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Postdoc: Wave kinetic description of anisotropic systems: recovery of isotropy and stability

Du 1 septembre 2024 au 31 août 2025

1 year, starting no later than September 2024
 Observatoire de la Côte d'Azur

Contacts : Giorgio Krstulovic krstulovic@oca.eu

This Postdoc project aims at understanding the propagation of weakly nonlinear waves in anisotropic media. The isotropy of the system will emerge either from external sources (forcing) or might be intrinsic to the waves due to the physics of the problem. The main questions to understand is how non-linear wave interactions helps to recover isotropy and the stability of certain out-of-equilibrium solutions. The scientific problem will be addressed using the wave turbulence theory and studying solutions of the associated wave kinetic equations. To complement theoretical predictions, the successful applicant will perform numerical simulations of the wave kinetic equation and the original dynamical equation describing the whole physics. This postdoc position is, therefore, theoretical with an important numerical part using existent numerical codes.

Waves are one of the most ubiquitous phenomena in nature. Wave systems are so diverse that they vary from the simplest everyday acoustic sound propagation to internal and inertial waves in the oceans and atmospheres, waves in quantum fluids, Alven waves in plasmas and many more.

In general, the equations of motion that describe wave systems are not linear, which makes wave dynamics rich, complex and interesting. Waves with different wavelengths interact and excite new waves at different scales, which will again interact with other waves and repeat the process at different scales. In this manner, non-linear wave systems can transfer energy along scales in a cascade process, leading what we know as wave turbulence. Such complex physics can, fortunately, be understood using the theory of weak wave turbulence. This theory is able to provide analytical predictions for the mean amplitude of waves at different scales, and explain and predict the energy cascade and the evolution of different statistical quantities. 

More specifically, the wave turbulence theory furnishes a wave kinetic equation (WKE), analogous to the Boltzmann equation, but where waves at different wave numbers play the role of particles. The rigorous derivation of the WKE, its applications and its predictions have triggered important multi-disciplinary research among mathematicians and theoretical and experimental physicists . 

Enormous progress has been achieved recently in understanding the wave turbulence theory for several systems, particularly when the system is isotropic. Unfortunately, nature is hardly isotropic, and the theory needs to be revised and adapted in such cases. For instance, oceans are typically stratified and exhibit an almost constant density gradient with deepness. For example, the figure shows the density fluctuations in a turbulent stratified fluid. Another example is the atmospheres of some planets, where the effect of planet rotation is important. Both systems admit waves propagating peculiarly, in which the dynamics are completely anisotropic.