In this post-doctorate, we propose to study the properties of the small scales of forced compressible homogeneous turbulence. More precisely, exact statistical relations similar to the Monin-Yaglom relation will be investigated. The idea, detailed in reference [1], is to understand how the transfer of circulicity is organized in the inertial range. Circulicity is a quantity associated with angular momentum and, by extension, with vortex motions. The analysis of its inertial properties allows to complete the description of the energy cascade already highlighted in previous works [2,3].

The objective of the post-doctorate is to carry out and exploit direct simulations of compressible homogeneous turbulence with forcing, in order to highlight the inertial properties of circulicity .

To this end, the post-doctoral student will be given access to the very large computing center (TGCC) as well as a code, Triclade, solving the compressible Navier-Stokes equations [4]. This code does not have a forcing mechanism and the first task will therefore be to add this functionality. Once this task has been accomplished, simulations will be carried out by varying the nature of the forcing and in particular the ratio between its solenoidal and dilatational components. These simulations will then be exploited by analyzing the transfer terms of circulicity.

[1] Soulard and Briard. Submitted to Phys. Rev. Fluids. Preprint at arXviv:2207.03761v1
[2] Aluie. Phys. Rev. Lett. 106(17):174502, 2011.
[3] Eyink and Drivas.Phys. Rev. X 8(1):011022, 2018.
[4] Thornber et al. Phys. Fluids 29:105107, 2017.