Monday, December 2nd 2024, 11h30, Room 454 A, Condorcet Building.

Two back-to-back presentations of 30 minutes each by two members of MSC.
Eléonore Duval (Laboratoire d’Acoustique de l’Université du Mans, Laboratoire de Physique de l’école normale supérieure, MSC)
Grégoire Le Lay (DSHE, MSC)

Eléonore Duval

Space-time parametric instabilities in a string

Abstract :
Periodic variations in the tension of a taut string induce parametric excitation of transverse motion when the forcing frequency is nearly twice the natural frequency of any transverse mode of the string. This phenomenon, first observed by Melde, is known as parametric resonance and occurs in harmonic oscillators driven at twice their natural frequency.

In this presentation, we reproduce Melde’s vibrating string experiment with a significant twist: we use a string made of a soft material, i.e. with a low Young’s modulus. Under longitudinal vibration, this allows spatial modulation alongside temporal modulation, leading to an atypical response distinct from the classic sub-harmonic instability. We observe the creation of pairs of sub-harmonic frequencies (e.g., f/3 and 2f/3, or f/4 and 3f/4, where f is the forcing frequency). A theoretical model based on multi-scale analysis is used to predict and describe the dynamics of these observations.

Grégoire Le Lay

Parametric co-amplification of waves on a rivulet

Abstract:
When injecting liquid in an air-filled vertical Hele-Shaw cell, it forms a rivulet in which the fluid flows downwards in between two meniscii forming a liquid bridge between the plates. The dynamics of the interface strongly depends on the fluid flow inside the rivulet, which itself is imposed by the geometry of the free surface. The resulting movement of the rivulet is the result of a competition between capillarity, inertia and viscous dissipation at the moving contact line. This makes the system exhibit complex behaviour even when using newtonian fluids that perfectly wets the glass.

While imposing an homogeneous, additive forcing to such a rivulet, we discovered that it induces a multiplicative coupling between longitudinal and transverse waves along the rivulet. These waves can parametrically amplify one another, even in regimes where both kind of perturbations are linearly damped. This results in a previously unreported instability that we describe and characterize, explaining the physical origin of the nontrivial coupling at play. We present a model for this instability and confirm its relevance using experimental evidence.

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