Hydrodynamic Grid Research Articles

SIMULATION OF A WELL JET PUMP WORKING PROCESS

A mathematical model of the movement of the working flow in the flow part of the jet pump was developed based on the use of a radial function of a complex variable with a shifted leakage center. According to the accepted model, the working fluid radially asymmetrically exits from the displaced leakage center in all directions. The distance to the center of the leak has an inverse effect on the rate of spread of the working fluid. The offset turn of the radial function allows you to take into account the misalignment of the working nozzle and the mixing chamber due to poor manufacturing of jet pump parts. The vector of the complex potential with a shifted origin is defined as the difference of vectors whose origin is at the center of coordinates, and the endpoints characterize the initial and final positions of the shifted function. Using the equation of the potential of velocities and the stream function, the relationship for the complex potential of the plane-radial and spatial working flow with one-way and two-way displacement of the leakage center is obtained. The kinematic picture of the movement of the working medium is determined by a spatial hydrodynamic grid formed by equipotential surfaces and flow surfaces of leakage functions, which has the form of orthogonally placed coaxial spheres and radial meridional planes. The leakage displacement determines the deviation of the axis of the working nozzle from the axis of the displacement chamber of the jet pump. It is established that the velocity profiles of the radial flow with a displaced leak lose their similarity and the series of kinematic curves cannot be replaced by a single dimensionless dependence that would determine the flow kinematics regardless of the distance between the leak point and the inlet cross- section of the mixing chamber of the jet pump. The displacement of the leakage center has an inverse effect on the radial flow rate and decreases with increasing distance to the mixing chamber. As the value of the leakage displacement increases, the asymmetry of the velocity profile increases and its unevenness increases. Superimposition of the obtained characteristic function of the asymmetric radial flow and the vortex function of the complex variable allows to determine the structure of the mixed flow equation when simulating the rotation process of the jet pump in the well.

The function of coefficients of added mass of water

The hydrodynamic effect of the water mass of the reservoir on the pressure face of the dam can be determined from the function of the coefficient of the added mass of water obtained in the Westergard solution. For an inclined pressure face, the design standards introduce a correction factor, which is recommended to be taken into account until the slope of the pressure face does not exceed 150; there are no such recommendations for earth dams, however, in the calculations of seismic resistance of earth dams, taking into account hydrodynamic water pressure is also important. Theoretically, the values of the coefficients of the added mass of water can be determined based on the numerical solution of the Laplace equation in the computational domain with given boundary conditions and the graphical-analytical construction of a hydrodynamic grid. Thus, in the MATLAB environment, computational schemes were built for different laying of the pressure head of the dam in the range from vertical to flat with laying 1:3, and orthogonal hydrodynamic grids were built, reflecting the solution of the Laplace equations concerning the functions of pressure and velocity potentials. For all problems, diagrams of the coefficients of the added mass of water are constructed, and they are compared with the Westergaard analytical solution. For practical use in the work, all solutions for constructing diagrams of the coefficients of the added mass of water are presented in the form of a nomogram.

Experimental research on the determination of the filtration characteristic on the base of low-pressure hydraulic engineering constructions on complex multi-layer ground

In this study, the issue of studying the filtration flow characteristics of hydraulic engineering constructions designed by building a hydrodynamic grid for the filtration flow area using the method of electrohydrodynamic similarity is considered. Given there is complexity and diversity of filtration deformation problems in base of hydraulic engineering constructions, we conduct experimental studies to determine the filtration flow characteristics in base of low-pressure hydraulic engineering constructions in a special model to determine the overall picture and qualitative assessment of these processes. Before observing the filtration deformation processes in the construction soil, the filtration coefficients of the soils in the soil were determined using the Darcy device. The purpose of determining the filtration coefficients of soils is the importance of using the value obtained in the laboratory under experimental work. Based on the experimental studies, graphs of the average filtration flow rate and specific flow rate depending on the water pressure were constructed. The theoretical results obtained were compared with existing analytical methods.

A local tensor type artificial viscosity for two-dimensional Lagrangian staggered grid hydrodynamics

We present a new local tensor type artificial viscosity for two-dimensional Lagrangian staggered grid hydrodynamics. The subcell viscous force is constructed in a manner that ensures dissipation of kinetic energy for the Cartesian coordinate system. Two types of viscosity limiting methods are proposed utilizing the reconstructed velocity gradient at nodal point. The new viscosity has the merit of damping mesh instabilities such as the hourglass and chevron null modes, which is in common with the Riemann problem based artificial viscosity proposed by N. Morgan et al. (2014) [25]. In contrast to the latter, the new viscous force would vanish in case the associated velocity jump corresponds to expansion and so that little dissipation error is produced in the computation of a rarefaction wave. The accuracy and robustness of the new viscosity is demonstrated via a series of benchmark tests.

EDGE: a new approach to suppressing numerical diffusion in adaptive mesh simulations of galaxy formation

ABSTRACT We introduce a new method to mitigate numerical diffusion in adaptive mesh refinement (AMR) simulations of cosmological galaxy formation, and study its impact on a simulated dwarf galaxy as part of the ‘EDGE’ project. The target galaxy has a maximum circular velocity of $21\, \mathrm{km}\, \mathrm{s}^{-1}$ but evolves in a region that is moving at up to $90\, \mathrm{km}\, \mathrm{s}^{-1}$ relative to the hydrodynamic grid. In the absence of any mitigation, diffusion softens the filaments feeding our galaxy. As a result, gas is unphysically held in the circumgalactic medium around the galaxy for $320\, \mathrm{Myr}$, delaying the onset of star formation until cooling and collapse eventually triggers an initial starburst at z = 9. Using genetic modification, we produce ‘velocity-zeroed’ initial conditions in which the grid-relative streaming is strongly suppressed; by design, the change does not significantly modify the large-scale structure or dark matter accretion history. The resulting simulation recovers a more physical, gradual onset of star formation starting at z = 17. While the final stellar masses are nearly consistent ($4.8 \times 10^6\, \mathrm{M}_{\odot }$ and $4.4\times 10^6\, \mathrm{M}_{\odot }$ for unmodified and velocity-zeroed, respectively), the dynamical and morphological structure of the z = 0 dwarf galaxies are markedly different due to the contrasting histories. Our approach to diffusion suppression is suitable for any AMR zoom cosmological galaxy formation simulations, and is especially recommended for those of small galaxies at high redshift.

Sensitivity study on the main tidal constituents of the Gulf of Tonkin by using the frequency-domain tidal solver in T-UGOm

Abstract. Consequences of tidal dynamics on hydro-sedimentary processes are a recurrent issue in estuarine and coastal processes studies, and accurate tidal solutions are a prerequisite for modeling sediment transport, especially in macro-tidal regions. The motivation for the study presented in this publication is to implement and optimize a model configuration that will satisfy this prerequisite in the frame of a larger objective in order to study the sediment dynamics and fate from the Red River Delta to the Gulf of Tonkin from a numerical hydrodynamical–sediment coupled model. Therefore, we focus on the main tidal constituents to conduct sensitivity experiments on the bathymetry and bottom friction parameterization. The frequency-domain solver available in the hydrodynamic unstructured grid model T-UGOm has been used to reduce the computational cost and allow for wider parameter explorations. Tidal solutions obtained from the optimal configuration were evaluated from tide measurements derived from satellite altimetry and tide gauges; the use of an improved bathymetry dataset and fine friction parameter adjustment significantly improved our tidal solutions. However, our experiments seem to indicate that the solution error budget is still dominated by bathymetry errors, which is the most common limitation for accurate tidal modeling.

An Exact Semi-Inverse Solution for the Family of Geophysical Problems of a Draining Slope

One of the main causes of the appearance of dangerous geophysical slope phenomena is water saturation of slopes and the negative hydrodynamic impact of a stream of underground waters on them. In this work, an exact semi-inverse hydromechanical solution for a family of geophysical problems of a draining slope is obtained based on the theory of functions of a complex variable. Using the method of consecutive conformal mappings, an analytical interrelation between areas of complex potential and N.E. Zhukovskii’s complex is established. The interrelation allows one to determine all the necessary parameters of the filtration area. An example of calculation with the determination of aquifuge lines, seepage area, depression surface, and lines of flow and equipotential lines with construction of an orthogonal and quadratic hydrodynamic grid of the filtration flow seeping the draining slope is presented. A short estimate of the filtration effect on the suffusion and landslide stability of the soil body of the draining slope is given.

Multidimensional Staggered Grid Residual Distribution Scheme for Lagrangian Hydrodynamics

We present the second-order multidimensional Staggered Grid Hydrodynamics Residual Distribution (SGH RD) scheme for Lagrangian hydrodynamics. The SGH RD scheme is based on the staggered finite element discretizations as in [Dobrev et al., SISC, 2012]. However, the advantage of the residual formulation over classical FEM approaches consists in the natural mass matrix diagonalization which allows one to avoid the solution of the linear system with the global sparse mass matrix while retaining the desired order of accuracy. This is achieved by using Bernstein polynomials as finite element shape functions and coupling the space discretization with the deferred correction type timestepping method. Moreover, it can be shown that for the Lagrangian formulation written in non-conservative form, our residual distribution scheme ensures the exact conservation of the mass, momentum and total energy. In this paper we also discuss construction of numerical viscosity approximations for the SGH RD scheme allowing to reduce the dissipation of the numerical solution. Thanks to the generic formulation of the staggered grid residual distribution scheme, it can be directly applied to both single- and multimaterial and multiphase models. Finally, we demonstrate computational results obtained with the proposed residual distribution scheme for several challenging test problems.

Type II migration strikes back – an old paradigm for planet migration in discs

ABSTRACT In this paper, we analyse giant gap-opening planet migration in proto-planetary discs, focusing on the type II migration regime. According to standard type II theory, planets migrate at the same rate as the gas in the disc, as they are coupled to the disc viscous evolution; however, recent studies questioned this paradigm, suggesting that planets migrate faster than the disc material. We study the problem through 2D long-time simulations of systems consistent with type II regime, using the hydrodynamical grid code fargo3d. Even though our simulations confirm the presence of an initial phase characterized by fast migration, they also reveal that the migration velocity slows down and eventually reaches the theoretical prediction if we allow the system to evolve for enough time. We find the same tendency to evolve towards the theoretical predictions at later times when we analyse the mass flow through the gap and the torques acting on the planet. This transient is related to the initial conditions of our (and previous) simulations, and is due to the fact that the shape of the gap has to adjust to a new profile, once the planet is set into motion. Secondly, we test whether the type II theory expectation that giant planet migration is driven by viscosity is consistent with our simulation by comparing simulations with the same viscosity and different disc masses (or vice versa). We find a good agreement with the theory, since when the discs are characterized by the same viscosity, the migration properties are the same.

Modeling the process of oil displacement by a heat carrier considering the capillary effect

The manuscript is aimed at improving the mathematical model of oil production in a heterogeneous environment with the use of a thermal mode of displacement considering the action of capillary effect. We have constructed an algorithm to solve numerically the respective nonlinear boundary value problem on multiphase filtering by introducing the function of quasi-potential and the respective, conjugated thereto, flow function . In this case, the quasi-potential is represented in the form thereby having essentially simplified the overall strategy to split the algorithm for solving the original problem.Owing to the algorithm, which is based on the ideas of methods for quasiconformal mapping and staged registration of parameters, we have carried out calculations of the hydrodynamic grid, velocity fields, temperature, saturation, taking into consideration the impact of a capillary effect and when ignoring it. In particular, the charts of saturation fields demonstrate a difference in the ratio of percentage content of a displacing fluid up to 15 % at temperatures above 80 °C, which explains the effect of capillary forces. Instead, at temperatures from 50 °С to 70 °С the difference is not noticeable, though at 50 °С and below the results of flooding slightly differ (to 5 %) for the worse in terms of the actual representation of the process. In this case, it is believed that the dynamic viscosities of phases change with a change in temperature, the fluid movement is slow and occurs without phase transitions, while functions of relative phase permeabilities and capillary pressure are the known and unambiguous saturation functions.Numerical calculations of multiphase non-isothermal filtering in the symmetry element at a five-point system of flooding have been presented. In this case, it was found that taking into account the capillary effect makes it possible to not only predict the location of stagnant zones, but also to more accurately estimate the time when a displacing reagent breaks through in an operational well in order to effectively perform respective waterproofing operations.

The Origins of Protostellar Core Angular Momenta

Abstract We present the results of a suite of numerical simulations designed to explore the origin of the angular momenta of protostellar cores. Using the hydrodynamic grid code Athena with a sink implementation, we follow the formation of protostellar cores and protostars (sinks) from the subvirial collapse of molecular clouds on larger scales to investigate the range and relative distribution of core properties. We find that the core angular momenta are relatively unaffected by large-scale rotation of the parent cloud; instead, we infer that angular momenta are mainly imparted by torques between neighboring mass concentrations and exhibit a log-normal distribution. Our current simulation results are limited to size scales ∼0.05 pc (∼104 au), but serve as first steps toward the ultimate goal of providing initial conditions for higher-resolution studies of core collapse to form protoplanetary disks.

Retrograde binaries of massive black holes in circumbinary accretion discs

We explore the hardening of a massive black hole binary embedded in a circum-binary gas disc when the binary and the gas are coplanar and the gas is counter-rotating. The secondary black hole, revolving in the direction opposite to the gas, experiences a drag from gas-dynamical friction and from direct accretion of part of it. Using two-dimensional (2D) hydrodynamical grid simulations we investigate the effect of changing the accretion prescriptions on the dynamics of the secondary black hole which in turn affect the binary hardening and eccentricity evolution. We find that realistic accretion prescriptions lead to results that differ from those inferred assuming accretion of all the gas within the Roche Lobe of the secondary black hole. Different accretion prescriptions result in different disc's surface densities which alter the black hole's dynamics back. Full 3D SPH realizations of a number of representative cases, run over a shorter interval of time, validate the general trends observed in the less computationally demanding 2D simulations. Initially circular black hole binaries increase only slightly their eccentricity which then oscillates around small values (<0.1) while they harden. By contrast, initially eccentric binaries become more and more eccentric. A semi-analytical model describing the black hole's dynamics under accretion only explores the late evolution stages of the binary in an otherwise unperturbed retrograde disc to illustrate how eccentricity evolves with time in relation to the shape of the underlying surface density distribution.

Simulation Model and Characteristics of the Cavitation Mixer with Hydrodynamic Grid

A promising method for obtaining homogeneous and high-dispersion emulsion is to create mixers with cavitation treatment of the mixed stream. The present research examines the hydrodynamic constant-flow mixer with a grid made of smooth cylinders as the agitator of cavitation. The authors offer a simulation model of a mixer based on hydrodynamic equations and experimental data of cavitation phenomena in the vortex wake of a cylinder. There has been considered and analyzed the characteristic of the cavitation mixer, which shows the relationship between relative loss of the total stream pressure, the grid geometrical parameter, the Reynolds number, and coefficients of hydraulic resistance of flow-part elements. It is shown that for every Reynolds number and a set of resistance coefficients there is optimum value of a grid geometrical parameter when losses of total pressure are minimum. The experimental characteristic of the mixer which shows correlation between minimum relative stream pressure loss and grid geometrical parameter is revealed. A simulation model and characteristics allow one to develop a hydrodynamic mixer with a minimum power consumption.

Grid independence behaviour of fluidized bed reactor simulations using the Two Fluid Model: Detailed parametric study

This short communication builds on previous work on the grid independence behaviour of the Two Fluid Model in reactive bubbling fluidized bed simulations. Regarding hydrodynamic grid independence behaviour (the numerical accuracy with which phase segregation was resolved), the particle relaxation time was confirmed as being directly proportional to the cell size achieving sufficiently grid independent behaviour. This relationship held over different particle sizes, particle densities, gas densities, gas viscosities and drag laws, but the slope of the proportionality changed for particle relaxation times above 0.4. For reactive grid independence behaviour (the numerical accuracy with which reactor performance was resolved), the relationship between the particle relaxation time and the sufficiently grid independent cell size was more complex, depending not only on the resolution of phase segregation, but also on the kinetic rate implemented and on the permeability of the emulsion phase. Simple and practical rules of thumb were proposed for estimating the sufficiently grid independent cell size for hydrodynamic and reactive simulations. For most practical purposes, the simpler and more accurate hydrodynamic grid independent cell size correlation can safely be used to run sufficiently accurate bubbling fluidized bed reactor simulations.

Analyzing the physics of non-tidal barotropic sea level anomaly events using multi-scale numerical modelling in Singapore regional waters

The hydrodynamic flows in the Singapore regional waters (SRW) are the result of a complex mix of tide, seasonal and meteorological effects. The study of non-tidal effects or sea level anomalies (SLA) in this region has shown that it is possible to model some of these anomalies. The present study addresses the non-tidal barotropic water levels and currents in the Singapore region in detail. This analysis includes a multi-scale approach, and addresses amongst others hydrodynamic model grid resolution and the importance of resolving non-linear tide–surge interaction. The results show that the water level and current anomalies phenomena in a complex region like SRW can be effectively modelled using an approach combining non-tidal barotropic and multi-scale numerical modelling. A detailed investigation of the levels of non-linear tide–surge interaction is carried out by simulating SLA events in the Singapore regional waters during North-East (positive SLA) and South-West (negative SLA) monsoons based on ECMWF numerical weather forcing conditions. The results of combining both approaches suggest that the finer grid resolution improves the accuracy of water level and current anomalies simulations. Furthermore, the results also indicate that for the simulations of non-tidal barotropic flows in this area, non-linear tide–surge interaction is important and should be taken into account. Finally, the behaviour of the non-tidal barotropic flow in the region and its changes with tidal variation in the shallow region of the Singapore Strait is now much better understood. Therefore, for reliable operational forecast of sea level, the inclusion of non-linear tide–surge interaction should be required in numerical models to reproduce both tides and surges with improved accuracy in this region.

Satellite-derived Digital Elevation Model (DEM) selection, preparation and correction for hydrodynamic modelling in large, low-gradient and data-sparse catchments

• SRTM DEM had higher accuracy than ASTER GDEM. • Vegetation smoothed DEM improved the hydrodynamic model results. • Hydrologically-corrected DEM improved the hydrodynamic model results. • The hydrodynamic model reached optimum performance at grid size of 120 m. Digital Elevation Models (DEMs) that accurately replicate both landscape form and processes are critical to support modelling of environmental processes. Topographic accuracy, methods of preparation and grid size are all important for hydrodynamic models to efficiently replicate flow processes. In remote and data-scarce regions, high resolution DEMs are often not available and therefore it is necessary to evaluate lower resolution data such as the Shuttle Radar Topography Mission (SRTM) and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) for use within hydrodynamic models. This paper does this in three ways: (i) assessing point accuracy and geometric co-registration error of the original DEMs; (ii) quantifying the effects of DEM preparation methods (vegetation smoothed and hydrologically-corrected) on hydrodynamic modelling relative accuracy; and (iii) quantifying the effect of the hydrodynamic model grid size (30–2000 m) and the associated relative computational costs (run time) on relative accuracy in model outputs. We initially evaluated the accuracy of the original SRTM (∼30 m) seamless C-band DEM (SRTM DEM) and second generation products from the ASTER (ASTER GDEM) against registered survey marks and altimetry data points from the Ice, Cloud, and land Elevation Satellite (ICESat). SRTM DEM (RMSE = 3.25 m,) had higher accuracy than ASTER GDEM (RMSE = 7.43 m). Based on these results, the original version of SRTM DEM, the ASTER GDEM along with vegetation smoothed and hydrologically corrected versions were prepared and used to simulate three flood events along a 200 km stretch of the low-gradient Thompson River, in arid Australia (using five metrics: peak discharge, peak height, travel time, terminal water storage and flood extent). The hydrologically corrected DEMs performed best across these metrics in simulating floods compared with vegetation smoothed DEMs and original DEMs. The response of model performance to grid size was non-linear and while the smaller grid sizes (⩽120 m) improved the hydrodynamic model results, these offered only slight improvements at very significant computational costs compared to grid size of 120 m, with grid sizes 250 m and greater decreasing in model accuracy. This study highlights the important impact that the quality of the underlying DEM has, and in particular how sensitive hydrodynamic models are to preparation methods and how important vegetation smoothing and hydrological correction of the base topographic data for modelling floods in low-gradient and multi-channel environments.

A coupling alternative to reactive transport simulations for long-term prediction of chemical reactions in heterogeneous CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; storage systems

Abstract. Fully coupled, multi-phase reactive transport simulations of CO2 storage systems can be approximated by a simplified one-way coupling of hydrodynamics and reactive chemistry. The main characteristics of such systems, and hypotheses underlying the proposed alternative coupling, are (i) that the presence of CO2 is the only driving force for chemical reactions and (ii) that its migration in the reservoir is only marginally affected by immobilisation due to chemical reactions. In the simplified coupling, the exposure time to CO2 of each element of the hydrodynamic grid is estimated by non-reactive simulations and the reaction path of one single batch geochemical model is applied to each grid element during its exposure time. In heterogeneous settings, analytical scaling relationships provide the dependency of velocity and amount of reactions to porosity and gas saturation. The analysis of TOUGHREACT fully coupled reactive transport simulations of CO2 injection in saline aquifer, inspired to the Ketzin pilot site (Germany), both in homogeneous and heterogeneous settings, confirms that the reaction paths predicted by fully coupled simulations in every element of the grid show a high degree of self-similarity. A threshold value for the minimum concentration of dissolved CO2 considered chemically active is shown to mitigate the effects of the discrepancy between dissolved CO2 migration in non-reactive and fully coupled simulations. In real life, the optimal threshold value is unknown and has to be estimated, e.g. by means of 1-D or 2-D simulations, resulting in an uncertainty ultimately due to the process de-coupling. However, such uncertainty is more than acceptable given that the alternative coupling enables using grids of the order of millions of elements, profiting from much better description of heterogeneous reservoirs at a fraction of the calculation time of fully coupled models.

A [formula omitted] dimensional viscous hydrodynamic code for relativistic heavy ion collisions

We describe the details of 3+1 dimensional relativistic hydrodynamic code for the simulations of quark–gluon/hadron matter expansion in ultra-relativistic heavy ion collisions. The code solves the equations of relativistic viscous hydrodynamics in the Israel–Stewart framework. With the help of ideal–viscous splitting, we keep the ability to solve the equations of ideal hydrodynamics in the limit of zero viscosities using a Godunov-type algorithm. Milne coordinates are used to treat the predominant expansion in longitudinal (beam) direction effectively. The results are successfully tested against known analytical relativistic inviscid and viscous solutions, as well as against existing 2+1D relativistic viscous code. Program summaryProgram title: vHLLECatalogue identifier: AETZ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETZ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 13825No. of bytes in distributed program, including test data, etc.: 92750Distribution format: tar.gzProgramming language: C++.Computer: any with a C++ compiler and the CERN ROOT libraries.Operating system: tested on GNU/Linux Ubuntu 12.04 x64 (gcc 4.6.3), GNU/Linux Ubuntu 13.10 (gcc 4.8.2), Red Hat Linux 6 (gcc 4.4.7).RAM: scales with the number of cells in hydrodynamic grid; 1900 Mbytes for 3D 160×160×100 grid.Classification: 1.5, 4.3, 12.External routines: CERN ROOT (http://root.cern.ch), Gnuplot (http://www.gnuplot.info/) for plotting the results.Nature of problem:relativistic hydrodynamical description of the 3-dimensional quark–gluon/hadron matter expansion in ultra-relativistic heavy ion collisions.Solution method:finite volume Godunov-type method.Running time:scales with the number of hydrodynamic cells; typical running times on Intel(R) Core(TM) i7-3770 CPU @ 3.40 GHz, single thread mode, 160×160×100 grid and p=ε/3 EoS (setup discussed in Sec. 4.4):7.6 sec/timestep for ideal hydro evolution;15.7 sec/timestep for viscous hydro evolution;37 sec/timestep for tabulated EoS and ideal hydro evolution.

A NEW DENSITY VARIANCE–MACH NUMBER RELATION FOR SUBSONIC AND SUPERSONIC ISOTHERMAL TURBULENCE

The probability density function (PDF) of the gas density in subsonic and supersonic, isothermal, driven turbulence is analyzed with a systematic set of hydrodynamical grid simulations with resolutions up to 1024^3 cells. We performed a series of numerical experiments with root mean square (r.m.s.) Mach number M ranging from the nearly incompressible, subsonic (M=0.1) to the highly compressible, supersonic (M=15) regime. We study the influence of two extreme cases for the driving mechanism by applying a purely solenoidal (divergence-free) and a purely compressive (curl-free) forcing field to drive the turbulence. We find that our measurements fit the linear relation between the r.m.s. Mach number and the standard deviation of the density distribution in a wide range of Mach numbers, where the proportionality constant depends on the type of the forcing. In addition, we propose a new linear relation between the standard deviation of the density distribution and the standard deviation of the velocity in compressible modes, i.e. the compressible component of the r.m.s. Mach number. In this relation the influence of the forcing is significantly reduced, suggesting a linear relation between the standard deviation of the density distribution and the standard deviation of the velocity in compressible modes, independent of the forcing, ranging from the subsonic to the supersonic regime.

Turbulence in the ICM from mergers, cool-core sloshing, and jets: results from a new multi-scale filtering approach

We have designed a simple multi-scale method that identifies turbulent motions in hydrodynamical grid simulations. The method does not assmume ant a-priori coherence scale to distinguish laminar and turbulent flows. Instead, the local mean velocity field around each cell is reconstructed with a multi-scale filtering technique, yielding the maximum scale of turbulent eddies by means of iterations. The method is robust, fast and easily applicable to any grid simulation. We present here the application of this technique to the study of spatial and spectral properties of turbulence in the intra cluster medium, measuring turbulent diffusion and anisotropy of the turbulent velocity field for a variety of driving mechanisms: a) accretion of matter in galaxy clusters (simulated with ENZO); b) sloshing motions around cool-cores (simulated with FLASH); c) jet outflows from active galactic nuclei, AGN (simulated with FLASH). The turbulent velocities driven by matter accretion in galaxy clusters are mostly tangential in the inner regions (inside the cluster virial radius) and isotropic in regions close to the virial radius. The same is found for turbulence excited by cool core sloshing, while the jet outflowing from AGN drives mostly radial turbulence motions near its sonic point and beyond. Turbulence leads to a diffusivity in the range =10^29-10^30 cm^2/s in the intra cluster medium. On average, the energetically dominant mechanism of turbulence driving in the intra cluster medium is represented by accretion of matter and major mergers during clusters evolution.