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Spatial structure of first and higher harmonic internal waves from a horizontally oscillating sphere

Published online by Cambridge University Press:  10 February 2011

E. V. ERMANYUK ,
J.-B. FLÓR  and
B. VOISIN
E. V. ERMANYUK*
Affiliation:
Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Science, Prospekt Lavrentyev 15, Novosibirsk 630090, Russia
J.-B. FLÓR
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, CNRS – Université de Grenoble, BP 53, 38041 Grenoble, France
B. VOISIN
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, CNRS – Université de Grenoble, BP 53, 38041 Grenoble, France
*
†Email address for correspondence: ermanyuk@hydro.nsc.ru
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Abstract

An experimental study is presented on the spatial structure of the internal wave field emitted by a horizontally oscillating sphere in a uniformly stratified fluid. The limits of linear theory and the nonlinear features of the waves are considered as functions of oscillation amplitude. Fourier decomposition is applied to separate first harmonic waves at the fundamental frequency and higher harmonic waves at multiples of this frequency. For low oscillation amplitude, of 10% of the sphere radius, only the first harmonic is significant and the agreement between linear theory and experiment is excellent. As the oscillation amplitude increases up to 30% of the radius, the first harmonic becomes slightly smaller than its linear theoretical prediction and the second and third harmonics become detectable. Two distinct cases emerge depending on the ratio Ω between the oscillation frequency and the buoyancy frequency. When Ω > 0.5, the second harmonic is evanescent and localized near the sphere in the plane through its centre perpendicular to the direction of oscillation, while the third harmonic is negligible. When Ω < 0.5, the second harmonic is propagative and appears to have an amplitude that exceeds the amplitude of the first harmonic, while the third harmonic is evanescent and localized near the sphere on either side of the plane through its centre perpendicular to the direction of oscillation. Moreover, the propagative first and second harmonics have radically different horizontal radiation patterns and are of dipole and quadrupole types, respectively.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 671 , 25 March 2011 , pp. 364 - 383
Copyright
Copyright © Cambridge University Press 2011

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