236
T. Dauxois et al.
∙ We propose a unique self-consistent experimental (and also numerical) set-up
that models a cascade of triadic interactions transferring energy from large-scale
monochromatic input to multi-scale internal wave motion.
∙ We provide explicit evidences of a wave turbulence framework for internal waves,
with a clear transition to a cascade of small-scale overturning events.
∙ We show how beyond the wave turbulence, this original set-up can induce mixing
that can be inferred from the calculation of the potential energy or directly by
measuring the stratification.
We take advantage of elaborate and recent signal processing tools (Hilbert transforms, time-frequency analysis, bicoherence, . . . ) to analyze experimental and numerical data. The observed model cascade employs wave attractors, whose significance
is realized for stratified and/or rotating fluids (i.e. for a very broad class of celestial
bodies) and for magnetized materials, attesting cross-disciplinary importance of the
present study for a broad scientific community.
Confinement of the fluid domain and focusing of wave energy at an attractor play
an important role in the cascade. However, these conditions are not very restrictive.
Under natural conditions internal waves can travel thousands of kilometers which
means that quite large bodies of water (for instance, seas) can be considered as confined domains. Also, since attractors can occur in laterally open domains [23], the
mechanism of the triadic wave cascade and the bulk mixing described in the present
paper is likely to occur in domains with multi-ridge topography as described in [3].
Physical systems supporting wave attractors are strong sources of natural wave
turbulence and provide an “internal wave mixing box” that can give useful insights,
in the laboratory, on abyssal mixing.
Acknowledgements This work was supported by the LABEX iMUST (ANR-10-LABX-0064) of
Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated
by the French National Research Agency (ANR). This work has achieved thanks to the resources
of PSMN from ENS de Lyon. E.V.E. gratefully acknowledges his appointment as a Marie Curie
incoming fellow at Laboratoire de physique ENS de Lyon. INS is gratefull for support Russian
Foundation for Basic Research 15-01-06363 and Russian Science Foundation 14-50-00095. Direct
numerical simulations were performed on supercomputer Lomonosov of Moscow State University.
We thank L. Maas, G. Pillet and H. Scolan for helpful discussions and D. Le Tourneau and M.
Moulin for technical assistance.
References
1. Morozov, E. G. (1995). Semidiurnial internal wave global field. Deep-Sea Research, I(42),
135–148.
2. Egbert, G. D., & Ray, R. D. (2000). Significant dissipation of tidal energy in the deep ocean
inferred from satellite altimeter data. Nature, 495, 775–778.
3. Polzin, K. L., Toole, J. M., Ledwell, J. R., & Schmitt, R. W. (1997). Spatial variability of
turbulent mixing in the Abyssal Ocean. Science, 276(5309), 93–96.
4. Nazarenko, S. V. (2011). Wave turbulence. Lecture Notes in Physics, Berlin: Springer.
5. Maas, L. R. M., Benielli, D., Sommeria, J., & Lam, F. P. A. (1997). Observations of an internal
wave attractor in a confined stably stratified fluid. Nature, 388, 557–561.
T. Dauxois et al.
∙ We propose a unique self-consistent experimental (and also numerical) set-up
that models a cascade of triadic interactions transferring energy from large-scale
monochromatic input to multi-scale internal wave motion.
∙ We provide explicit evidences of a wave turbulence framework for internal waves,
with a clear transition to a cascade of small-scale overturning events.
∙ We show how beyond the wave turbulence, this original set-up can induce mixing
that can be inferred from the calculation of the potential energy or directly by
measuring the stratification.
We take advantage of elaborate and recent signal processing tools (Hilbert transforms, time-frequency analysis, bicoherence, . . . ) to analyze experimental and numerical data. The observed model cascade employs wave attractors, whose significance
is realized for stratified and/or rotating fluids (i.e. for a very broad class of celestial
bodies) and for magnetized materials, attesting cross-disciplinary importance of the
present study for a broad scientific community.
Confinement of the fluid domain and focusing of wave energy at an attractor play
an important role in the cascade. However, these conditions are not very restrictive.
Under natural conditions internal waves can travel thousands of kilometers which
means that quite large bodies of water (for instance, seas) can be considered as confined domains. Also, since attractors can occur in laterally open domains [23], the
mechanism of the triadic wave cascade and the bulk mixing described in the present
paper is likely to occur in domains with multi-ridge topography as described in [3].
Physical systems supporting wave attractors are strong sources of natural wave
turbulence and provide an “internal wave mixing box” that can give useful insights,
in the laboratory, on abyssal mixing.
Acknowledgements This work was supported by the LABEX iMUST (ANR-10-LABX-0064) of
Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated
by the French National Research Agency (ANR). This work has achieved thanks to the resources
of PSMN from ENS de Lyon. E.V.E. gratefully acknowledges his appointment as a Marie Curie
incoming fellow at Laboratoire de physique ENS de Lyon. INS is gratefull for support Russian
Foundation for Basic Research 15-01-06363 and Russian Science Foundation 14-50-00095. Direct
numerical simulations were performed on supercomputer Lomonosov of Moscow State University.
We thank L. Maas, G. Pillet and H. Scolan for helpful discussions and D. Le Tourneau and M.
Moulin for technical assistance.
References
1. Morozov, E. G. (1995). Semidiurnial internal wave global field. Deep-Sea Research, I(42),
135–148.
2. Egbert, G. D., & Ray, R. D. (2000). Significant dissipation of tidal energy in the deep ocean
inferred from satellite altimeter data. Nature, 495, 775–778.
3. Polzin, K. L., Toole, J. M., Ledwell, J. R., & Schmitt, R. W. (1997). Spatial variability of
turbulent mixing in the Abyssal Ocean. Science, 276(5309), 93–96.
4. Nazarenko, S. V. (2011). Wave turbulence. Lecture Notes in Physics, Berlin: Springer.
5. Maas, L. R. M., Benielli, D., Sommeria, J., & Lam, F. P. A. (1997). Observations of an internal
wave attractor in a confined stably stratified fluid. Nature, 388, 557–561.