We have recently described the resonance of the vertical oscillations of a ludion (or Descartes diver) in a stably stratified fluid together with the internal gravity waves it emits and its bifurcation to horizontal swimming [1]. In search of an associated pilot wave dynamics and a possible quantum hydrodynamic analogy similarly to Couder walkers [2,3], we analyze the motions of a ludion in cylindrical or rectangular containers (corrals) in the hope of revealing a possible interaction between its swimming and its own internal gravity wave field. According to the ratio of the forcing frequency to the Brunt-Väisälä frequency, the ludion can indeed explore the horizontal plane where it is constrained on average, following fixed points, periodic or chaotic attractors. Without drawing yet any definitive conclusions from this study, we are hopeful that a wave-driven dynamics exists also in our system and hence opens the way to a new hydrodynamic quantum analogy.

1- Le Gal P., Morales Castillo B., Hernandez-Zapata S., Ruiz Chavarria G. (2022). Swimming of a ludion in a stratified sea. J. Fluid Mech., 931, A14.

2- Couder Y., Protière S., Fort E., Boudaoud A. (2005). Walking and orbiting droplets. Nature 437, 208. Couder Y. and Fort E. (2006) Phys. Rev. lett. 97,154101.

3- Bush J.W.M. (2015).Pilot-wave hydrodynamics. Ann. Rev. Fluid Mech. 47, 269–292. Bush J.W.M. and Oza A. U. (2020). Hydrodynamic quantum analogs, Rep. Prog. Phys. 84, 1.