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Resonantly excited regular and chaotic motions in a rectangular wave tank

Published online by Cambridge University Press:  26 April 2006

Wu-Ting Tsai ,
Dick K. P. Yue  and
Kenneth M. K. Yip
Wu-Ting Tsai
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Dick K. P. Yue
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Kenneth M. K. Yip
Affiliation:
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

We consider the resonant excitation of surface waves inside a rectangular wave tank of arbitrary water depth with a flap-type wavemaker on one side. Depending on the length and width of the tank relative to the sinusoidal forcing frequency of the wave paddle, three classes of resonant mechanisms can be identified. The first two are the well-known synchronous, resonantly forced longitudinal standing waves, and the subharmonic, parametrically excited transverse (cross) waves. These have been studied by a number of investigators, notably in deep water. We rederive the governing equations and show good comparisons with the experimental data of Lin & Howard (1960). The third class is new and involves the simultaneous resonance of the synchronous longitudinal and subharmonic cross-waves and their internal interactions. In this case, temporal chaotic motions are found for a broad range of parameter values and initial conditions. These are studied by local bifurcation and stability analyses, direct numerical simulations, estimations of the Lyapunov exponents and power spectra, and examination of Poincaré surfaces. To obtain a global criterion for widespread chaos, the method of resonance overlap (Chirikov 1979) is adopted and found to be remarkably effective.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 216 , July 1990 , pp. 343 - 380
Copyright
© 1990 Cambridge University Press

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