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Swimming of a ludion in a stratified sea

Published online by Cambridge University Press:  24 November 2021

P. Le Gal Open the ORCID record for P. Le Gal [Opens in a new window] ,
B. Castillo Morales ,
S. Hernandez-Zapata Open the ORCID record for S. Hernandez-Zapata [Opens in a new window]  and
G. Ruiz Chavarria Open the ORCID record for G. Ruiz Chavarria [Opens in a new window]
P. Le Gal*
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE, 49 rue F. Joliot Curie, 13384 Cédex 13 Marseille, France
B. Castillo Morales
Affiliation:
Departamento de Fìsica, Facultad de Ciencias, Universidad Nacional Autonoma de México, 04510 México
S. Hernandez-Zapata
Affiliation:
Departamento de Fìsica, Facultad de Ciencias, Universidad Nacional Autonoma de México, 04510 México
G. Ruiz Chavarria
Affiliation:
Departamento de Fìsica, Facultad de Ciencias, Universidad Nacional Autonoma de México, 04510 México
*
†Email address for correspondence: legal@irphe.univ-mrs.fr
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Abstract

We describe and model experimental results on the dynamics of a ‘ludion’ – a neutrally buoyant body – immersed in a layer of stably stratified salt water. By oscillating a piston inside a cylinder communicating with a narrow (in one of its horizontal dimensions) vessel containing the stably stratified layer of salt water, it is easy to periodically vary the hydrostatic pressure of the fluid. The ludion or Cartesian diver, initially positioned at its equilibrium height and free to move horizontally, can then oscillate vertically when forced by the pressure oscillations. Depending on the ratio of the forcing frequency to the Brunt–Väisälä frequency of the stratified fluid, the ludion can emit its own internal gravity waves that we measure by a classical particle image velocimetry technique. Our experimental results describe first the resonance of the vertical motions of the ludion when excited at different frequencies. A theoretical oscillator model is then derived taking into account added mass and added friction coefficients and its predictions are compared with the experimental data. Then, for the larger oscillation amplitudes, we observe and describe a bifurcation towards free horizontal motions. Although the internal gravity wave frequencies are affected by the Doppler shift induced by the horizontal displacement velocities, it seems that, contrary to surface waves associated with Couder walkers (Couder et al. Nature, vol. 437, 2005, p. 238) they are not the cause of the horizontal swimming. This does not, however, exclude possible interactions between the ludion and internal gravity waves and possible hydrodynamic quantum analogies to be explored in the future.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Nonlinear Dynamical Systems: Low-dimensional models Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , A14
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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