Coexistence of acoustic waves and turbulence in low Mach number compressible flows

Abstract

In this work, direct numerical simulations of the compressible fluid equations in turbulent regimes are performed. The behavior of the flow is either dominated by purely turbulent phenomena or by the generation of sound waves in it. Previous studies suggest that three different types of turbulence may happen at the low Mach number limit in polytropic flows: Nearly incompressible, modally equipartitioned compressible, and compressible wave. The distinction between these types of turbulence is investigated here applying different kinds of forcing. Scaling of density fluctuations with Mach number, comparison of the ratio of transverse velocity fluctuations to longitudinal fluctuations, and spectral decomposition of fluctuations are used to distinguish the nature of these solutions. From the study of the spatio-temporal spectra and correlation times, we quantify the contribution of the waves to the total energy of the system. Also, in the dynamics of a compressible flow, three associated correlation times are considered: the non-linear time of local interaction between scales, the sweeping time or non-local time of large scales on small scales, and the time associated with acoustic waves (sound). We observed that different correlation times dominate depending on the wave number (k), the Mach number, and the type of forcing.

Energy budget in decaying compressible MHD turbulence

“…2010; Yang et al. 2016 a ; Cerretani & Dmitruk 2019), e.g. from divergence-free to curl-free, which plays an important role in amplification of the magnetic field (Federrath et al.…”

“…(Note that the requirement that is the formal condition found for NI behaviour in hydrodynamics (Klainerman & Majda 1981) and in high beta MHD (Matthaeus & Brown 1988). However the more restrictive scaling has also been examined in some numerical studies (Ghosh & Matthaeus 1992; Cerretani & Dmitruk 2019). ) As the strength of acoustic waves becomes comparable to the vortical motions, i.e.…”

“…Another related aspect which could arise from shocks is the k −2 (Roberts & Goldstein 1987;Burlaga, Mish & Roberts 1989;Bec & Khanin 2007;Wang et al 2013;Bruno et al 2014;Yang et al 2016a) or shallower than k −2 (Siscoe et al 1968;Borovsky 2010) spectrum. The compressibility can be controlled by virtue of varying kinetic energy injection (Kida & Orszag 1990;Federrath et al 2010;Yang et al 2016a;Cerretani & Dmitruk 2019), e.g. from divergence-free to curl-free, which plays an important role in amplification of the magnetic field (Federrath et al 2011).…”

“…pure acoustic waves. One physically plausible feature in this model is the dominance of acoustic waves over vortical motions, as suggested by Ghosh & Matthaeus (1992) and Cerretani & Dmitruk (2019), but there is no theoretical basis on the scaling for velocity fluctuations nor for density variations.…”

Critical Balance and the Physics of MHD Turbulence

“…It is also the case that turbulence and waves are not antithetical or mutually exclusive. They may, however, be associated with different frequency and/or lengthscale ranges (e.g., Dmitruk et al 2004;Dmitruk & Matthaeus 2009;Andrés et al 2017;Cerretani & Dmitruk 2019). In particular, the turbulence can be of relatively low frequency (for the energy-containing scales) and the wave activity at relatively high frequencies.…”