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SUMMARY:Experimental nonlinear waves along a torus of fluid - Eric Falcon 
 (Université Paris Cité)
DTSTART:20221021T103000Z
DTEND:20221021T110000Z
UID:TALK182609@talks.cam.ac.uk
DESCRIPTION:In this talk\, I will show that a periodic\, curved and one-di
 mensional system leads to significant differences compared to classical st
 raight 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 p
 ropagating along the torus\, leading to a rich spectral signature in the f
 orm of several propagation modes [1]. Then\, I will focus on nonlinear wav
 es obtained for a strong enough forcing. In particular\, I will highlight 
 the observation of subsonic elevation solitons which are due to the period
 icity of the system. These effects are explained by applying periodic boun
 dary 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 t
 his geometry. Finally\, I will discuss the presence of a three-wave resona
 nt interaction in this system resulting from the interaction between two p
 ropagation modes [3]. Our works thus paves the way to observe other nonlin
 ear phenomena such as wave turbulence\, soliton gas\, or recurrence in thi
 s specific geometry.\n&nbsp\;\nWe thank the support of the French National
  Research Agency (ANR SoGood No. ANR-21-CE30-0061-04) and the Simons Found
 ation MPS No. 651463 (USA).\n&nbsp\;\n[1] F. Novkoski\, E. Falcon and C.-T
 . Pham\, Physical Review Letters 127\, 144504 (2021) Experimental Dispersi
 on Relation of Surface Waves Along a Torus of Fluid\n[2] F. Novkoski\, C.-
 T. Pham\, E. Falcon\, Europhysics Letters (EPL) 139\, 53003 (2022) Experim
 ental observation of periodic Korteweg-de Vries solitons along a torus of 
 fluid\n[3] F. Novkoski\, C.-T. Pham\, E. Falcon in preparation (2022) Expe
 rimental observation of triadic resonant instability between sloshing and 
 gravity-capillary surface waves\n&nbsp\;\nCo-authors: F. Novkoski (Univ. P
 aris Cit&eacute\;)\, C.-T. Pham (Univ. Paris-Saclay)
LOCATION:Seminar Room 1\, Newton Institute
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