arXiv subjects

Grégoire Le Lay

Publications and source records attributed to Grégoire Le Lay.

5 recordsLinked to original sources

arXiv2026

Viscous Bending Mitigates the Spontaneous Meandering of Rivulets in Hele-Shaw Cells

We investigate the spontaneous meandering of slender rivulets in Hele-Shaw cells and identify the physical mechanism that selects the most unstable wavenumber, a quantity that has remained elusive even since the identification of the instability threshold [Daerr et al., Phys. Rev. Lett. 106, 184501 (2011)]. Earlier criteria did not distinguish between wavelengths and thus predicted an undiscriminated amplification of arbitrarily short perturbations. By incorporating viscous bending into the depth-averaged Navier-Stokes equations, we show that this effect is responsible for the selection of a fastest-growing mode, answering a question that has remained open for 15 years. We answer the open question of whether the meandering instability is absolute or convective. Our analysis also provides a simpler alternative derivation of the instability criterion, based on a low-viscosity assumption, and finally it yields a new physical interpretation of the mechanism: the destabilization arises directly from friction effects, instead of being caused by inertial forces. Together, these results complete the linear-stability picture of rivulet meandering in confined geometries, and establish viscous bending as a key parameter governing wavelength selection. They lay the groundwork for future exploration of the nonlinear features of the spontaneous meandering instability.

physics.flu-dyn↗

arXiv2026

Dancing rivulets in an air-filled Hele-Shaw cell

We study the behaviour of a thin fluid filament (a rivulet) flowing in an air-filled Hele-Shaw cell. Transverse and longitudinal deformations can propagate on this rivulet, although both are linearly attenuated in the parameter range we use. On this seemingly simple system, we impose an external acoustic forcing, homogeneous in space and harmonic in time. When the forcing amplitude exceeds a given threshold, the rivulet responds nonlinearly, adopting a peculiar pattern. We investigate the dance of the rivulet both experimentally using spatiotemporal measurements, and theoretically using a model based on depth-averaged Navier-Stokes equations. The instability is due to a three-wave resonant interaction between waves along the rivulet, the resonance condition fixing the pattern wavelength. Although the forcing is additive, the amplification of transverse and longitudinal waves is effectively parametric, being mediated by the linear response of the system to the homogeneous forcing. Our model successfully explains the mode selection and phase-locking between the waves, it notably allows us to predict the frequency dependence of the instability threshold. The dominant spatiotemporal features of the generated pattern are understood through a multiple-scale analysis.

physics.flu-dyn↗

arXiv2025

Phase-Locking Parametric Instability Coupling Longitudinal and Transverse Waves on Rivulets in a Hele-Shaw Cell

We report an instability exhibited by a fluid system when coupling two distinct types of waves, both linearly damped. While none of them is unstable on its own, they amplify one another, resulting in a previously unreported convective instability. An external excitation is used to induce a parametric cross-coupling between longitudinal and transverse deformations of a liquid bridge between two vertical glass plates. Coherent amplification results in waves satisfying a synchronization condition, which selects a precise wavelength. We derive a model for this instability using depth-averaged Navier-Stokes equations, showing the physical origin of the coamplification, and confirm its relevance experimentally. Our findings open new perspectives in the study of parametrically controlled pattern formation, and invites the search for analogous parametric cross-coupling instabilities in other systems exhibiting distinct wave types, from plasma to elastic media.

cond-mat.soft↗

arXiv2024

Magnetic levitation in the field of a rotating dipole

It is well known that two permanent magnets of fixed orientation will either always repel or attract one another regardless of the distance between them. However, if one magnet is rotated at sufficient speed, a stable position at a given equilibrium distance can exist for a second free magnet. The equilibrium is produced by magnetic forces alone, which are strong enough to maintain a levitating state under gravity. We show that a stable levitation can be obtained when the rotating magnet is tilted from the rotation axis, with no offset in its position. In this regime, the levitating magnet remains centered and its spinning rate remains negligible, while its magnetic moment precesses in synchronization with the driving magnet. We provide a physical explanation of the levitation through a model relying on static dipolar interactions between the two magnets and present experimental results which validate the proposed theory.

physics.class-ph↗

arXiv2020

The life and fate of a bubble in a geometrically-perturbed Hele-Shaw channel

Motivated by the desire to understand complex transient behaviour in fluid flows, we study the dynamics of an air bubble driven by the steady motion of a suspending viscous fluid within a Hele-Shaw channel with a centred depth perturbation. Using both experiments and numerical simulations of a depth-averaged model, we investigate the evolution of an initially centred bubble of prescribed volume as a function of flow rate and initial shape. The experiments exhibit a rich variety of organised transient dynamics, involving bubble break up as well as aggregation and coalescence of interacting neighbouring bubbles. The long-term outcome is either a single bubble or multiple separating bubbles, positioned along the channel in order of increasing velocity. Up to moderate flow rates, the life and fate of the bubble are reproducible and can be categorised by a small number of characteristic behaviours that occur in simply-connected regions of the parameter plane. Increasing the flow rate leads to less reproducible time evolutions with increasing sensitivity to initial conditions and perturbations in the channel. Time-dependent numerical simulations that allow for break up and coalescence are found to reproduce most of the dynamical behaviour observed experimentally including enhanced sensitivity at high flow rate. An unusual feature of this system is that the set of steady and periodic solutions can change during temporal evolution because both the number of bubbles and their size distribution evolve due to break up and coalescence events. Calculation of stable and unstable solutions in the single- and two-bubble cases reveals that the transient dynamics are orchestrated by weakly-unstable solutions of the system termed edge states that can appear and disappear as the number of bubbles changes.

physics.flu-dyn↗