Cascades of temperature and entropy fluctuations in compressible turbulence

Abstract

Cascades of temperature and entropy fluctuations are studied by numerical simulations of stationary three-dimensional compressible turbulence with a heat source. The fluctuation spectra of velocity, compressible velocity component, density and pressure exhibit the $-5/3$ scaling in an inertial range. The strong acoustic equilibrium relation between spectra of the compressible velocity component and pressure is observed. The $-5/3$ scaling behaviour is also identified for the fluctuation spectra of temperature and entropy, with the Obukhov–Corrsin constants close to that of a passive scalar spectrum. It is shown by Kovasznay decomposition that the dynamics of the temperature field is dominated by the entropic mode. The average subgrid-scale (SGS) fluxes of temperature and entropy normalized by the total dissipation rates are close to 1 in the inertial range. The cascade of temperature is dominated by the compressible mode of the velocity field, indicating that the theory of a passive scalar in incompressible turbulence is not suitable to describe the inter-scale transfer of temperature in compressible turbulence. In contrast, the cascade of entropy is dominated by the solenoidal mode of the velocity field. The different behaviours of cascades of temperature and entropy are partly explained by the geometrical properties of SGS fluxes. Moreover, the different effects of local compressibility on the SGS fluxes of temperature and entropy are investigated by conditional averaging with respect to the filtered dilatation, demonstrating that the effect of compressibility on the cascade of temperature is much stronger than on the cascade of entropy.

Energy budget in decaying compressible MHD turbulence

“…This paper has maintained a focus on conversion between energy types in decaying compressible MHD turbulence, and as such we have not delved into subjects that are related to various aspects of our study. There are, of course, numerous studies of compressible hydrodynamics that examine turbulence cascade properties; many of these are numerical, as in recent examples by Wang et al (2013Wang et al ( , 2019; in total these are far too numerous to review here, and we refer the reader to our reference list and the bibliographies contained therein. The present study of energy balance and conversion between incompressive energy reservoirs and compressive energy reservoirs in MHD is necessarily a richer subject than the numerous analogous studies in hydrodynamics (Kida & Orszag 1990, 1992Miura & Kida 1995;Pan & Johnsen 2017).…”

“…In this work, we decompose the velocity field into solenoidal and compressive parts following Helmholtz decomposition as used in Kida & Orszag (1990, 1992), Miura & Kida (1995), Pan & Johnsen (2017), Wang et al. (2019). The decay of energy in a turbulent MHD system is both an interesting academic problem and also an important practical one.…”

“…For example, characteristics for three separate propagating linear eigenmodes -the Alfvén mode, the slow magnetosonic mode and the fast magnetosonic mode have been studied using numerical simulations (Cho & Lazarian 2002;Kowal & Lazarian 2010;Yang et al 2018;Makwana & Yan 2020) and observations (Yao et al 2011;Howes et al 2012;Klein et al 2012). In this work, we decompose the velocity field into solenoidal and compressive parts following Helmholtz decomposition as used in Kida & Orszag (1990, 1992, Miura & Kida (1995), Pan & Johnsen (2017), Wang et al (2019). The decay of energy in a turbulent MHD system is both an interesting academic problem and also an important practical one.…”

Transfer of internal energy fluctuation in compressible isotropic turbulence with vibrational non-equilibrium

“…are rarely investigated. Wang et al (2019) numerically investigated the cascades of temperature and entropy fluctuations in the stationary compressible isotropic turbulence with the large-scale thermal forcing. The introduction of large-scale thermal forcing was found to have significant impacts on the properties of compressible turbulence, such as the flow compressibility and the transfers of temperature and entropy.…”

Effect of flow topology on the kinetic energy flux in compressible isotropic turbulence

“…The flow structures and statistical features of compressible turbulence are more complex than those of incompressible turbulence, due to the nonlinear couplings of the solenoidal mode, compressible mode and thermodynamic mode in compressible turbulence (Samtaney, Pullin & Kosovic 2001;Pirozzoli & Grasso 2004 Wang et al 2018aWang et al , 2019. The local flow-field topology based on the three invariants of velocity gradient tensor was investigated in a wide range of compressible turbulence, including decaying compressible isotropic turbulence (Suman & Girimaji 2010;Danish, Suman & Girimaji 2016b), compressible turbulent boundary layers (Wang & Lu 2012;Chu & Lu 2013;Bechlars & Sandberg 2017a,b), compressible turbulent mixing layers (Vaghefi & Madnia 2015;Mathew, Ghosh & Friedrich 2016), supersonic turbulent pipes, nozzle and diffuser flows (Kumari et al 2018) and compressible turbulent flames (Cifuentes et al 2014(Cifuentes et al , 2016Wacks & Chakraborty 2016a;Wacks, Chakraborty & Klein 2016b;Papapostolou et al 2017;Lai, Wacks & Chakraborty 2018;Wacks, Konstantinou & Chakraborty 2018).…”