Postdoc: Wave Turbulence in geophysical systems

Waves are one of the most ubiquitous phenomena in Nature. Wave systems are so diverse that 
they permeate the physical world, from the simplest everyday acoustic sound propagation to 
internal and inertial waves in the oceans and atmospheres, waves in quantum fluids, Alfven 
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, nonlinear 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 stationary and in idealised conditions, with forcing and dissipation ranges well 
separated, wave phases randomised, wave amplitudes weak. 

Unfortunately, Nature is 
almost never in such idealised situations. Thus, one has to explore the robustness and validity of the wave turbulence approach beyond the 
idealised cases and, when this approach starts to fail, try to find extensions and corrections to the WKE descriptions. In addition to predicting 
the wave spectra, important practical questions arise on how these spectra affect the transport 
processes, for example mixing by the oceanic internal waves and momentum transfer through 
the surface by the water waves. 

This Postdoc project aims at understanding the propagation and interactions of weakly nonlinear 
waves in geophysical media. The main question to understand is how well the non-linear 
wave systems are described by the respective wave kinetic equations (WKEs). The 
secondary, but equally important questions are how to correct WKE to adopt it to cases 
when the idealised theory fails, and how to predict transport processes caused by wave 
turbulence. The scientific problem will be addressed using the wave turbulence theory (in both 
idealised and non-idealised settings) 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. 

Based on the data arising from numerics, a study will be 
undertaken on how to improve the WKE description in non-idealised (realistic) situations and 
how to predict the transport properties. This postdoc position is, therefore, theoretical with an 
important numerical part using existent numerical codes.

Applicant profile:

Applicants should have some background in fluid mechanics and numerical methods. A good 
general knowledge of statistical physics and mathematical methods for physics will be 
appreciated. Additionally, the postdoc researcher will gain knowledge in high-performance 
computing (HPC) and develop expertise in non-linear physics, statistical mechanics, and fluid 
mechanics.

Research environment:

The successful applicant will join the team “Nonlinear and Non-equilibrium Physics” led by 
Sergey Nazarenko, a CNRS researcher at the INPHYNI (https://inphyni.univ-cotedazur.fr/). 

The group comprises experts in classical, wave and quantum turbulence, nonlinear optical and 
biological systems. The successful applicant will also take advantage of already established 
international collaborations of the group. 

In addition, this project will carried out in close collaboration with Giorgio Krustolovic, also a 
member of the SIMONS Collaboration.

Enquiries and Application Process:

To apply for this postdoc position or enquire about the project, please contact Sergey 
Nazarenko (Sergey.Nazarenko at Sergey.Nazarenko at unice.fr) in the first instance.

Additional information:

The successful applicant will be part of the SIMONS Collaboration Wave Turbulence.
Sergey Nazarenko and Giorgio Krstulovic are both members of this international collaboration. 
The postdoc researcher will be in a rich environment where experts from different countries meet regularly.