Wave driven dynamics of a ludion in a stratified fluid

A Cartesian diver or ludion whose buoyancy varies in response to an external oscillating pressure, emits internal gravity waves when placed in a density stratified fluid. Recent experiments on oscillating ludions [1] have shown that wave-particle interactions lead to a symmetry breaking process, resulting in the ludion self-locomotion in the horizontal plane. The emitted waves can interact with distant walls and affect back the ludion motion. Such long-range interactions mediated by the traveling internal waves result in a complex dynamics and can possibly reproduce some aspects of wave-particle duality that usually characterizes quantum objects [2,3]. We will present here direct 2D numerical simulations of the dynamics of a circular ludion in stratified fluid. The code is based on a hybrid finite- volume lattice-Boltzmann method [4] coupled to an immersed boundary method [5]. We will describe the bifurcation to self-locomotion, the different forces (coming from a Doppler effect [6] but also a Casimir effect [7]) that act on the ludion and finally the attractors of the ludion trajectories and their subsequent quantizations.

[1] Le Gal et al., J. Fluid Mech. (2022), 931, A14. doi:10.1017/jfm.2021.931

[2] Couder and Fort, Phys. Rev. Lett. (2006), 97, 154101. doi:10.1103/PhysRevLett.97.154101

[3] Harris et al., Phys. Rev. E (2013), 88, 011001. doi:10.1103/PhysRevE.88.011001

[4] Gsell et al., Phys. Rev. E (2020), 101, 023309. doi:10.1103/PhysRevE.101.023309

[5] Gsell and Favier, J. Comp. Phys. (2021), 435, 110265. doi:10.1016/j.jcp.2021.110265

[6] Martischang et al., arXiv (2307.06642). https://arxiv.org/abs/2307.06642

[7] Casimir, Proc. Kon. Ned. Akad. Wet. (1948), 4, 261-263.