Cosmological fluid mechanics with adaptively refined large eddy simulations

Schmidt, Wolfgang; Almgren, Ann S.; Braun, H.; Engels, Jan Frederik; Niemeyer, J. C.; Schulz, Jochen; Mekuria, Remudin Reshid; Aspden, A. J.; Bell, John B.

doi:10.1093/mnras/stu501

Cited by 47 publications

(105 citation statements)

References 61 publications

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“…The character of the ICM gas flows and the presence of turbulence in our simulated cluster is consistent with other highresolution simulation studies in the literature (e.g., Dolag et al 2005;Vazza et al 2011a;Miniati 2014;Schmidt et al 2014), with quantitative differences related to the specific analysis techniques. In the limited context of high-resolution grid-based simulations of non-radiative clusters, the pressure support from turbulence in the cluster core has, for example, been estimated in the range ∼ 5 − 15% of the gas pressure using the total, global gas velocity dispersion (e.g., Lau et al 2009;Nelson et al 2014), or, say ∼ 5 − 20% from large-scale, incoherent, but fixed scale velocity distributions, Vazza et al (2011a).…”

Section: Comparison To Previous Worksupporting

confidence: 89%

“…Previous studies (Ryu et al 2008;Vazza et al 2014;Miniati 2014;Schmidt et al 2014) and our results below suggest that ICM turbulent motions are predominantly solenoidal in character. The distinguishing property of solenoidal turbulence is, of course, that the motions are rotational; that is, they have non-vanishing local vorticity, ω = ∇ × v = 0.…”

Section: Enstrophy As a Metric For Solenoidal Turbulencesupporting

confidence: 74%

“…4.2. See Zhu et al (2010); Schmidt et al (2014) for previous analogous turbulence dissipation analyses in clusters. We will examine this issue more broadly for the ISC simulations in a subsequent paper.…”

Section: Enstrophy As a Metric For Solenoidal Turbulencementioning

confidence: 99%

“…Gaspari et al 2014;Schmidt et al 2014) or structure functions (Vazza et al 2011a;Miniati 2014Miniati , 2015.…”

Section: How Where and When Is Solenoidal Turbulence Generated In Thmentioning

confidence: 99%

“…These motions may be driven by processes originating on galactic scales (e.g., star burst winds, AGN outflows and bubbles, (e.g., O'Neill et al 2009;Morsony et al 2010;Mendygral et al 2012;Gaspari et al 2012)), possibly ICM-based magneto-thermal instabilities (e.g., Kunz et al 2011;ZuHone et al 2013), but especially by cluster-scale processes associated with cluster formation out of cosmological, large-⋆ Email:franco.vazza@hs.uni-hamburg.de scale structure (e.g., Dolag et al 2005;Vazza et al 2006;Ryu et al 2008;Lau et al 2009;Vazza et al 2011a;ZuHone 2011;Miniati 2014;Schmidt et al 2014). …”

Section: Introductionmentioning

confidence: 99%

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Turbulence and vorticity in Galaxy clusters generated by structure formation

Vazza

Jones

Brüggen

et al. 2016

Mon. Not. R. Astron. Soc.

118

150

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Turbulence is a key ingredient for the evolution of the intracluster medium, whose properties can be predicted with high resolution numerical simulations. We present initial results on the generation of solenoidal and compressive turbulence in the intracluster medium during the formation of a small-size cluster using highly resolved, non-radiative cosmological simulations, with a refined monitoring in time. In this first of a series of papers, we closely look at one simulated cluster whose formation was distinguished by a merger around z ∼ 0.3. We separate laminar gas motions, turbulence and shocks with dedicated filtering strategies and distinguish the solenoidal and compressive components of the gas flows using Hodge-Helmholtz decomposition. Solenoidal turbulence dominates the dissipation of turbulent motions (∼ 95%) in the central cluster volume at all epochs. The dissipation via compressive modes is found to be more important (∼ 30% of the total) only at large radii ( 0.5 r vir ) and close to merger events. We show that enstrophy (vorticity squared) is good proxy of solenoidal turbulence. All terms ruling the evolution of enstrophy (i.e. baroclinic, compressive, stretching and advective terms) are found to be significant, but in amounts that vary with time and location. Two important trends for the growth of enstrophy in our simulation are identified: first, enstrophy is continuously accreted into the cluster from the outside, and most of that accreted enstrophy is generated near the outer accretion shocks by baroclinic and compressive processes. Second, in the cluster interior vortex stretching is dominant, although the other terms also contribute substantially.

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Section: Comparison To Previous Worksupporting

confidence: 89%

Section: Enstrophy As a Metric For Solenoidal Turbulencesupporting

confidence: 74%

Section: Enstrophy As a Metric For Solenoidal Turbulencementioning

confidence: 99%

“…Gaspari et al 2014;Schmidt et al 2014) or structure functions (Vazza et al 2011a;Miniati 2014Miniati , 2015.…”

Section: How Where and When Is Solenoidal Turbulence Generated In Thmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Turbulence and vorticity in Galaxy clusters generated by structure formation

Vazza

Jones

Brüggen

et al. 2016

Mon. Not. R. Astron. Soc.

118

150

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Large Eddy Simulations in Astrophysics

Schmidt

2015

Living Rev Comput Astrophys

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In this review, the methodology of large eddy simulations (LES) is introduced and applications in astrophysics are discussed. As theoretical framework, the scale decomposition of the dynamical equations for neutral fluids by means of spatial filtering is explained. For cosmological applications, the filtered equations in comoving coordinates are also presented. To obtain a closed set of equations that can be evolved in LES, several subgrid scale models for the interactions between numerically resolved and unresolved scales are discussed, in particular the subgrid scale turbulence energy equation model. It is then shown how model coefficients can be calculated, either by dynamical procedures or, a priori, from high-resolution data. For astrophysical applications, adaptive mesh refinement is often indispensable. It is shown that the subgrid scale turbulence energy model allows for a particularly elegant and physically well motivated way of preserving momentum and energy conservation in AMR simulations. Moreover, the notion of shear-improved models for inhomogeneous and non-stationary turbulence is introduced. Finally, applications of LES to turbulent combustion in thermonuclear supernovae, star formation and feedback in galaxies, and cosmological structure formation are reviewed.arXiv:1404.2483v1 [astro-ph.CO] 9 Apr 2014 tial subrange is very narrow for computationally feasible resolutions because the bottleneck effect distorts the spectrum over a large range of high wave numbers below the Nyquist wavenumber [30,27,114]. It appears that LES with an explicit SGS model, such as the K-equation model, can reduce the bottleneck effect to some degree and reproduce scalings from ILES or DNS at lower resolution [45,128,109]. However, more systematic studies covering the parameters space of forced compressible turbulence are necessary to confirm this effect.There are, of course, alternative methods of scale separation and a large variety of SGS models (for a comprehensive overview, see the monographs [103,39]). An example are the Camassa-Holm equations, which follow from the incompressible Navier-Stokes equations by decomposing the trajectories of fluid elements into mean and fluctuating parts in the Lagrangian framework [21]. Since the filtered component of the velocity is defined by an inverse Helmholtz operator of the form (1 − α 2 ∇ 2 ) −1 , which is explicitly applied to determine the turbulent stresses in the filtered velocity equation, the resulting model is called Lagrangian-averaged Navier-Stokes α-model (LANS-α). Depending on the choice of α, the variables computed in LES based on LANS-α are typically smoothed over length scales somewhat larger than the grid resolution. In other words, this type of simulation partially resolves the sub-filter scales, which improves the controllability of the model. While there is no handle on the competition between the SGS model and numerical truncation errors on the grid scale in convectional LES, LANS-α can, in principle, alleviate this problem by adjusting the balance between ...

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The relation between gas density and velocity power spectra in galaxy clusters: High-resolution hydrodynamic simulations and the role of conduction

Gaspari

Churazov

Nagai

et al. 2014

A&A

119

147

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Exploring the power spectrum of fluctuations and velocities in the intracluster medium (ICM) can help us to probe the gas physics of galaxy clusters. Using high-resolution 3D plasma simulations, we study the statistics of the velocity field and its intimate relation with the ICM thermodynamic perturbations. The normalization of the ICM spectrum (related to density, entropy, or pressure fluctuations) is linearly tied to the level of large-scale motions, which excite both gravity and sound waves due to stratification. For a low 3D Mach number M ∼ 0.25, gravity waves mainly drive entropy perturbations, which are traced by preferentially tangential turbulence. For M > 0.5, sound waves start to significantly contribute and pass the leading role to compressive pressure fluctuations, which are associated with isotropic (or slightly radial) turbulence. Density and temperature fluctuations are then characterized by the dominant process: isobaric (low M), adiabatic (high M), or isothermal (strong conduction). Most clusters reside in the intermediate regime, showing a mixture of gravity and sound waves, hence drifting toward isotropic velocities. Remarkably, regardless of the regime, the variance of density perturbations is comparable to the 1D Mach number, M 1D ∼ δρ/ρ. This linear relation allows us to easily convert between gas motions and ICM perturbations (δρ/ρ < 1), which can be exploited by the available Chandra, XMM data and by the forthcoming Astro-H mission. At intermediate and small scales (10-100 kpc), the turbulent velocities develop a tight Kolmogorov cascade. The thermodynamic perturbations (which can be generally described by log-normal distributions) act as effective tracers of the velocity field, in broad agreement with the Kolmogorov-Obukhov-Corrsin advection theory. The cluster radial gradients and compressive features induce a flattening in the cascade of the perturbations. Thermal conduction, on the other hand, acts to damp the thermodynamic fluctuations, washing out the filamentary structures and steepening the spectrum, while leaving the velocity cascade unaltered. The ratio of the velocity and density spectrum thus inverts the downtrend shown by the non-diffusive models, as it widens up to ∼5. This new key diagnostic can robustly probe the presence of conductivity in the ICM. We produce X-ray images of the velocity field, showing how future missions (e.g. Astro-H, Athena) can detect velocity dispersions of a few 100 km s −1 (M > 0.1 in massive clusters), allowing us to calibrate the linear relation and to constrain relative perturbations down to just a few percent.

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Cosmological fluid mechanics with adaptively refined large eddy simulations

Cited by 47 publications

References 61 publications

Turbulence and vorticity in Galaxy clusters generated by structure formation

Turbulence and vorticity in Galaxy clusters generated by structure formation

Large Eddy Simulations in Astrophysics

The relation between gas density and velocity power spectra in galaxy clusters: High-resolution hydrodynamic simulations and the role of conduction

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