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Internal solitary waves in a two-fluid system with a free surface

Published online by Cambridge University Press:  08 September 2016

Tsubasa Kodaira ,
Takuji Waseda ,
Motoyasu Miyata  and
Wooyoung Choi
Tsubasa Kodaira
Affiliation:
Department of Oceanography, Dalhousie University, 1355 Oxford Street, Halifax, NS, Canada
Takuji Waseda
Affiliation:
Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8563, Japan
Motoyasu Miyata
Affiliation:
Faculty of Liberal Arts, The Open University of Japan, Chiba 261-8586, Japan
Wooyoung Choi*
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102-1982, USA
*
†Email address for correspondence: wychoi@njit.edu
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Abstract

Internal solitary waves in a system of two fluids, silicone oil and water, bounded above by a free surface are studied both experimentally and theoretically. By adjusting an extra volume of silicone oil released from a reservoir, a wide range of amplitude waves are generated in a wave tank. Wave profiles as well as wave speeds are measured using multiple wave probes and are then compared with both the weakly nonlinear Korteweg–de Vries (KdV) models and the strongly nonlinear Miyata–Choi–Camassa (MCC) models. As the density difference between the two fluids in the experiment is relatively small (approximately 14 %), but non-negligible, special attention is paid to the effect of the boundary condition at the top surface. The nonlinear models valid for rigid-lid (RL) and free-surface (FS) boundary conditions are considered separately. It is found that the solitary wave of the FS model for a given amplitude is consistently narrower than that of the RL model and it propagates at a slightly lower speed. Due to strong nonlinearity in the internal-wave motion, the weakly nonlinear KdV models fail to describe the measured internal solitary wave profiles of intermediate and large wave amplitudes. The strongly nonlinear MCC-FS model agrees better with the measurements than the MCC-RL model, which indicates that the free-surface boundary condition at the top surface is crucial in describing the internal solitary waves in the experiment correctly. Leaving the top surface free in the experiment allows us to observe small and relatively short wave packets on the top surface, particularly when the amplitude of the internal solitary wave is large. Once excited, the wave packet is located above the front half of the internal solitary wave and propagates with a speed close to that of the internal solitary wave underneath. A simple resonance mechanism between short surface waves and long internal waves without and with nonlinear effects is examined to estimate the characteristic wavelength of modulated short surface waves, which is found to be in good agreement with the observed wavelength when nonlinearity is taken into account. Using ray theory, the evolution of short surface waves in the presence of a background current induced by an internal solitary wave is also investigated to examine the location of the modulated surface wave packet.

JFM classification

Geophysical and Geological Flows: Internal waves Waves/Free-surface Flows: Solitary waves Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 804 , 10 October 2016 , pp. 201 - 223
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Copyright
© 2016 Cambridge University Press 

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Footnotes

‡

Deceased 5 August 2013.

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