Density-weighted Velocity Research Articles

Turbulence, thermal pressure, and their dynamical effects on cosmic baryonic fluid

ABSTRACT We employ the IllustrisTNG simulation data to investigate the turbulent and thermal motions of the cosmic baryonic fluid. With continuous wavelet transform techniques, we define the pressure spectra, or density-weighted velocity power spectra, as well as the spectral ratios, for both turbulent and thermal motions. We find that the magnitude of the turbulent pressure spectrum grows slightly from $z=4$ to 2 and increases significantly from $z=2$ to 1 at large scales, suggesting progressive turbulence injection into the cosmic fluid, whereas from $z=1$ to 0, the spectrum remains nearly constant, indicating that turbulence may be balanced by energy transfer and dissipation. The magnitude of the turbulent pressure spectra also increases with environmental density, with the highest density regions showing a turbulent pressure up to six times that of thermal pressure. We also explore the dynamical effects of turbulence and thermal motions, discovering that while thermal pressure provides support against structure collapse, turbulent pressure almost counteracts this support, challenging the common belief that turbulent pressure supports gas against overcooling.

Cosmological Parameter Constraints from the SDSS Density and Momentum Power Spectra

We extract the galaxy density and momentum power spectra from a subset of early-type galaxies in the Sloan Digital Sky Survey (SDSS) DR7 main galaxy catalog. Using galaxy distance information inferred from the improved fundamental plane described in Yoon and Park, we reconstruct the peculiar velocities of the galaxies and generate number density and density-weighted velocity fields, from which we extract the galaxy density and momentum power spectra. We compare the measured values to the theoretical expectation of the same statistics, assuming an input Λ cold dark matter (CDM) model and using a third-order perturbative expansion. After validating our analysis pipeline with a series of mock data sets, we apply our methodology to the SDSS data and arrive at constraints and at a mean redshift . Our result is consistent with the Planck cosmological best-fit parameters for the ΛCDM model. The momentum power spectrum is found to be strongly contaminated by small-scale velocity dispersion, which suppresses power by on intermediate scales k ∼ 0.05 h Mpc−1.

Assessment of the mixing-limited hypothesis with first-principles simulation results

Starting with two well-tested, one-dimensional models of non-evaporating, mixing-limited sprays, governing equations for liquid mass and two-phase momentum for each model can be manipulated to reveal the formal similarity between momentum and liquid volume fraction. The consequence of this similarity is that momentum, when properly non-dimensionalized, is equal to the liquid volume fraction at any time and at any axial location within a non-evaporating, mixing-limited spray with a constant rate of injection. An alternative, the more well-known similarity between mass fraction and velocity, is also mathematically evident. We compare predictions of this mathematical analysis to high-fidelity, first-principles simulation results of a non-evaporating spray to assess the validity of the theoretical similarity. The analysis of the simulation not only confirms the mathematical derivations but also points to subtlety in the definition of the spray velocity. In particular, the density-weighted velocity is required to observe similarity. The requirement of density-weighted velocity means that similarity tests require knowledge of both phase velocities. The agreement also works to confirm that the first-principles simulations are indeed mixing-limited, despite the finite nature of domain size and resolution.

Optimal Location of Exit Doors for Efficient Evacuation of Crowds at Gathering Places

This work deals with the optimal design for the location of the exit doors at meeting places (such as sports centers, public squares, street markets, transport stations, etc.) to guarantee a safer emergency evacuation in events of a sporting, social, entertainment or religious type. This problem is stated as an optimal control problem of nonlinear partial differential equations, where the state system is a reformulation of the Hughes model (coupling the eikonal equation for a density-weighted walking velocity of pedestrians and the continuity equation for conservation of the pedestrian density), the control is the location of the exit doors at the domain boundary (subject to several geometric constraints), and the cost function is related to the evacuation rate. We provide a full numerical algorithm for solving the problem (a finite element technique for the discretization and a gradient-free procedure for the optimization), and show several numerical results for a realistic case.

Redshift space power spectrum beyond Einstein-de Sitter kernels

We develop a framework to compute the redshift space power spectrum (PS), with kernels beyond Einstein-de Sitter (EdS), that can be applied to a wide variety of generalized cosmologies. We build upon a formalism that was recently employed for standard cosmology in Chen, Vlah & White (2020), and utilize an expansion of the density-weighted velocity moment generating function that explicitly separates the magnitude of the k-modes and their angle to the line-of-sight direction dependencies. We compute the PS for matter and biased tracers to 1-loop Perturbation Theory (PT) and show that the expansion has a correct infrared and ultraviolet behavior, free of unwanted divergences. We also add Effective Field Theory (EFT) counterterms, necessary to account for small-scale contributions to PT, and employ an IR-resummation prescription to properly model the smearing of the BAO due to large scale bulk flows within Standard-PT. To demonstrate the applicability of our formalism, we apply it on the ΛCDM and the Hu-Sawicki f(R) models, and compare our numerical results against the elephant suite of N-body simulations, finding very good agreement up to k = 0.27 Mpc-1 h at z = 0.5 for the first three non-vanishing Legendre multipoles of the PS. To our knowledge, the model presented in this work is the most accurate theoretical EFT-PT for modified gravity to date, being the only one that accounts for beyond linear local biasing in redshift-space. Hence, we argue our RSD modeling is a promising tool to construct theoretical templates in order to test deviations from ΛCDM using real data obtained from the next stage of cosmological surveys such as DESI and LSST.

Wide-angle effects for peculiar velocities

ABSTRACT The line-of-sight peculiar velocities of galaxies contribute to their observed redshifts, breaking the translational invariance of galaxy clustering down to a rotational invariance around the observer. This becomes important when the line-of-sight direction varies significantly across a survey, leading to what are known as ‘wide-angle’ effects in redshift-space distortions. Wide-angle effects will also be present in measurements of the momentum field, i.e. the galaxy density-weighted velocity field, in upcoming peculiar velocity surveys. In this work, we study how wide-angle effects modify the predicted correlation function and power spectrum for momentum statistics, both in autocorrelation and in cross-correlation with the density field. Using both linear theory and the Zel'dovich approximation, we find that deviations from the plane-parallel limit are large and could become important in data analysis for low-redshift surveys. We point out that even multipoles in the cross-correlation between density and momentum are non-zero regardless of the choice of line of sight, and therefore contain new cosmological information that could be exploited. We discuss configuration space, Fourier space, and spherical analyses; providing exact expressions in each case rather than relying on an expansion in small angles. We hope these expressions will be of use in the analysis of upcoming surveys for redshift-space distortions and peculiar velocities.

The exergy concept and compressible turbulence

Turbulence models facilitated by Kolmogorov’s theory play an important role for compressible flows. Typically the basis of these models is the power spectrum of the velocity $${\mathbf {u}}$$ or of the density-weighted velocity $${\mathbf {w}}\equiv \rho ^{1/3}{\mathbf {u}}$$ . While for incompressible flow the quantity turbulent kinetic energy characterises turbulent motions, from the thermodynamic point of view, due to fluctuations of the density and the temperature other kinds of energies play a role at the different scales in compressible turbulence. We generalise the power spectrum of the velocity $${\mathbf {u}}$$ from incompressible flows to compressible flows by introducing the exergy spectrum as an application of the exergy concept. Furthermore, we discuss the application of the concept of turbulent exergy to turbulence modelling and demonstrate this approach with a direct numerical simulation and a Large-Eddy-Simulation of homogeneous isotropic turbulence. The advantage of turbulence modelling based on turbulent exergy is shown on the example of the Approximate Deconvolution Model (ADM) where, at smallest scales for its newly introduced entropy formulation, more available energy is extracted from the flow, and this occurs in a more physical way than for the classical equation set of the model using the total energy.

Intrinsic alignment statistics of density and velocity fields at large scales: Formulation, modeling, and baryon acoustic oscillation features

The kinematic Sunyaev-Zel'dovich effect enables us to directly probe the density-weighted velocity field up to very large cosmic scales. We investigate the effects of intrinsic alignments (IAs) of dark-matter halo shapes on cosmic density and velocity fields on such large scales. In the literature IAs have been detected up to $\sim 100~h^{-1}{\rm Mpc}$ using the gravitational shear-intrinsic ellipticity correlation and the alignment correlation function. In this paper we introduce the corresponding various velocity statistics: the (density-weighted) velocity-intrinsic ellipticity correlation as well as the alignment pairwise infall momentum, momentum correlation function, and density-weighted pairwise velocity dispersion. We derive theoretical expressions for these velocity alignment statistics for the first time based on the assumption that the density fluctuation is a Gaussian random field. Using large-volume, high-resolution $N$-body simulations, we measure the alignment statistics of density and velocity fields. The behaviors of IAs in the velocity statistics are similar to those in the density statistics, except that the halo orientations are aligned with the velocity field up to scales larger than those with the density field, $r\gg 100~h^{-1}{\rm Mpc}$, because of a factor of the wave number in the linear relation between the density and velocity fields in Fourier space, $v\propto \delta/k$. We show that the detected IAs of the velocity field can be well predicted by the linear alignment model. We also demonstrate that the baryon acoustic oscillation features can be detected in both the conventional and alignment velocity statistics. Our results indicate that observations of IAs with the velocity field on large scales can provide additional information on cosmological models, complementary to those with the density field.

The redshift-space momentum power spectrum – II. Measuring the growth rate from the combined 2MTF and 6dFGSv surveys

ABSTRACTMeasurements of the growth rate of structure, fσ8, in the low-redshift Universe allow stringent tests of the cosmological model. In this work, we provide new constraints on fσ8 at an effective redshift of z = 0.03 using the combined density and velocity fields measured by the 2MTF and 6dFGSv surveys. We do this by applying a new estimator of the redshift-space density and momentum (density-weighted velocity) power spectra, developed in the first paper of this series, to measured redshifts and peculiar velocities from these data sets. We combine this with models of the density and momentum power spectra in the presence of complex survey geometries and with an ensemble of simulated galaxy catalogues that match the survey selection functions and galaxy bias. We use these simulations to estimate the errors on our measurements and identify possible systematics. In particular, we are able to identify and remove biases caused by the non-Gaussianity of the power spectra by applying the Box-Cox transformation to the power spectra prior to fitting. After thorough validation of our methods we recover a constraint of $f\sigma _8(z_{\mathrm{eff}}=0.03)=0.404^{+0.082}_{-0.081}$ from the combined 2MTF and 6dFGSv data. This measurement is fully consistent with the expectations of general relativity and the Λ cold dark matter cosmological model. It is also comparable and complementary to constraints using different techniques on similar data, affirming the usefulness of our method for extracting cosmology from velocity fields.

Stratified Kelvin–Helmholtz turbulence of compressible shear flows

Abstract. We study scaling laws of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin–Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16 3842) and three-dimensional (with a spatial resolution of 5123) configurations utilizing different compressibility characteristics such as shocks. For three-dimensional turbulence, we find that both the kinetic energy and density-weighted energy spectra follow the classical Kolmogorov k-5/3 inertial scaling. This phenomenon is observed due to the fact that the power density spectrum of three-dimensional turbulence yields the same k-5/3 scaling. However, we demonstrate that there is a significant difference between these two spectra in two-dimensional turbulence since the power density spectrum yields a k-5/3 scaling. This difference may be assumed to be a reason for the k-7/3 scaling observed in the two-dimensional density-weight kinetic every spectra for high compressibility as compared to the k−3 scaling traditionally assumed with incompressible flows. Further inquiries are made to validate the statistical behavior of the various configurations studied through the use of the Helmholtz decomposition of both the kinetic velocity and density-weighted velocity fields. We observe that the scaling results are invariant with respect to the compressibility parameter when the density-weighted definition is used. Our two-dimensional results also confirm that a large inertial range of the solenoidal component with the k−3 scaling can be obtained when we simulate with a lower compressibility parameter; however, the compressive spectrum converges to k−2 for a larger compressibility parameter.

Vorticity statistics based on velocity and density-weighted velocity in premixed reactive turbulence

ABSTRACTThe local and non-local statistics of vorticity (i.e. curl of velocity vector ) and pseudo-vorticity (i.e. curl of density-weighted velocity vector ) have been investigated in detail based on a direct numerical simulation (DNS) database of freely propagating statistically planar flames in different regimes of premixed turbulent combustion. It has been found that the relative orientation of can be significantly different to that of for small values of the Karlovitz number and large values of the Reynolds number. The vorticity shows, depending on the case, considerable alignment with either the most extensive or compressive principal strain rate. In contrast, has been found to align with the intermediate principal strain rate for all cases. The transport statistics of Reynolds averaged enstrophy (i.e. ) and pseudo-enstrophy (i.e. ) have been investigated in detail. The non-local vorticity statistics in turbulent premixed combustion have been investigated based on the vorticity line segment (VLS) structure, which is defined with respect to each grid point as the part of the (pseudo) vorticity line bounded by the two adjacent extremal points of the (pseudo) vorticity magnitude. VLS can be characterised by the segment length and the (pseudo) vorticity magnitude difference across the segment, i.e. (Δω*) Δω. Strong dilatation effects tend to increase VLS length, whereas turbulent convection disturbs the flow field resulting in shorter VLS. The joint PDFs between the segment length and (Δω) Δω* are found to be symmetric, whereas the joint PDFs between the segment length and the pseudo-vorticity magnitude difference across the VLS in the flame normal direction show significant asymmetry, which is primarily determined by density variation across the flame front and turbulence intensity.

Understanding redshift space distortions in density-weighted peculiar velocity

Observations of the kinetic Sunyaev-Zel'dovich (kSZ) effect measure the density-weighted velocity field, a potentially powerful cosmological probe. This paper presents an analytical method to predict the power spectrum and two-point correlation function of the density-weighted velocity in redshift space, the direct observables in kSZ surveys. We show a simple relation between the density power spectrum and the density-weighted velocity power spectrum that holds for both dark matter and halos. Using this relation, we can then extend familiar perturbation expansion techniques to the kSZ power spectrum. One of the most important features of density-weighted velocity statistics in redshift space is the change in sign of the cross-correlation between the density and density-weighted velocity at mildly small scales due to nonlinear redshift space distortions. Our model can explain this characteristic feature without any free parameters. As a result, our results can precisely predict the non-linear behavior of the density-weighted velocity field in redshift space up to ∼ 30 h−1 Mpc for dark matter particles at the redshifts of z=0.0, 0.5, and 1.0.

Powerful radiative jets in supercritical accretion discs around non-spinning black holes

We describe a set of simulations of super-critical accretion onto a non-rotating supermassive BH. The accretion flow is radiation pressure dominated and takes the form of a geometrically thick disk with twin low-density funnels around the rotation axis. For accretion rates $\gtrsim 10 \dot M_{\rm Edd}$, there is sufficient gas in the funnel to make this region optically thick. Radiation from the disk first flows into the funnel, after which it accelerates the optically thick funnel gas along the axis. The resulting jet is baryon-loaded and has a terminal density-weighted velocity $\approx 0.3c$. Much of the radiative luminosity is converted into kinetic energy by the time the escaping gas becomes optically thin. For an observer viewing down the axis, the isotropic equivalent luminosity of total energy is as much as $10^{48}\,\rm erg\,s^{-1}$ for a $10^7 M_\odot$ BH accreting at $10^3$ Eddington. Therefore, energetically, the simulated jets are consistent with observations of the most powerful tidal disruption events, e.g., Swift J1644. The jet velocity is, however, too low to match the Lorentz factor $\gamma > 2$ inferred in J1644. There is no such conflict in the case of other tidal disruption events. Since favorably oriented observers see isotropic equivalent luminosities that are highly super-Eddington, the simulated models can explain observations of ultra-luminous X-ray sources, at least in terms of luminosity and energetics, without requiring intermediate mass black holes. Finally, since the simulated jets are baryon-loaded and have mildly relativistic velocities, they match well the jets observed in SS433. The latter are, however, more collimated than the simulated jets. This suggests that, even if magnetic fields are not important for acceleration, they may perhaps still play a role in confining the jet.

Streamline segment statistics of premixed flames with nonunity Lewis numbers.

The interaction of flame and surrounding fluid motion is of central importance in the fundamental understanding of turbulent combustion. It is demonstrated here that this interaction can be represented using streamline segment analysis, which was previously applied in nonreactive turbulence. The present work focuses on the effects of the global Lewis number (Le) on streamline segment statistics in premixed flames in the thin-reaction-zones regime. A direct numerical simulation database of freely propagating thin-reaction-zones regime flames with Le ranging from 0.34 to 1.2 is used to demonstrate that Le has significant influences on the characteristic features of the streamline segment, such as the curve length, the difference in the velocity magnitude at two extremal points, and their correlations with the local flame curvature. The strengthenings of the dilatation rate, flame normal acceleration, and flame-generated turbulence with decreasing Le are principally responsible for these observed effects. An expression for the probability density function (pdf) of the streamline segment length, originally developed for nonreacting turbulent flows, captures the qualitative behavior for turbulent premixed flames in the thin-reaction-zones regime for a wide range of Le values. The joint pdfs between the streamline length and the difference in the velocity magnitude at two extremal points for both unweighted and density-weighted velocity vectors are analyzed and compared. Detailed explanations are provided for the observed differences in the topological behaviors of the streamline segment in response to the global Le.

A Kolmogorov-like exact relation for compressible polytropic turbulence

AbstractCompressible hydrodynamic turbulence is studied under the assumption of a polytropic closure. Following Kolmogorov, we derive an exact relation for some two-point correlation functions in the asymptotic limit of a high Reynolds number. The inertial range is characterized by: (i) a flux term implying in particular the enthalpy; and (ii) a purely compressible term $\mathcal{S}$ which may act as a source or a sink for the mean energy transfer rate. At subsonic scales, we predict dimensionally that the isotropic $k^{-5/3}$ energy spectrum for the density-weighted velocity field ($\rho ^{1/3} \boldsymbol {v}$), previously obtained for isothermal turbulence, is modified by a polytropic contribution, whereas at supersonic scales $\mathcal{S}$ may impose another scaling depending on the polytropic index. In both cases, it is shown that the fluctuating sound speed is a key ingredient for understanding polytropic compressible turbulence.

On the universality of supersonic turbulence

Compressible turbulence shapes the structure of the interstellar medium of our Galaxy and likely plays an important role also during structure formation in the early Universe. The density PDF and the power spectrum of such compressible, supersonic turbulence are the key ingredients for theories of star formation. However, both the PDF and the spectrum are still a matter of debate, because theoretical predictions are limited and simulations of supersonic turbulence require enormous resolutions to capture the inertial-range scaling. To advance our limited knowledge of compressible turbulence, we here present and analyse the world's largest simulations of supersonic turbulence. We compare hydrodynamic models with numerical resolutions of 256^3-4096^3 mesh points and with two distinct driving mechanisms, solenoidal (divergence-free) driving and compressive (curl-free) driving. We find convergence of the density PDF, with compressive driving exhibiting a much wider and more intermittent density distribution than solenoidal driving. Analysing the power spectrum of the turbulence, we find a pure velocity scaling close to Burgers turbulence with P(v) k^(-2) for both driving modes in our hydrodynamical simulations with Mach = 17. The spectrum of the density-weighted velocity rho^(1/3)v, however, does not provide the previously suggested universal scaling for supersonic turbulence. We find that the power spectrum P(rho^(1/3)v) scales with wavenumber as k^(-1.74) for solenoidal driving, close to incompressible Kolmogorov turbulence, k^(-5/3), but is significantly steeper with k^(-2.10) for compressive driving. We show that this is consistent with a recent theoretical model for compressible turbulence that predicts P(rho^(1/3)v) k^(-19/9) in the presence of a strong div(v) component as is produced by compressive driving and remains remarkably constant throughout the supersonic turbulent cascade.

Equation of motion for a sphere in non-uniform compressible flows

AbstractLinearized viscous compressible Navier–Stokes equations are solved for the transient force on a spherical particle undergoing unsteady motion in an inhomogeneous unsteady ambient flow. The problem is formulated in a reference frame attached to the particle and the force contributions from the undisturbed ambient flow and the perturbation flow are separated. Using a density-weighted velocity transformation and reciprocal relation, the total force is first obtained in the Laplace domain and then transformed to the time domain. The total force is separated into the quasi-steady, inviscid unsteady, and viscous unsteady contributions. The above rigorously derived particle equation of motion can be considered as the compressible extension of the Maxey–Riley–Gatignol equation of motion and it incorporates interesting physics that arises from the combined effects of inhomogeneity and compressibility.

NUMERICAL SIMULATIONS OF DRIVEN RELATIVISTIC MAGNETOHYDRODYNAMIC TURBULENCE

A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging neutron stars, X-ray binaries, some supernovae, and the early universe. In order to elucidate the basic properties of the relativistic magnetohydrodynamical (RMHD) turbulence present in these systems, we present results from numerical simulations of fully developed driven turbulence in a relativistically warm, weakly magnetized and mildly compressible ideal fluid. We have evolved the RMHD equations for many dynamical times on a uniform grid with 1024^3 zones using a high order Godunov code. We observe the growth of magnetic energy from a seed field through saturation at about 1% of the total fluid energy. We compute the power spectrum of velocity and density-weighted velocity and conclude that the inertial scaling is consistent with a slope of -5/3. We compute the longitudinal and transverse velocity structure functions of order p up to 11, and discuss their possible deviation from the expected scaling for non-relativistic media. We also compute the scale-dependent distortion of coherent velocity structures with respect to the local magnetic field, finding a weaker scale dependence than is expected for incompressible non-relativistic flows with a strong mean field.

Reconstruction of neighboring plasma environment along a satellite path by a barotropic plasma model

We develop a barotropic plasma model for the reconstruction of steady two-dimensional magnetic and plasma fields based on the single-point measurements from a satellite along its path. The model can be accurately integrated numerically because it avoids certain numerical singularities and it also avoids an ill-conditioned mapping between plasma entropy and the density-weighted velocity stream function. Our barotropic plasma model is applied to investigate the structure and dynamics in a magnetic reconnection event reported previously. The resulting two-dimensional maps of plasma and field configurations show far more complex features than depicted in most schematics of magnetic reconnection sites. The complicated patterns contain significant changes in plasma flow directions on the reconstruction plane as well as highly structured plasma flows and magnetic compressions perpendicular to it.

Exact Relation for Correlation Functions in Compressible Isothermal Turbulence

Compressible isothermal turbulence is analyzed under the assumption of homogeneity and in the asymptotic limit of a high Reynolds number. An exact relation is derived for some two-point correlation functions which reveals a fundamental difference with the incompressible case. The main difference resides in the presence of a new type of term which acts on the inertial range similarly as a source or a sink for the mean energy transfer rate. When isotropy is assumed, compressible turbulence may be described by the relation -2/3ε(eff)r = F(r)(r), where F(r) is the radial component of the two-point correlation functions and ε(eff) is an effective mean total energy injection rate. By dimensional arguments, we predict that a spectrum in k(-5/3) may still be preserved at small scales if the density-weighted fluid velocity ρ(1/3)u is used.