Abstract
When a container of water is vibrated, its response can be described in terms of large-scale standing waves—the eigenmodes of the system. The belief that enclosed continuous media always possess eigenmodes is deeply rooted. Internal gravity waves in uniformly stratified fluids, however, present a counterexample. Such waves propagate at a fixed angle to the vertical that is determined solely by the forcing frequency, and a sloping side wall of the container will therefore act as a lens, resulting in ray convergence or divergence. An important consequence of this geometric focusing is the prediction1 that, following multiple reflections, these waves will evolve onto specific paths—or attractors—whose locations are determined only by the frequency. Here we report the results of laboratory experiments that confirm that internal-wave attractors, rather than eigenmodes, determine the response of a confined, stably stratified fluid over a broad range of vibration frequencies. The existence of such attractors could be important for mixing processes in ocean basins and lakes, and may be useful for analysing oscillations of the Earth's liquid core and the stability of spinning, fluid-filled spacecraft.
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Acknowledgements
We thank G. van der Plas and S. Dalziel for help with post-processing of the data, and C. Staquet and B. Voisin for suggestions.
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Maas, L., Benielli, D., Sommeria, J. et al. Observation of an internal wave attractor in a confined, stably stratified fluid. Nature 388, 557–561 (1997). https://doi.org/10.1038/41509
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DOI: https://doi.org/10.1038/41509
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