Scale decomposition in compressible turbulence

Aluie, Hussein

doi:10.1016/j.physd.2012.12.009

Cited by 134 publications

(196 citation statements)

References 37 publications

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“…What we do know is that turbulence in the interstellar medium is highly compressible and supersonic (Larson 1981;Heyer & Brunt 2004;Roman-Duval et al 2011;Hennebelle & Falgarone 2012), significantly exceeding the complexity of incompressible turbulence (Kolmogorov 1941;Frisch 1995). Supersonic, compressible turbulence is difficult to study analyti-E-mail: christoph.federrath@anu.edu.au † E-mail: supratik.banerjee@uni-koeln.de cally, but some important steps have been taken (Lazarian & Pogosyan 2000;Boldyrev et al 2002;Lazarian & Esquivel 2003;Schmidt et al 2008;Galtier & Banerjee 2011;Aluie 2011Aluie , 2013Banerjee & Galtier 2013, 2014. In order to unravel the statistics and properties of turbulence in detail, however, one must ultimately resort to full 3D computer simulations.…”

Section: Introductionmentioning

confidence: 99%

The density structure and star formation rate of non-isothermal polytropic turbulence

Federrath

Banerjee²

2015

Monthly Notices of the Royal Astronomical Society

119

128

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The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF). Interstellar turbulence is non-universal, with a wide range of Mach numbers, magnetic fields strengths, and driving mechanisms. Although some of these parameters were explored, most previous works assumed that the gas is isothermal. However, we know that cold molecular clouds form out of the warm atomic medium, with the gas passing through chemical and thermodynamic phases that are not isothermal. Here we determine the role of temperature variations by modelling non-isothermal turbulence with a polytropic equation of state (EOS), where pressure and temperature are functions of gas density, P ∼ ρ Γ , T ∼ ρ Γ−1 . We use grid resolutions of 2048 3 cells and compare polytropic exponents Γ = 0.7 (soft EOS), Γ = 1 (isothermal EOS), and Γ = 5/3 (stiff EOS). We find a complex network of non-isothermal filaments with more small-scale fragmentation occurring for Γ < 1, while Γ > 1 smoothes out density contrasts. The density probability distribution function (PDF) is significantly affected by temperature variations, with a power-law tail developing at low densities for Γ > 1. In contrast, the PDF becomes closer to a lognormal distribution for Γ 1. We derive and test a new density variance -Mach number relation that takes Γ into account. This new relation is relevant for theoretical models of the SFR and IMF, because it determines the dense gas mass fraction of a cloud, from which stars form. We derive the SFR as a function of Γ and find that it decreases by a factor of ∼ 5 from Γ = 0.7 to Γ = 5/3.

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Section: Introductionmentioning

confidence: 99%

The density structure and star formation rate of non-isothermal polytropic turbulence

Federrath

Banerjee²

2015

Monthly Notices of the Royal Astronomical Society

119

128

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“…Due to the modification in the definition of the correlation functions, the nongravitational part of (33) differs from that obtained in Galtier and Banerjee [50]. Interestingly, one can show that the velocity-pressure-dilatation correlation does not appear in this exact relation which was claimed previously [63].…”

Section: A In Terms Of Two-point Differencesmentioning

confidence: 68%

“…In addition, we concentrate on the inertial zone (which is assumed to exist for compressible turbulence [62,63]), where the viscous effects can be neglected and the external forcing is assumed to be the only source of the energy input…”

Section: A In Terms Of Two-point Differencesmentioning

confidence: 99%

Exact relations for energy transfer in self-gravitating isothermal turbulence

Banerjee

Kritsuk

2017

Phys. Rev. E

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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 (Galtier and Banerjee, Phys. Rev. Lett., 107, 134501, 2011; Banerjee and Galtier, Phys. Rev. E, 87, 013019, 2013), the current exact relation shows that the pressure dilatation terms plays 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 kinetic and thermodynamic potential energy, 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.

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“…Each of these subjects can potentially receive a strong transformative impact from compressible DNS/LES at the exascale. Recent advances in theory of compressible turbulence have provided important reference points for validation of numerical solutions, ensuring that the flops would not be wasted [41][42][43][44].…”

Section: Appendix Amentioning

confidence: 99%

Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows

Kotov

Yee

Wray

et al. 2016

Journal of Computational Physics

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The Yee & Sjögreen adaptive numerical dissipation control in high order scheme (High Order Filter Methods for Wide Range of Compressible Flow Speeds, ICOSAHOM 09, 2009) is further improved for DNS and LES of shock-free turbulence and low speed turbulence with shocklets. There are vastly different requirements in the minimization of numerical dissipation for accurate turbulence simulations of different compressible flow types and flow speeds. Traditionally, the method of choice for shock-free turbulence and low speed turbulence are by spectral, high order central or high order compact schemes with high order linear filters. With a proper control of a local flow sensor, appropriate amount of numerical dissipation in high order shock-capturing schemes can have spectral-like accuracy for compressible low speed turbulent flows. The development of the method includes an adaptive flow sensor with automatic selection on the amount of numerical dissipation needed at each flow location for more accurate DNS and LES simulations with less tuning of parameters for flows with a wide range of flow speed regime during the time-accurate evolution, e.g., time varying random forcing. An automatic selection of the different flow sensors catered to the different flow types is constructed. A Mach curve and high-frequency oscillation indicators are used to reduce the tuning of parameters in controlling the amount of shock-capturing numerical dissipation to be employed for shockfree turbulence, low speed turbulence and turbulence with strong shocks. In Kotov et al. (High Order Numerical Methods for LES of Turbulent Flows with Shocks, ICCFD8, Chengdu, Sichuan, China, July 14-18, 2014) the LES of a turbulent flow with a strong shock by the Yee & Sjögreen scheme indicated a good agreement with the filtered DNS data. A work in progress for the application of the adaptive flow sensor for compressible turbulence with time-varying random forcing is forthcoming. The present study examines the versatility of the Yee & Sjögreen scheme for DNS and LES of traditional low speed flows without forcing. Special attention is focused on the accuracy performance of this scheme using the Smagorinsky and the Germano-Lilly SGS models.Published by Elsevier Inc.

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Scale decomposition in compressible turbulence

Cited by 134 publications

References 37 publications

The density structure and star formation rate of non-isothermal polytropic turbulence

The density structure and star formation rate of non-isothermal polytropic turbulence

Exact relations for energy transfer in self-gravitating isothermal turbulence

Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows

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