Self-organization of local streamline structures and energy transfer rate in compressible plasma turbulence

We examine how local streamline topology and energy cascade rate self-organize in plasma turbulence for both compressible and incompressible regimes. Using a fully-compressible Hall-magnetohydrodynamic simulation, we quantify the subgrid-scale energy transfer and analyze its relationship to streamline structures by means of grandient tensor geometric invariants of the velocity field. Our results highlight how streamline topology is crucial for diagnosing turbulence: for nearly-incompressible fluctuations the energy is primarily transferred to smaller scales through strain-dominated and stable-vortical structures, while is back-transferred towards larger scales through unstable-vortical structures. Compressible fluctuations, on the contrary, do not show a clear topological selection of the energy transfer since the overall direction of the local cascade rate is found to be determined by the sign of $-\nabla\cdot u$ (plasma volumetric compression or expansion).