PhD student on the topic Solitons and nonlinear waves in fluid black hole analogues (M/F)

European Commission; France; Sur place; EUR 20 000 - 40 000; Plein temps

Résumé du poste

Une opportunité de doctorat en acoustique est ouverte au Laboratoire de Mécanique et d'Acoustique. Ce projet de recherche se concentre sur l'étude des solitons et leur stabilité dans des systèmes fluides complexes, avec des applications potentielles aux analogies d trous noirs. Le candidat idéal aura un Master en physique ou ingénierie, avec des compétences en analyse numérique.

Qualifications

• Master requis en physique ou ingénierie.
• Compétences en analyse numérique et théorie des ondes nécessaires.
• Intérêt pour la recherche sur la dynamique des fluides est un plus.

Responsabilités

• Étudier la stabilité des flows connectés aux analogies d' trous noirs.
• Utiliser des approches analytiques et numériques.
• Conception d'obstacles pour contrôler les instabilités.

Connaissances

Analyse numérique

Théorie des ondes

Fluides et acoustique

Formation

Master en physique ou ingénierie

Description du poste

Organisation/Company CNRS Department Laboratoire de Mécanique et d'Acoustique Research Field Engineering » Materials engineering Physics » Acoustics Researcher Profile First Stage Researcher (R1) Country France Application Deadline 16 Jul 2025 - 23:59 (UTC) Type of Contract Temporary Job Status Full-time Hours Per Week 35 Offer Starting Date 1 Oct 2025 Is the job funded through the EU Research Framework Programme? Not funded by a EU programme Is the Job related to staff position within a Research Infrastructure? No

Offer Description

The PhD will take place in the Laboratory of Mechanics and Acoustics (LMA). It will be co-supervized by Bruno Lombard and Antonin Coutant.

Solitons are special types of waves that can spread without deformation over long distances. This particular behavior has its origin in a balance between nonlinear effects and dispersion. Solitons may appear in many different physical systems, but the best known context is probably that of water surface waves. In this case, in the shallow water limit, long wavelength perturbations obey the Korteweg-de Vries equation (KdV). Soliton solutions of the KdV equation are now well understood. However, the problem becomes much more delicate when you leave the ideal regime of the KdV equation. In particular, if the water is not stationary but flows on a submerged obstacle, many new phenomena arise, such as hydraulic jumps or undular jumps.

A subject apparently unrelated to water wave physics is that of artificial black holes. If the water flows faster than the velocity of the waves, they can be trapped in the fast-flow region, analogous to light waves being trapped in the gravitational field of a black hole. The location where the flow speed crosses the wave speed is analogous to the horizon of a black hole: the point of no return beyond which the light is trapped inside. Mathematically, the analogy is established by showing that linear waves propagate over a variable flow by obeying a wave equation in a curved space-time, as in general relativity. Although the effect of wave dispersion in these fluid analogues of black holes has been studied in depth, the effect of nonlinearities is still poorly understood.

Theoretically, a wide range of flow structure has been found, but experimentally, only a much smaller set is observed. This raises the question of the stability of these stationary solutions. In general, the mathematical demonstration of stability or instability in fluid mechanics is a very difficult problem. But in the context of the KdV equation, we have a panel of powerful tools at our disposal: linear analysis, Whitham modulation theory, inverse scattering, or direct numerical resolution. The aim of this thesis topic is to understand the stability of the different flows, with an analytical and numerical approach, and then to study the consequences for experiments of similar black holes. In a second stage, we will ask ourselves how to control instability in order to obtain flows more faithful to analogy. This can be done, for example, by the careful design of submerged obstacles, which eliminate unwanted instability.

The PhD is will be funded by the JCJC WaDiToMe ANR.