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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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References

REFERENCES

Abad, M. & Souhar, M. 2004 Effects of the history force on a noscillating rigid sphere at low Reynolds number. Exp. Fluids 36, 775–782.CrossRefGoogle Scholar
Ackerson, B.J. 2020 Cartesian diver plus. Phys. Teach. 58 (2), 84–85.CrossRefGoogle Scholar
Basset, A.B. 1888 Treatise of Hydrodynamics, Vol. 2. Deighton Bell.Google Scholar
Biró, I., Gábor Szabó, K., Gyüre, B.B., Jánosi, I.M. & Tél, T. 2008 Power-law decaying oscillations of neutrally buoyant spheres in continuously stratified fluid. Phys. Fluids 20 (5), 051705.CrossRefGoogle Scholar
Boussinesq, J. 1885 Sur la résistance qu'oppose un fluide indéfini au repos sans pesanteur au mouvement varié d'une sphère solide qu'il mouille sur toute sa surface quand les vitesses restent bien continues et assez faibles pour que leurs carrés et produits soient négligeables. C. R. Acad. Sci. Paris 100, 935–937.Google Scholar
Bush, J.W.M. 2015 Pilot-wave hydrodynamics. Annu. Rev. Fluid Mech. 47, 269–292.CrossRefGoogle Scholar
Cairns, J., Munk, W. & Winant, C. 1979 On the dynamics of neutrally buoyant capsules; an experimental drop in Lake Tahoe. Deep-Sea Res. A 26 (4), 369–381.CrossRefGoogle Scholar
Candelier, F., Mehaddi, R. & Vauquelin, O. 2014 The history force on a small particle in a linearly stratified fluid. J. Fluid Mech. 749, 184–200.CrossRefGoogle Scholar
Chashechkin, Y.D. & Prikhod'ko, Y.V. 2007 Regular and singular flow components for stimulated and free oscillations of a sphere in continuously stratified liquid. Dokl. Phys. 52 (5), 261–265.CrossRefGoogle Scholar
Couder, Y., Protière, S., Fort, E. & Boudaoud, A. 2005 Dynamical phenomena: walking and orbiting droplets. Nature 437, 208.CrossRefGoogle ScholarPubMed
Deng, J. & Caulfield, C.P. 2018 Horizontal locomotion of a vertically flapping oblate spheroid. J. Fluid Mech. 840, 688–708.CrossRefGoogle Scholar
Deng, J., Xue, J., Mao, X. & Caulfield, C.P. 2017 Coherent structures in interacting vortex rings. Phys. Rev. Fluids 2, 022701.CrossRefGoogle Scholar
Desaguliers, J.T. 1744 A Course of Experimental Philosophy, Vol. 2. W. Innys.Google Scholar
Ermanyuk, E.V. 2000 The use of impulse response functions for evaluation of added mass and damping coefficient of a circular cylinder oscillating in linearly stratified fluid. Exp. Fluids 28, 152–159.CrossRefGoogle Scholar
Ermanyuk, E.V. & Gavrilov, N. 2002 Force on a body in a continuously stratified fluid. Part 1. Circular cylinder. J. Fluid Mech. 451, 421–443.CrossRefGoogle Scholar
Ermanyuk, E.V. & Gavrilov, N. 2003 Force on a body in a continuously stratified fluid. Part 2. Sphere. J. Fluid Mech. 494, 33–50.CrossRefGoogle Scholar
Flynn, M.R., Onu, K. & Sutherland, B.R. 2003 Internal wave excitation by a vertically oscillating sphere. J. Fluid Mech. 494, 65–93.CrossRefGoogle Scholar
Güémez, J., Fiolhais, C. & Fiolhais, M. 2002 The cartesian diver and the fold catastrophe. Am. J. Phys. 70 (7), 710–714.CrossRefGoogle Scholar
Ho, I., Pucci, G., Oza, A.U. & Harris, D.M. 2021 Capillary surfers: wave-driven particles at a fluid interface. arXiv:2102.11694.CrossRefGoogle Scholar
Lai, R.Y.S. & Lee, C-M. 1981 Added mass of a spheroid oscillating in a linearly stratified fluid. Intl J. Engng Sci. 19, 1411–1420.CrossRefGoogle Scholar
Larsen, L.H. 1969 Oscillations of a neutrally buoyant sphere in a stratified fluid. Deep-Sea Res. 16 (6), 587–603.Google Scholar
Lin, Q., Boyer, D.L. & Fernando, H.J.S. 1994 Flows generated by the periodic horizontal oscillations of a sphere in a linearly stratified fluid. J. Fluid Mech. 263, 245–270.CrossRefGoogle Scholar
Magiotti, R. 1648 Renitenza Certissima dell'acqua alla Compressione. Moneta.Google Scholar
Magnaudet, J. & Mercier, M.J. 2020 Particles, drops, and bubbles moving across sharp interfaces and stratified layers. Annu. Rev. Fluid Mech. 52 (1), 61–91.CrossRefGoogle Scholar
Motygin, O.V. & Sturova, I.V. 2002 Wave motions in a two layer fluid driven by small oscillations of a cylinder intersecting the interface. Fluid Dyn. 37, 600–613.CrossRefGoogle Scholar
Mowbray, D.E. & Rarity, B.S.H. 1967 The internal wave pattern produced by a sphere moving vertically in a density stratified liquid. J. Fluid Mech. 30 (3), 489–495.CrossRefGoogle Scholar
Oster, G. 1965 Density gradients. Sci. Am. 213 (2), 70–79.CrossRefGoogle Scholar
Perrard, S., Labousse, M., Miskin, M., Fort, E. & Couder, Y. 2014 Self-organization into quantized eigenstates of a classical wave-driven particle. Nat. Commun. 5, 3219.CrossRefGoogle ScholarPubMed
Ramananarivo, S., Fang, F., Oza, A., Zhang, J. & Ristroph, L. 2016 Flow interactions lead to orderly formations of flapping wings in forward flight. Phys. Rev. Fluids 1, 071201.CrossRefGoogle Scholar
Stevenson, T.N. 1969 Axisymmetric internal waves generated by a travelling oscillating body. J. Fluid Mech. 35 (2), 219–224.CrossRefGoogle Scholar
Sungar, N., Tambasco, L.D., Pucci, G., Sáenz, P.J. & Bush, J.W.M. 2017 Hydrodynamic analog of particle trapping with the talbot effect. Phys. Rev. Fluids 2, 103602.CrossRefGoogle Scholar
Sutherland, B.R., Dalziel, S.B., Hughes, G.O. & Linden, P.F. 1999 Visualization and measurement of internal waves by ‘synthetic schlieren’. Part 1. Vertically oscillating cylinder. J. Fluid Mech. 390, 93–126.CrossRefGoogle Scholar
Tatsuno, M. & Bearman, P.W. 1990 A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low stokes numbers. J. Fluid Mech. 211, 157–182.CrossRefGoogle Scholar
Thielicke, W. & Stamhuis, E. 2014 PIVlab–towards user-friendly, affordable and accurate digital particle image velocimetry in matlab. J. Open. Res. Softw. 2 (1), e30.CrossRefGoogle Scholar
Vandenberghe, N., Zhang, J. & Childress, S. 2004 Symmetry breaking leads to forward flapping flight. J. Fluid Mech. 506, 147–155.CrossRefGoogle Scholar
Voisin, B. 2007 Added mass effects on internal wave generation. In 5th International Symposium on Environmental Hydraulics (ed. D.L. Boyer & O. Alexandrova), Compact disk of the Conference.Google Scholar
Winant, C.D. 1974 The descent of neutrally buoyant floats. Deep-Sea Res. 21 (6), 445–453.Google Scholar
Yick, K.Y., Torres, C.R., Peacock, T. & Stocker, R. 2009 Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers. J. Fluid Mech. 632, 49–68.CrossRefGoogle Scholar