for enabling a continual skipping state.


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Copyright
Copyright © Cambridge University Press 2011

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