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Internal wave attractors examined using laboratory experiments and 3D numerical simulations

Published online by Cambridge University Press:  14 March 2016

C. Brouzet ,
I. N. Sibgatullin ,
H. Scolan ,
E. V. Ermanyuk  and
T. Dauxois
C. Brouzet
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
I. N. Sibgatullin
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France Institute of Mechanics and Department of Mechanics and Mathematics, Moscow State University, Moscow 119192, Russia Institute for System Programming, Russian Academy of Sciences, Moscow 109004, Russia
H. Scolan
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France Atmospheric, Oceanic and Planetary Physics, Department of Physics, University of Oxford, Parks Rd, Oxford OX1 3PU, UK
E. V. Ermanyuk
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, Novosibirsk 630090, Russia
T. Dauxois*
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
*
†Email address for correspondence: Thierry.dauxois@ens-lyon.fr
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Abstract

In the present paper, we combine numerical and experimental approaches to study the dynamics of stable and unstable internal wave attractors. The problem is considered in a classic trapezoidal set-up filled with a uniformly stratified fluid. Energy is injected into the system at global scale by the small-amplitude motion of a vertical wall. Wave motion in the test tank is measured with the help of conventional synthetic schlieren and particle image velocimetry techniques. The numerical set-up closely reproduces the experimental one in terms of geometry and the operational range of the Reynolds and Schmidt numbers. The spectral element method is used as a numerical tool to simulate the nonlinear dynamics of a viscous salt-stratified fluid. We show that the results of 3D calculations are in excellent qualitative and quantitative agreement with the experimental data, including the spatial and temporal parameters of the secondary waves produced by triadic resonance instability. Further, we explore experimentally and numerically the effect of lateral walls on secondary currents and spanwise distribution of velocity amplitudes in the wave beams. Finally, we test the assumption of a bidimensional flow and estimate the error made in synthetic schlieren measurements due to this assumption.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Instability: Instability Geophysical and Geological Flows: Internal waves
Type
Papers
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Journal of Fluid Mechanics , Volume 793 , 25 April 2016 , pp. 109 - 131
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© 2016 Cambridge University Press 

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