Conformal invariance of weakly compressible two-dimensional turbulence.

We study conformal invariance of vorticity clusters in weakly compressible two-dimensional turbulence at low Mach numbers. On the basis of very high resolution direct numerical simulation we demonstrate the scaling invariance of the inverse cascade with scaling close to Kolmogorov prediction. In this range of scales, the statistics of zero-vorticity isolines are found to be compatible with those of critical percolation, thus generalizing the results obtained in incompressible Navier-Stokes turbulence.

Dust-Polarization Maps for Local Interstellar Turbulence.

We show that simulations of magnetohydrodynamic turbulence in the multiphase interstellar medium yield an E/B ratio for polarized emission from Galactic dust in broad agreement with recent Planck measurements. In addition, the B-mode spectra display a scale dependence that is consistent with observations over the range of scales resolved in the simulations. The simulations present an opportunity to understand the physical origin of the E/B ratio and a starting point for more refined models of Galactic emission of use for both current and future cosmic microwave background experiments.

Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids.

Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by Banerjee and Galtier [Phys. Rev. E 93, 033120 (2016)2470-004510.1103/PhysRevE.93.033120; J. Phys. A: Math. Theor. 50, 015501 (2017)1751-811310.1088/1751-8113/50/1/015501], an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic, and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be nontrivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.

Exact relations for energy transfer in self-gravitating isothermal turbulence.

Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (S. Galtier and S. Banerjee, Phys. Rev. Lett. 107, 134501 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.134501; S. Banerjee and S. Galtier, Phys. Rev. E 87, 013019 (2013)PLEEE81539-375510.1103/PhysRevE.87.013019), the current exact relation shows that the pressure dilatation terms play practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike the kinetic and thermodynamic potential energies, the gravitational contribution is absent from the flux term. An estimate shows that, for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.

Dissipative structures in supersonic turbulence.

We show that density-weighted moments of the dissipation rate, epsilonl, averaged over a scale l, in supersonic turbulence can be successfully explained by the She and Lévêque model [Phys. Rev. Lett. 72, 336 (1994)]. A general method is developed to measure the two parameters of the model, gamma and d, based directly on their physical interpretations as the scaling exponent of the dissipation rate in the most intermittent structures (gamma) and the dimension of the structures (d). We find that the best-fit parameters (gamma=0.71 and d=1.90) derived from the epsilonl scalings in a simulation of supersonic turbulence at Mach 6 agree with their direct measurements, confirming the validity of the model in supersonic turbulence.