A Compressible Turbulence Model for Pressure—Strain

This work focuses on the performance and validation of compressible turbulence models for the pressure-strain correlation. Considering the Launder Reece and Rodi (LRR) incompressible model for the pressure-strain correlation, Adumitroaie et al., Huang et al., and Marzougui et al., used different modeling approaches to develop turbulence models, taking into account compressibility effects for this term. Two numerical coefficients are dependent on the turbulent Mach number, and all of the remaining coefficients conserve the same values as in the original LRR model. The models do not correctly predict the compressible turbulence at a high-speed shear flow. So, the revision of these models is the major aim of this study. In the present work, the compressible model for the pressure-strain correlation developed by Khlifi−Lili, involving the turbulent Mach number, the gradient, and the convective Mach numbers, is used to modify the linear mean shear strain and the slow terms of the previous models. The models are tested in two compressible turbulent flows: homogeneous shear flow and the newly developed plane mixing layers. The predicted results of the proposed modifications of the Adumitroaie et al., Huang et al., and Marzougui et al., models and of its universal versions are compared with direct numerical simulation (DNS) and experiment data. The results show that the important parameters of compressibility in homogeneous shear flow and in the mixing layers are well predicted by the proposal models.

Energetic Particle Acceleration in Compressible Magnetohydrodynamic Turbulence

Magnetohydrodynamic (MHD) turbulence is an important agent of energetic particle acceleration. Focusing on the compressible properties of magnetic turbulence, we adopt the test particle method to study the particle acceleration from Alfvén, slow, and fast modes in four turbulence regimes that may appear in a realistic astrophysical environment. Our studies show that (1) the second-order Fermi mechanism drives the acceleration of particles in the cascade processes of three modes by particle-turbulence interactions, regardless of whether the shock wave appears; (2) not only can the power spectra of maximum-acceleration rates reveal the inertial range of compressible turbulence, but also recover the scaling and energy ratio relationship between the modes; (3) fast mode dominates the acceleration of particles, especially in the case of super-Alfvénic and supersonic turbulence, slow mode dominates the acceleration for sub-Alfvénic turbulence in the very-high-energy range, and the acceleration of Alfvén mode is significant at the early stage of the acceleration; (4) particle acceleration from three modes results in a power-law distribution in the certain range of evolution time. From the perspective of particle-wave mode interaction, this paper promotes the understanding for both the properties of turbulence and the behavior of particle acceleration, which will help provide insight into astrophysical processes involved in MHD turbulence.

Mirror Diffusion of Cosmic Rays in Highly Compressible Turbulence Near Supernova Remnants

Recent gamma-ray observations have revealed inhomogeneous diffusion of cosmic rays (CRs) in the interstellar medium (ISM). This is expected, as the diffusion of CRs depends on the properties of turbulence, which can vary widely in the multiphase ISM. We focus on the mirror diffusion arising in highly compressible turbulence in molecular clouds (MCs) around supernova remnants (SNRs), where the magnetic mirroring effect results in significant suppression of diffusion of CRs near CR sources. Significant energy loss via proton–proton interactions due to slow diffusion flattens the low-energy CR spectrum, while the high-energy CR spectrum is steepened due to the strong dependence of mirror diffusion on CR energy. The resulting broken power-law spectrum of CRs matches well the gamma-ray spectrum observed from SNR/MC systems, e.g., IC443 and W44.