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Measurement of the velocity field in parametrically excited solitary waves

Published online by Cambridge University Press:  14 August 2014

Leonardo Gordillo  and
Nicolás Mujica
Leonardo Gordillo*
Affiliation:
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile Laboratoire ‘Matière et Systèmes Complexes’ (MSC), UMR 7057 CNRS, Université Paris 7 Diderot, 75205 Paris CEDEX 13, France
Nicolás Mujica
Affiliation:
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
*
†Email address for correspondence: [email protected]
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Abstract

Parametrically excited solitary waves emerge as localized structures in high-aspect-ratio free surfaces subject to vertical vibrations. Herein, we provide the first experimental characterization of the hydrodynamics of these waves using particle image velocimetry. We show that the underlying velocity field of parametrically excited solitary waves is primarily composed of a subharmonic oscillatory component. Our results confirm the accuracy of Hamiltonian models with added dissipation in describing this field. Remarkably, our measurements also uncover the onset of a streaming velocity field which we show to be as important as other crucial nonlinear terms in the current theory. Using vorticity equations, we show that the streaming pattern arises from the coupling of the potential bulk flow with the oscillating boundary layers on the vertical walls. Numerical simulations provide good agreement between this model and experiments.

JFM classification

Instability: Parametric instability Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 754 , 10 September 2014 , pp. 590 - 604
Copyright
© 2014 Cambridge University Press 

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Gordillo supplementary movie

The movie shows the evolution through a whole cycle of the oscillatory velocity field of a parametrically excited solitary wave. The sequence displays the sloshing motion of the localized structure at the center of the trough viewed from the front (x-z plane). The laser sheet was placed at y s=1.07 cm (see axis orientation in figure 1). The white background indicates regions occupied by the fluid. The free-surface and bottom position as well as the velocity field (displayed in a coarse resolution) were obtained experimentally from images.

Download Gordillo supplementary movie(Video)
Video 844.9 KB

Gordillo supplementary movie

This sequence of images shows the emergence of a streaming pattern that becomes noticeable after the camera and laser pulses are synchronized with the oscillating structure. The phase of the parametrically excited solitary wave is here fixed at θs=π. The other parameters are the same than in Movie 1. The video also shows the streaming velocity field obtained by means of PIV. For other physical or processing parameters, please refer to the full article.

Download Gordillo supplementary movie(Video)
Video 6.9 MB

Gordillo supplementary movie

In this video, we provide a complementary view from the side (y-z plane) of the oscillating velocity field of a parametrically excited solitary wave. In this case, the structure is pinned to a lateral wall and the laser sheet was fixed at xs=9.23 cm. As in Movie 1, the white background displays the regions occupied by the fluid. The higher resolution allows to solve the advancing and receding meniscii at front and lateral walls of the trough.

Download Gordillo supplementary movie(Video)
Video 2.1 MB

Gordillo supplementary movie

As in Movie 2, we show a sequence of images where the streaming field becomes perceptible but now from a side view (y-z plane). Notice that near both meniscii, particle clusters are hard to follow due to the high shear within the region. We also depict the velocity field obtained by applying the PIV on a sequence of images. For more details, please refer to the full article.

Download Gordillo supplementary movie(Video)
Video 8.8 MB