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Role of the basin boundary conditions in gravity wave turbulence

Published online by Cambridge University Press:  16 September 2015

L. Deike ,
B. Miquel ,
P. Gutiérrez ,
T. Jamin ,
B. Semin ,
M. Berhanu ,
E. Falcon  and
F. Bonnefoy
L. Deike
Affiliation:
Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 75013 Paris, France
B. Miquel
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Univ Paris 06, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France
P. Gutiérrez
Affiliation:
Laboratoire SPHYNX, SPEC, DSM, UMR 3680 CNRS, CEA-Saclay, 91191 Gif-sur-Yvette, France
T. Jamin
Affiliation:
Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 75013 Paris, France
B. Semin
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Univ Paris 06, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France
M. Berhanu
Affiliation:
Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 75013 Paris, France
E. Falcon*
Affiliation:
Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 75013 Paris, France
F. Bonnefoy
Affiliation:
Laboratoire LHEEA, UMR 6598 CNRS, Ecole Centrale de Nantes, 44321 Nantes, France
*
†Email address for correspondence: eric.falcon@univ-paris-diderot.fr
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Abstract

Gravity wave turbulence is investigated experimentally in a large wave basin in which irregular waves are generated unidirectionally. The roles of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. A quasi-one-dimensional field of nonlinear waves propagates towards the beach, where they are damped whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency power law with an exponent that increases continuously with the forcing amplitude up to a value close to $-4$. The physical mechanisms involved most likely differ with the boundary condition used, but cannot be easily discriminated with only temporal measurements. We also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation that highlights the important role of a large-scale Fourier mode. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov–Zakharov constant of the weak turbulence theory is evaluated and found to be compatible with a recently obtained theoretical value.

JFM classification

Turbulent Flows: Intermittency Waves/Free-surface Flows: Surface gravity waves Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , pp. 196 - 225
Copyright
© 2015 Cambridge University Press 

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Footnotes

‡

Present address: Scripps Institution of Oceanography, University of California San Diego, 9500 Gilman DriveLa Jolla, CA 92093, USA.

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