scholarly journals Turbulent density and pressure fluctuations in the stratified intracluster medium

2020 ◽  
Vol 500 (4) ◽  
pp. 5072-5087
Author(s):  
Rajsekhar Mohapatra ◽  
Christoph Federrath ◽  
Prateek Sharma
Keyword(s):  
Surface Brightness ◽  
Isotropic Turbulence ◽  
Pressure Fluctuations ◽  
Density Fluctuations ◽  
Turbulence Theory ◽  
Intracluster Medium ◽  
Stratified Turbulence ◽  
Hydrodynamic Simulations ◽  
Pressure Scale ◽  
Parameter Ranges

ABSTRACT Turbulent gas motions are observed in the intracluster medium (ICM). The ICM is density-stratified, with the gas density being highest at the centre of the cluster and decreasing radially outwards. As a result of this, Kolmogorov (homogeneous, isotropic) turbulence theory does not apply to the ICM. The gas motions are instead explained by anisotropic stratified turbulence, with the stratification quantified by the perpendicular Froude number (Fr⊥). These turbulent motions are associated with density and pressure fluctuations, which manifest as perturbations in X-ray surface brightness maps of the ICM and as thermal Sunyaev–Zeldovich effect (SZ) fluctuations, respectively. In order to advance our understanding of the relations between these fluctuations and the turbulent gas velocities, we have conducted 100 high-resolution hydrodynamic simulations of stratified turbulence (2562 × 384–10242 × 1536 resolution elements), in which we scan the parameter space of subsonic rms Mach number ($\mathcal {M}$), Fr⊥, and the ratio of entropy and pressure scale heights (RPS = HP/HS), relevant to the ICM. We develop a new scaling relation between the standard deviation of logarithmic density fluctuations (σs, where s = ln (ρ/$\langle$ρ$\rangle$)), $\mathcal {M}$, and Fr⊥, which covers both the strongly stratified (Fr⊥ ≪ 1) and weakly stratified (Fr⊥ ≫ 1) turbulence regimes: $\sigma _{\rm s}^2=\ln (1+b^2\mathcal {M}^4+0.10/(\mathrm{Fr}_\perp +0.25/\sqrt{\mathrm{Fr}_\perp })^2\mathcal {M}^2R_{\rm PS})$, where b ∼ 1/3 for solenoidal turbulence driving studied here. We further find that logarithmic pressure fluctuations σ(ln P/ < P >) are independent of stratification and scale according to the relation $\sigma _{(\ln {\bar{P}})}^2=\ln (1+b^2\gamma ^2\mathcal {M}^4)$, where $\bar{P}=P/\left\langle P \right\rangle $ and γ is the adiabatic index of the gas. We have tested these scaling relations to be valid over the parameter ranges $\mathcal {M} = 0.01$–0.40, Fr⊥ = 0.04–10.0, and RPS = 0.33–2.33.

scholarly journals Turbulence in stratified atmospheres: implications for the intracluster medium

2020 ◽  
Vol 493 (4) ◽  
pp. 5838-5853 ◽  
Author(s):  
Rajsekhar Mohapatra ◽  
Christoph Federrath ◽  
Prateek Sharma
Keyword(s):  
Power Spectrum ◽  
Radial Profile ◽  
Power Spectra ◽  
Density Fluctuations ◽  
Total Power ◽  
Intracluster Medium ◽  
Stratified Turbulence ◽  
Density Spectrum ◽  
Velocity Fluctuations ◽  
Hydrodynamical Simulations

ABSTRACT The gas motions in the intracluster medium (ICM) are governed by turbulence. However, since the ICM has a radial profile with the centre being denser than the outskirts, ICM turbulence is stratified. Stratified turbulence is fundamentally different from Kolmogorov (isotropic, homogeneous) turbulence; kinetic energy not only cascades from large to small scales, but it is also converted into buoyancy potential energy. To understand the density and velocity fluctuations in the ICM, we conduct high-resolution (10242 × 1536 grid points) hydrodynamical simulations of subsonic turbulence (with rms Mach number $\mathcal {M}\approx 0.25$) and different levels of stratification, quantified by the Richardson number Ri, from Ri = 0 (no stratification) to Ri = 13 (strong stratification). We quantify the density, pressure, and velocity fields for varying stratification because observational studies often use surface brightness fluctuations to infer the turbulent gas velocities of the ICM. We find that the standard deviation of the logarithmic density fluctuations (σs), where s = ln (ρ/ < ρ($z$) >), increases with Ri. For weakly stratified subsonic turbulence (Ri ≲ 10, $\mathcal {M}\lt 1$), we derive a new σs–$\mathcal {M}$–Ri relation, $\sigma _\mathrm{ s}^2=\ln (1+b^2\mathcal {M}^4+0.09\mathcal {M}^2 \mathrm{Ri} H_\mathrm{ P}/H_\mathrm{ S})$, where b = 1/3–1 is the turbulence driving parameter, and HP and HS are the pressure and entropy scale heights, respectively. We further find that the power spectrum of density fluctuations, P(ρk/ < ρ >), increases in magnitude with increasing Ri. Its slope in k-space flattens with increasing Ri before steepening again for Ri ≳ 1. In contrast to the density spectrum, the velocity power spectrum is invariant to changes in the stratification. Thus, we find that the ratio between density and velocity power spectra strongly depends on Ri, with the total power in density and velocity fluctuations described by our σs–$\mathcal {M}$–Ri relation. Pressure fluctuations, on the other hand, are independent of stratification and only depend on $\mathcal {M}$.

scholarly journals Turbulent thermal diffusion in strongly stratified turbulence: Theory and experiments

2017 ◽  
Vol 2 (6) ◽  
Author(s):  
G. Amir ◽  
N. Bar ◽  
A. Eidelman ◽  
T. Elperin ◽  
N. Kleeorin ◽  
...  
Keyword(s):  
Thermal Diffusion ◽  
Turbulence Theory ◽  
Stratified Turbulence ◽  
Theory And Experiments

scholarly journals Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 157
Author(s):  
Duane Rosenberg ◽  
Annick Pouquet ◽  
Raffaele Marino
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Potential Vorticity ◽  
Isotropic Turbulence ◽  
Joint Probability ◽  
Buoyancy Flux ◽  
Turbulent Regime ◽  
Stratified Turbulence ◽  
Low Dissipation ◽  
Linear And Nonlinear

We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.

Experiments of Compressible Homogeneous and Isotropic Turbulence Interacting With Expansion Waves

2003 ◽  
Author(s):  
Savvas S. Xanthos ◽  
Yiannis Andreopoulos
Keyword(s):  
Mach Number ◽  
Shock Tube ◽  
Total Pressure ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Pressure Fluctuations ◽  
Incident Shock ◽  
Expansion Waves ◽  
Curvature Effects ◽  
Homogeneous And Isotropic Turbulence

The interaction of traveling expansion waves with grid-generated turbulence was investigated in a large-scale shock tube research facility. The incident shock and the induced flow behind it passed through a rectangular grid, which generated a nearly homogeneous and nearly isotropic turbulent flow. As the shock wave exited the open end of the shock tube, a system of expansion waves was generated which traveled upstream and interacted with the grid-generated turbulence; a type of interaction free from streamline curvature effects, which cause additional effects on turbulence. In this experiment, wall pressure, total pressure and velocity were measured indicating a clear reduction in fluctuations. The incoming flow at Mach number 0.46 was expanded to a flow with Mach number 0.77 by an applied mean shear of 100 s−1. Although the strength of the generated expansion waves was mild, the effect on damping fluctuations on turbulence was clear. A reduction of in the level of total pressure fluctuations by 20 per cent was detected in the present experiments.

scholarly journals Numerical study of pressure and velocity fluctuations in nearly isotropic turbulence

1978 ◽  
Vol 88 (4) ◽  
pp. 685-709 ◽  
Author(s):  
U. Schumann ◽  
G. S. Patterson
Keyword(s):  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Numerical Study ◽  
Pressure Fluctuations ◽  
Reynolds Numbers ◽  
Companion Paper ◽  
Real Space ◽  
Pressure Gradients ◽  
Velocity Statistics ◽  
Decaying Turbulence

The spectral method of Orszag & Patterson has been extended to calculate the static pressure fluctuations in incompressible homogeneous decaying turbulence at Reynolds numbers Reλ [lsim ] 35. In real space 323 points are treated. Several cases starting from different isotropic initial conditions have been studied. Some departure from isotropy exists owing to the small number of modes at small wavenumbers. Root-mean-square pressure fluctuations, pressure gradients and integral length scales have been evaluated. The results agree rather well with predictions based on velocity statistics and on the assumption of normality. The normality assumption has been tested extensively for the simulated fields and found to be approximately valid as far as fourth-order velocity correlations are concerned. In addition, a model for the dissipation tensor has been proposed. The application of the present method to the study of the return of axisymmetric turbulence to isotropy is described in the companion paper.

scholarly journals Turbulence decay in the density-stratified intracluster medium

2019 ◽  
Vol 487 (1) ◽  
pp. 1072-1081 ◽  
Author(s):  
Xun Shi ◽  
Congyao Zhang
Keyword(s):  
Mach Number ◽  
Gravitational Potential ◽  
Energy Flow ◽  
Density Fluctuation ◽  
Isotropic Turbulence ◽  
Density Stratification ◽  
Intracluster Medium ◽  
Energy Evolution ◽  
Homogeneous Isotropic Turbulence ◽  
Number Relation

Abstract Turbulence evolution in a density-stratified medium differs from that of homogeneous isotropic turbulence described by the Kolmogorov picture. We evaluate the degree of this effect in the intracluster medium (ICM) with hydrodynamical simulations. We find that the buoyancy effect induced by ICM density stratification introduces qualitative changes to the turbulence energy evolution, morphology, and the density fluctuation–turbulence Mach number relation, and likely explains the radial dependence of the ICM turbulence amplitude as found previously in cosmological simulations. A new channel of energy flow between the kinetic and the potential energy is opened up by buoyancy. When the gravitational potential is kept constant with time, this energy flow leaves oscillations to the energy evolution, and leads to a balanced state of the two energies where both asymptote to power-law time evolution with slopes shallower than that for the turbulence kinetic energy of homogeneous isotropic turbulence. We discuss that the energy evolution can differ more significantly from that of homogeneous isotropic turbulence when there is a time variation of the gravitational potential. Morphologically, ICM turbulence can show a layered vertical structure and large horizontal vortical eddies in the central regions with the greatest density stratification. In addition, we find that the coefficient in the linear density fluctuation–turbulence Mach number relation caused by density stratification is in general a variable with position and time.

Experimental investigation of turbulent density fluctuations and noise generation from heated jets

2007 ◽  
Vol 591 ◽  
pp. 73-96 ◽  
Author(s):  
J. PANDA
Keyword(s):  
Rayleigh Scattering ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Correlation Coefficients ◽  
Density Fluctuations ◽  
Frequency Noise ◽  
Noise Sources ◽  
Plume Temperature ◽  
Jet Velocity ◽  
Temperature Constant

Low-frequency noise sources in heated single-stream jets were identified by cross-correlating turbulent density fluctuations ρ′ with the far-field sound pressure fluctuations p′. The turbulent density fluctuations were measured by a molecular Rayleigh-scattering technique. For a fixed jet velocity Uj, the normalized correlation coefficient 〈ρ′; p′〉/(ρ′rmsp′rms is found to increase progressively with an increase in the plume temperature (subscript rms stands for root-mean-square). The result indicates an improvement of the noise radiation efficiency with heating. Directly measured noise spectra from fixed velocity jets with increasing temperature ratio show confusing trends. However, if such spectra are normalized by theplume density, then a consistent trend of increasing noise level with increased plume temperature emerges. The increased noise is the most prominent at the low-frequency end, consistent with the correlation data. The effect of increasing jet velocity keeping the plume temperature constant was also studied. The correlation coefficients were found to improve significantly with velocity; a result consistent with prior observation from unheated jets. Additional findings on the time-averaged density variations and the changes in the air density fluctuations with increasing plume temperature are also discussed.

scholarly journals Radar cross sections for mesospheric echoes at Jicamarca

2009 ◽  
Vol 27 (7) ◽  
pp. 2675-2684 ◽  
Author(s):  
G. A. Lehmacher ◽  
E. Kudeki ◽  
A. Akgiray ◽  
L. Guo ◽  
P. Reyes ◽  
...  
Keyword(s):  
Cross Sections ◽  
Isotropic Turbulence ◽  
Solar Proton ◽  
Thin Layers ◽  
Turbulence Theory ◽  
Homogeneous Isotropic Turbulence ◽  
Radar Cross Sections ◽  
Order Of Magnitude ◽  
Summer Echoes ◽  
Thick Layers

Abstract. Radar cross sections (RCS) of mesospheric layers at 50 MHz observed at Jicamarca, Peru, range from 10−18 to 10−16 m−1, three orders of magnitudes smaller than cross sections reported for polar mesospheric winter echoes during solar proton events and six orders of magnitude smaller than polar mesospheric summer echoes. Large RCS are found in thick layers around 70 km that also show wide radar spectra, which is interpreted as turbulent broadening. For typical atmospheric and ionospheric conditions, volume scattering RCS for stationary, homogeneous, isotropic turbulence at 3 m are also in the range 10−18 to 10−16 m−1, in reasonable agreement with measurements. Moreover, theory predicts maximum cross sections around 70 km, also in agreement with observations. Theoretical values are still a matter of order-of-magnitude estimation, since the Bragg scale of 3 m is near or inside the viscous subrange, where the form of the turbulence spectrum is not well known. In addition, steep electron density gradients can increase cross-sections significantly. For thin layers with large RCS and narrow spectra, isotropic turbulence theory fails and scattering or reflection from anisotropic irregularities may gain relevance.

scholarly journals Turbulence in nearly incompressible fluids: density spectrum, flows, correlations and implication to the interstellar medium

2005 ◽  
Vol 12 (1) ◽  
pp. 139-148 ◽  
Author(s):  
S. Dastgeer ◽  
G. P. Zank
Keyword(s):  
Interstellar Medium ◽  
Pressure Fluctuations ◽  
Thermal Fluctuation ◽  
Passive Scalar ◽  
Density Fluctuations ◽  
Density Spectrum ◽  
Electron Density Fluctuations ◽  
Nonlinear Fluid ◽  
Solar Wind Electron

Abstract. Interstellar scintillation and angular radio wave broadening measurements show that interstellar and solar wind (electron) density fluctuations exhibit a Kolmogorov-like k-5/3 power spectrum extending over many decades in wavenumber space. The ubiquity of the Kolmogorov-like interstellar medium (ISM) density spectrum led to an explanation based on coupling incompressible magnetohydrodynamic (MHD) fluctuations to density fluctuations through a "pseudosound" relation within the context of "nearly incompressible" (NI) hydrodynamics (HD) and MHD models. The NI theory provides a fundamentally different explanation for the observed ISM density spectrum in that the density fluctuations can be a consequence of passive scalar convection due to background incompressible fluctuations. The theory further predicts generation of long-scale structures and various correlations between the density, temperature and the (magneto) acoustic as well as convective pressure fluctuations in the compressible ISM fluids in different thermal regimes that are determined purely by the thermal fluctuation level. In this paper, we present the results of our two dimensional nonlinear fluid simulations, exploring various nonlinear aspects that lead to inertial range ISM turbulence within the context of a NI hydrodymanics model. In qualitative agreement with the NI predictions and the in-situ observations, we find that i) the density fluctuations exhibit a Kolmogorov-like spectrum via a passive convection in the field of the background incompressible fluctuations, ii) the compressible ISM fluctuations form long scale flows and structures, and iii) the density and the temperature fluctuations are anti-correlated.

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