Missions

Wave turbulence offers the possibility of a deep understanding of physical systems composed of a set of random waves interacting in a non-linear fashion. The reason for this is, firstly, the possibility of analytically deriving a set of integro-differential equations for spectral cumulants - the so-called kinetic equations - which are free from the closure problem classically encountered in vortex turbulence. To obtain this natural asymptotic closure, the wave amplitude is used as a small parameter. Secondly, exact solutions can be found from the kinetic equations (Kolmogorov-Zakharov spectra). Thirdly, these exact solutions correspond to power-law spectra that can be compared with the data. The number of experiments, observations and diagnostics has grown considerably over the past two decades, and today, thanks also to direct numerical simulations, wave turbulence has become a cutting-edge field from which new fundamental questions have been raised. Applications range from gravity waves on the ocean surface, inertial waves in rotational hydrodynamics, Alfvén waves in plasma physics and gravitational waves in cosmology.

Most of the visible matter in the universe (99%) is in the plasma state, where waves and turbulence are omnipresent. At the largest scale, we find the Alfvén wave (A), which is the fundamental mode of incompressible magnetohydrodynamics (MHD). While this mode is preserved in compressible MHD, two other modes emerge: the fast (F) and slow (S) magneto-acoustic modes. In a magnetic plasma where thermal pressure is dominated by magnetic pressure, the F-wave can have a strong impact on turbulent dynamics. In 2023, a theory of F-wave turbulence was developed. The candidate will study this regime using direct numerical simulations. The aim will be to analyze how the weak regime can be reached and what is the relationship between A, F and S waves (Task 1). International collaboration is envisaged for this study. From a theoretical point of view, we will try to simplify the theory of F-wave turbulence as much as possible.

Modeling coronal heating in magnetic loops is a challenging problem due to the rich physics that includes solar atmospheric stratification, boundary conditions with photospheric convection, waves and turbulence. The candidate will study this question (Task 2) in the Hall MHD approximation in order to model heating events produced at scales below MHD. In these numerical simulations, waves will be used to propagate information along the uniform magnetic field, and dissipation will be studied in transverse planes. Small-scale events are expected to have different statistics from MHD heating events, as the turbulent dynamics are different. This work focuses mainly on numerical simulations, diagnostics and comparison with observations.

Wave turbulence is a regime found in many different systems, sometimes with strong similarities. From experience, it is always interesting to establish links between different problems. As part of a possible Task 3, and depending on the candidate's background, it may be possible to study related topics such as turbulence made of gravitational waves, plasma/odd waves in the interstellar medium and/or the link with the anomalous dissipation.

Activities

Activities include the following aspects:
- direct numerical simulation
- analysis of numerical data
- publication of scientific results

Skills

- PhD in plasma physics, astrophysics or fluid mechanics
- publications in peer-reviewed journals
- programming experience in Python and data analysis
- interest in theoretical physics
- good knowledge of spoken and written English

Work Context

The Plasma Physics Laboratory is a CNRS research unit (around 115 people), partly located on the École Polytechnique site south of Paris (accessible by metro and RER B), where the work will be carried out. It comprises three teams specializing in fusion plasmas, cold plasmas and space plasmas. The successful candidate will join the space plasmas team.

Constraints and risks

None.

Additional Information

None.