Density-velocity Correlations Research Articles

The effects of non-linearity on the growth rate constraint from velocity correlation functions

ABSTRACT The two-point statistics of the cosmic velocity field, measured from galaxy peculiar velocity (PV) surveys, can be used as a dynamical probe to constrain the growth rate of large-scale structures in the Universe. Most works use the statistics on scales down to a few tens of Megaparsecs, while using a theoretical template based on the linear theory. In addition, while the cosmic velocity is volume-weighted, the observable line-of-sight velocity two-point correlation is density-weighted, as sampled by galaxies, and therefore the density–velocity correlation term also contributes, which has often been neglected. These effects are fourth order in powers of the linear density fluctuation $\delta _{\rm L}^4$, compared to $\delta _{\rm L}^2$ of the linear velocity correlation function, and have the opposite sign. We present these terms up to $\delta _{\rm L}^4$ in real space based on the standard perturbation theory, and investigate the effect of non-linearity and the density–velocity contribution on the inferred growth rate fσ8, using N-body simulations. We find that for a next-generation PV survey of volume $\sim {\cal O}(500 \, h^{-1} \, {\rm Mpc})^3$, these effects amount to a shift of fσ8 by ∼10 per cent and is comparable to the forecasted statistical error when the minimum scale used for parameter estimation is $r_{\rm min} = 20 \, h^{-1} \, {\rm Mpc}$.

A priori tests of subgrid-scale models in an anisothermal turbulent channel flow at low mach number

The subgrid-scale modelling of a low Mach number strongly anisothermal turbulent flow is investigated using direct numerical simulations. The study is based on the filtering of the low Mach number equations, suited to low Mach number flows with highly variable fluid properties. The results are relevant to formulations of the filtered low Mach number equations established with the classical filter or the Favre filter. The two most significant subgrid terms of the filtered low Mach number equations are considered. They are associated with the momentum convection and the density-velocity correlation. We focus on eddy-viscosity and eddy-diffusivity models. Subgrid-scale models from the literature are analysed and two new models are proposed. The subgrid-scale models are compared to the exact subgrid term using the instantaneous flow field of the direct numerical simulation of a strongly anisothermal fully developed turbulent channel flow. There is no significant differences between the use of the classical and Favre filter regarding the performance of the models. We suggest that the models should take into account the asymptotic near-wall behaviour of the filter length. Eddy-viscosity and eddy-diffusivity models are able to represent the energetic contribution of the subgrid term but not its effect in the flow governing equations. The AMD and scalar AMD models are found to be in better agreement with the exact subgrid terms than the other investigated models in the a priori tests.

A posteriori tests of subgrid-scale models in strongly anisothermal turbulent flows

This paper studies the large-eddy simulation of anisothermal low Mach number turbulent channel flows. We consider the large-eddy simulations of the low Mach number equations in two formulations, the velocity formulation and the Favre formulation. In both formulations, we investigate the subgrid-scale modeling of the two most significant subgrid terms of the filtered low Mach number equations: the momentum convection subgrid term and the density-velocity correlation subgrid term. To this end, the predictions of large-eddy simulations implementing the models are compared to filtered direct numerical simulations. We address several types of subgrid-scale models: functional eddy-viscosity or eddy-diffusivity models, structural models, tensorial models, and dynamic versions of these models. For the momentum convection subgrid term, we recommend the use of the scale-similarity model and the constant-parameter or dynamic tensorial anisotropic minimum-dissipation (AMD) model. For the density-velocity correlation subgrid term, several models are able to improve temperature-related statistics, for instance, the AMD model and the scale-similarity model. More accurate results are obtained with the Favre formulation than with the velocity formulation.

Measuring the filamentary structure of interstellar clouds through wavelets

Context.The ubiquitous presence of filamentary structures in the interstellar medium asks for an unbiased characterization of their properties including a stability analysis.Aims.We propose a novel technique to measure the spectrum of filaments in any two-dimensional data set. By comparing the power in isotropic and anisotropic structures we can measure the relative importance of spherical and cylindrical collapse modes.Methods.Using anisotropic wavelets we can quantify and distinguish local and global anisotropies and measure the size distribution of filaments. The wavelet analysis does not require any assumptions on the alignment or shape of filaments in the maps, but directly measures their typical spatial dimensions. In a rigorous test program, we calibrate the scale dependence of the method and test the angular and spatial sensitivity. We apply the method to molecular line maps from magneto-hydrodynamic (MHD) simulations and observed column-density maps fromHerschelobservations.Results.When applying the anisotropic wavelet analysis to the MHD data, we find that the observed filament sizes depend on the combination of magnetic-field-dominated density–velocity correlations and radiative transfer effects. This can be exploited by observing tracers with different optical depth to measure the transition from a globally ordered large-scale structure to small-scale filaments with entangled field lines. The unbiased view toHerschelcolumn-density maps does not confirm a universal characteristic filament width. The map of the Polaris Flare shows an almost scale-free filamentary spectrum up to the size of the dominating filament of about 0.4 pc. For the Aquila molecular cloud the range of filament widths is limited to 0.05–0.2 pc. The filaments in Polaris show no preferential direction in contrast to the global alignment that we trace in Aquila.Conclusions.By comparing the power in isotropic and anisotropic structures we can measure the relative importance of spherical and cylindrical collapse modes and their spatial distribution.

A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation

The explicit algebraic Reynolds stress model of Wallin and Johansson [J. Fluid Mech. 403, 89 (2000)] is extended to compressible and variable-density turbulent flows. This is achieved by correctly taking into account the influence of the mean dilatation on the rapid pressure-strain correlation. The resulting model is formally identical to the original model in the limit of constant density. For two-dimensional mean flows the model is analyzed and the physical root of the resulting quartic equation is identified. Using a fixed-point analysis of homogeneously sheared and strained compressible flows, we show that the new model is realizable, unlike the previous model. Application of the model together with a K − ω model to quasi one-dimensional plane nozzle flow, transcending from subsonic to supersonic regime, also demonstrates realizability. Negative “dilatational” production of turbulence kinetic energy competes with positive “incompressible” production, eventually making the total production negative during the spatial evolution of the nozzle flow. Finally, an approach to include the baroclinic effect into the dissipation equation is proposed and an algebraic model for density-velocity correlations is outlined to estimate the corrections associated with density fluctuations. All in all, the new model can become a significant tool for CFD (computational fluid dynamics) of compressible flows.

Statistics of velocity centroids: effects of density-velocity correlations and non-Gaussianity

We continue with our previous work on statistics of velocity centroids, to retrieve information about the scaling properties of an underlying turbulent velocity field from spectroscopic observations. We use synthetic data sets with extreme effects of velocity-density correlations that we create artificially, which also have a non-Gaussian distribution of fluctuations. We confirm that centroids can be used to obtain the scaling properties of the turbulent velocity when the ratio of the density dispersion to the mean density is less than unity, regardless of velocity-density correlations and non-Gaussianity. It was found that extreme velocity-density correlations can distort the statistics of velocity centroids, impeding the recovery of the turbulent velocity spectral index from centroids. We show that such correlations introduce high-order moments to the maps of centroids, which we disregarded in previous work, but that they are only important when the density dispersion is large in comparison with the mean density. It was also found that non-Gaussian velocity and/or density distort the statistics of centroids too, but to a lower degree than extreme cross-correlations.

On the Use of Fractional Brownian Motion Simulations to Determine the Three‐dimensional Statistical Properties of Interstellar Gas

Based on fractional Brownian motion (fBm) simulations of three-dimensional gas density and velocity fields, we present a study of the statistical properties of spectroimagery observations (channel maps, integrated emission, and line centroid velocity) in the case of an optically thin medium at various temperatures. The power spectral index ?W of the integrated emission is confirmed to be that of the three-dimensional density field (?n) provided that the medium's depth is at least of the order of the largest transverse scale in the image, and the power spectrum of the centroid velocity map is found to have the same index ?C as that of the velocity field (?v). Further tests with non-fBm density and velocity fields show that this last result holds and is not modified by the effects of density-velocity correlations. A comparison is made with the theoretical predictions of Lazarian & Pogosyan.

Turbulence modulation in jet diffusion flames: Modeling and experiments

Turbulence in a diffusion flame is modulated by thermal expansion, buoyancy effects and lift-off. Aside from simple shear-generated sources density-velocity correlations, π′u ″ i represent additional source terms in the Reynolds-stress equations that distort the shear-generated turbulence anisotropy. A modeled transport equation and several zero-order models of π′u ″ i are analyzed and their effect on flame predictions with a Favre averaged second-order moment closure for velocity and scalar transport is investigated. The chemical reaction is described by chemical equilibrium and laminar flamelet modeling. The latter is shown to have limitations in application due to differential diffusion. Two attached, vertical H 2/N 2-air flames with the same Reynolds numbers but different Froude numbers are investigated numerically and experimentally. The desired data base for an overall comparison is provided by comprehensive 3D-LDV, coherent anti-Stokes Raman spectroscopy and spontaneous Raman spectroscopy measurements. The calculations yield correct results in all measured profiles of velocity, temperature and species concentrations. It is shown that only one zero-order model and the transport equation of π′u ″ i are adequate. The neglect of those terms will falsify the prediction of decay rates, fluctuations and flame shapes. The magnitude of errors depends on the local Froude number which decreases downstream. The increase in the influence of buoyancy leads to smaller decay rates of axial velocity and to enhanced scalar mixing. Furthermore, turbulence intensities are reduced, and scalar fluctuations and anisotropy are enlarged. The experimentally observed visible flame length shortening with decreasing, density weighted Froude number is reproduced by the presented model.

Validation of a k- ε model based on `experimental results in a thermally stable stratified turbulent boundary layer

A 2D ( k- ε) turbulence model was developed for use with dilatable flows at high Reynolds numbers. A new approach relative to the modelling of the density-velocity correlation term is proposed, and a relation concerning the Prandtl turbulent number was used taking into account both the wall and gravity effects. This model was validated by experimental results obtained at the E.C.L. Fluid Mechanics and Acoustics laboratory on a stable thermally stratified turbulent boundary layer developing at a quickly cooled smooth boundary surface.

Measurement of scalar-velocity correlations in a turbulent diffusion flame

Simultaneous measurements of scattered light intensity and axial velocity have been made in a turbulent hydrogen diffusion flame in a co-flowing stream with accelerating and decelerating pressure gradients. The light-scatter signal obtained from the seeded nozzle fluid is used as a measure of hydrogen element concentration, and is processed to derive records of density and mixture fraction which are correlated in digitized form with the simultaneously recorded streamwise velocity component. Results reported here include the mean and r.m.s. fluctuation of the streamwise velocity component and the density and correlations of the streamwise velocity component with the mixture fraction and the density as well as other correlations and Favre or density weighted averages. It is shown that the density velocity correlation is only large enough to make a few percent difference between the Favre and conventional mean velocities but that such correlations are important in the determination of the excess momentum flux. Correlations between velocity and mixture fraction are comparable with those found in isothermal flow but change sign where the excess velocity changes sign. The correlation between density and velocity shows similar behaviour and is shown to have a significant effect on the turbulent kinetic energy balance.

Prediction of turbulent diffusion flames with a four-equation turbulence model

For turbulent flame prediction a four-equation turbulence model consisting of the turbulent kinetic energy, the dissipation rate and the density-velocity correlations using unweighted statistics is suggested. The fluctuating concentrations are taken into account by using Spalding's (1971) equation for the variance of the mixture fraction f and by defining the probability density function of f as beta-function. The thermodynamic model for the combustion of H 2 with air assumes infinitely fast reaction in a global single step. Preliminary results are shown for the calculation of Kent and Bilger (1972) turbulent H 2-air diffusion flame. For this flame with fluctuating density the inclusion of the velocity-density correlations appears to be essential, because they have a strong effect especially on the development of the turbulent viscosity and the mean velocity and mass fraction profiles. Consequently the mean concentrations are in good agreement with the experimental results.