Inverse cascade of kinetic energy in two-dimensional β-Plane magnetohydrodynamic turbulence

<p>Numerical studies of two-dimensional β-plane homogeneous magnetohydrodynamic turbulence are presented. The study of the fundamental properties of such turbulence allows understanding the evolution of various astrophysical objects from the Sun and stars to planetary systems, galaxies, and galaxy clusters. Energy spectra and cascade process in two-dimensional β-plane MHD are studied.</p><p>In this work the equations of two-dimensional magnetohydrodynamics with the Coriolis force in the β-plane approximation are used for the qualitative analysis and numerical simulation of processes in plasma astrophysics. The equations are solved on a square box of edge size 2π with periodic boundary conditions applying a the pseudospectral method using the 2/3 rule for dealiasing. The results of numerical simulation of two-dimensional β-plane MHD turbulence with a spatial resolution of 1024 × 1024 and 4096 × 4096 with different Rossby parameters β and different Reynolds numbers are presented.</p><p>It is found that only unsteady zonal flows with complex temporal dynamics are formed in two-dimensional β-plane magnetohydrodynamic turbulence. It is shown that flow nonstationarity is due to the appearance of isotropic magnetic islands caused by the Lorentz force in the system. The formation of Iroshnikov–Kraichnan spectrum is shown in the early stages of evolution of two-dimensional β-plane magnetohydrodynamic turbulence. The self-similarity of the decay of Iroshnikov–Kraichnan spectrum is studied. On long time scale violation of self-similarity of the decay and formation of Kolmogorov spectrum is discovered. The inverse cascade of kinetic energy, which is characteristic of the detected Kolmogorov spectrum, provides the formation of zonal flows.</p><p>This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00016).</p>

POD Spectrum of the Wake behind a Circular Cylinder

The wake dynamics behind a long circular cylinder in cross-flow was studied using the POD method. The temporal parts of POD modes, Chronoses, are subjected to frequency analysis. Five groups of modes are distinguished according to the frequency contents. The low order high energy modes contain the vortex shedding frequency or its harmonics up to 3rd order plus Kolmogorov spectrum. The higher order modes are characterized by combination of Kolmogorov spectrum with the white noise spectrum, its importance grows with the mode order. The very high order modes are characterised by the white noise spectrum only.

A Validation Study of the Compressible Rayleigh–Taylor Instability Comparing the Ares and Miranda Codes

The compressible Rayleigh–Taylor (RT) instability is studied by performing a suite of large eddy simulations (LES) using the Miranda and Ares codes. A grid convergence study is carried out for each of these computational methods, and the convergence properties of integral mixing diagnostics and late-time spectra are established. A comparison between the methods is made using the data from the highest resolution simulations in order to validate the Ares hydro scheme. We find that the integral mixing measures, which capture the global properties of the RT instability, show good agreement between the two codes at this resolution. The late-time turbulent kinetic energy and mass fraction spectra roughly follow a Kolmogorov spectrum, and drop off as k approaches the Nyquist wave number of each simulation. The spectra from the highest resolution Miranda simulation follow a Kolmogorov spectrum for longer than the corresponding spectra from the Ares simulation, and have a more abrupt drop off at high wave numbers. The growth rate is determined to be between around 0.03 and 0.05 at late times; however, it has not fully converged by the end of the simulation. Finally, we study the transition from direct numerical simulation (DNS) to LES. The highest resolution simulations become LES at around t/τ ≃ 1.5. To have a fully resolved DNS through the end of our simulations, the grid spacing must be 3.6 (3.1) times finer than our highest resolution mesh when using Miranda (Ares).