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Resonant-wave signature of an oscillating and translating disturbance in a two-layer density stratified fluid

Published online by Cambridge University Press:  06 April 2011

MOHAMMAD-REZA ALAM ,
YUMING LIU  and
DICK K. P. YUE
MOHAMMAD-REZA ALAM
Affiliation:
Department of Mechanical Engineering, Center for Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
YUMING LIU
Affiliation:
Department of Mechanical Engineering, Center for Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
DICK K. P. YUE*
Affiliation:
Department of Mechanical Engineering, Center for Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: yue@mit.edu
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Abstract

We investigate the nonlinear wave signature of a translating and oscillating disturbance under the influence of ambient waves in a two-layer fluid. The main interests are the generation and features of the far-field waves due to nonlinear wave resonances. We show, using perturbation theory, that free waves on the surface and/or interface can be produced by triad-resonant interactions, a mechanism not obtained in a homogeneous fluid. These occur among the radiated waves due to the disturbance motion (disturbance waves); and between the disturbance waves and free ocean waves (ambient waves). Such resonance-generated waves can appear upstream or downstream, and may propagate away from or towards the disturbance. In realistic situations where ambient waves and disturbance oscillations contain multiple frequencies, numerous resonant and near-resonant interactions at second and higher orders may occur, making the theoretical analysis of the problem intractable. For this purpose, we develop a direct simulation capability using a high-order spectral method, which provides independent validation of the theoretical predictions. Our investigations show that, under specific but realistic conditions, resonance interactions may lead to significant far-field short waves that are more amenable to remote sensing. If the characteristics of the disturbance are known, we illustrate how nonlinear wave resonances provide a mechanism for more precise estimation of ocean stratification properties using surface wave measurements. Finally we show that when a moving disturbance oscillates at multiple frequencies, ensuing multiple resonances may lead to energy spreading across a broader spectrum, resulting in the loss of information about the body motion.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 477 - 494
Copyright
Copyright © Cambridge University Press 2011

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