Experimental nonlinear waves along a torus of fluid

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• Eric Falcon (Université Paris Cité)
• Friday 21 October 2022, 11:30-12:00
• Seminar Room 1, Newton Institute.

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HY2W04 - Statistical mechanics, integrability and dispersive hydrodynamics

In this talk, I will show that a periodic, curved and one-dimensional system leads to significant differences compared to classical straight geometries for wave propagation. By means of an original technique, we have experimentally succeeded in forming a stable torus of liquid [1,2]. I will first show the dispersion relation of linear azimuthal waves propagating along the torus, leading to a rich spectral signature in the form of several propagation modes [1]. Then, I will focus on nonlinear waves obtained for a strong enough forcing. In particular, I will highlight the observation of subsonic elevation solitons which are due to the periodicity of the system. These effects are explained by applying periodic boundary conditions to a Korteweg-de Vries equation yielding also a nonlinear dependence of the soliton velocity on its amplitude. The periodic inverse scattering transform is also implemented and experimentally validated in this geometry. Finally, I will discuss the presence of a three-wave resonant interaction in this system resulting from the interaction between two propagation modes [3]. Our works thus paves the way to observe other nonlinear phenomena such as wave turbulence, soliton gas, or recurrence in this specific geometry.   We thank the support of the French National Research Agency (ANR SoGood No. ANR -21-CE30-0061-04) and the Simons Foundation MPS No. 651463 (USA).   [1] F. Novkoski, E. Falcon and C.-T. Pham, Physical Review Letters 127, 144504 (2021) Experimental Dispersion Relation of Surface Waves Along a Torus of Fluid [2] F. Novkoski, C.-T. Pham, E. Falcon, Europhysics Letters (EPL) 139, 53003 (2022) Experimental observation of periodic Korteweg-de Vries solitons along a torus of fluid [3] F. Novkoski, C.-T. Pham, E. Falcon in preparation (2022) Experimental observation of triadic resonant instability between sloshing and gravity-capillary surface waves   Co-authors: F. Novkoski (Univ. Paris Cité), C.-T. Pham (Univ. Paris-Saclay)

This talk is part of the Isaac Newton Institute Seminar Series series.

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