The conservative cascade of kinetic energy in compressible turbulence

The physical nature of compressible turbulence is of fundamental importance in a variety of astrophysical settings. We present the first direct evidence that mean kinetic energy cascades conservatively beyond a transitional "conversion" scale-range despite not being an invariant of the compressible flow dynamics. We use high-resolution three-dimensional simulations of compressible hydrodynamic turbulence on $512^3$ and $1024^3$ grids. We probe regimes of forced steady-state isothermal flows and of unforced decaying ideal gas flows. The key quantity we measure is pressure dilatation cospectrum, $E^{PD}(k)$, where we provide the first numerical evidence that it decays at a rate faster than $k^{-1}$ as a function of wavenumber. This is sufficient to imply that mean pressure dilatation acts primarily at large-scales and that kinetic and internal energy budgets statistically decouple beyond a transitional scale-range. Our results suggest that an extension of Kolmogorov's inertial-range theory to compressible turbulence is possible.Comment: 14 pages, 4 figure

Statistics of incompressible hydrodynamic turbulence: An alternative approach

Using a recent alternative form of the Kolmogorov-Monin exact relation for fully developed hydrodynamics (HD) turbulence, the incompressible energy cascade rate is computed. Under this current theoretical framework, for three-dimensional (3D) freely decaying homogeneous turbulence, the statistical properties of the fluid velocity (u), vorticity (ω= ×u), and Lamb vector (L=ω×u) are numerically studied. For different spatial resolutions, the numerical results show that can be obtained directly as the simple products of two-point increments of u and L, without the assumption of isotropy. Finally, the results for the largest spatial resolutions show a clear agreement with the cascade rates computed from the classical four-thirds law for isotropic homogeneous HD turbulence.Fil: Andrés, Nahuel. Universidad de Buenos Aires. Facultad de Cs.exactas y Naturales. Departamento de Física. Grupo de Plasmas Astrofisicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Laboratoire de Physique des Plasmas; FranciaFil: Banerjee, Supratik. Indian Institute Of Technology Kanpur; Indi

Conditions for sustainment of magnetohydrodynamic turbulence driven by Alfvén waves

In a number of space and astrophysical plasmas,turbulence is driven by the supply of wave energy. In the context of incompressible magnetohydrodynamics (MHD) there are basic physical reasons, associated with conservation of cross helicity, why this kind of driving may be ineffective in sustaining turbulence. Here an investigation is made into some basic requirements for sustaining steady turbulence and dissipation in the context of incompressible MHD in a weakly inhomogeneous open field line region, driven by the supply of unidirectionally propagating waves at a boundary. While such wave driving cannot alone sustain turbulence, the addition of reflection permits sustainment. Another sustainment issue is the action of the nonpropagating or quasi-two dimensional part of the spectrum; this is particularly important in setting up a steady cascade. Thus, details of the waveboundary conditions also affect the ease of sustaining a cascade. Supply of a broadband spectrum of waves can overcome the latter difficulty but not the former, that is, the need for reflections. Implications for coronal heating and other astrophysical applications, as well as simulations, are suggested

Plasma turbulence at ion scales: a comparison between PIC and Eulerian hybrid-kinetic approaches

Kinetic-range turbulence in magnetized plasmas and, in particular, in the context of solar-wind turbulence has been extensively investigated over the past decades via numerical simulations. Among others, one of the widely adopted reduced plasma model is the so-called hybrid-kinetic model, where the ions are fully kinetic and the electrons are treated as a neutralizing (inertial or massless) fluid. Within the same model, different numerical methods and/or approaches to turbulence development have been employed. In the present work, we present a comparison between two-dimensional hybrid-kinetic simulations of plasma turbulence obtained with two complementary approaches spanning about two decades in wavenumber - from MHD inertial range to scales well below the ion gyroradius - with a state-of-the-art accuracy. One approach employs hybrid particle-in-cell (HPIC) simulations of freely-decaying Alfv\'enic turbulence, whereas the other consists of Eulerian hybrid Vlasov-Maxwell (HVM) simulations of turbulence continuously driven with partially-compressible large-scale fluctuations. Despite the completely different initialization and injection/drive at large scales, the same properties of turbulent fluctuations at $k_\perp\rho_i\gtrsim1$ are observed. The system indeed self-consistently "reprocesses" the turbulent fluctuations while they are cascading towards smaller and smaller scales, in a way which actually depends on the plasma beta parameter. Small-scale turbulence has been found to be mainly populated by kinetic Alfv\'en wave (KAW) fluctuations for $\beta\geq1$, whereas KAW fluctuations are only sub-dominant for low-$\beta$.Comment: 18 pages, 4 figures, accepted for publication in J. Plasma Phys. (Collection: "The Vlasov equation: from space to laboratory plasma physics"