Showing papers on "Turbulence published in 2007"

Hairpin vortex organization in wall turbulencea)

Abstract: Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.

Large-scale influences in near-wall turbulence

Abstract: Hot-wire data acquired in a high Reynolds number facility are used to illustrate the need for adequate scale separation when considering the coherent structure in wall-bounded turbulence. It is found that a large-scale motion in the log region becomes increasingly comparable in energy to the near-wall cycle as the Reynolds number increases. Through decomposition of fluctuating velocity signals, it is shown that this large-scale motion has a distinct modulating influence on the small-scale energy (akin to amplitude modulation). Reassessment of DNS data, in light of these results, shows similar trends, with the rate and intensity of production due to the near-wall cycle subject to a modulating influence from the largest-scale motions.

The Statistics of Supersonic Isothermal Turbulence

Abstract: We present results of large-scale three-dimensional simulations of supersonic Euler turbulence with the piecewise parabolic method and multiple grid resolutions up to 2048 3 points. Our numerical experiments describe non-magnetized driven turbulent o ws with an isothermal equation of state and an rms Mach number of 6. We discuss numerical resolution issues and demonstrate convergence, in a statistical sense, of the inertial range dynamics in simulations on grids larger than 512 3 points. The simulations allowed us to measure the absolute velocity scaling exponents for the rst time. The inertial range velocity scaling in this strongly compressible regime deviates substantially from the incompressible Kolmogorov laws. The slope of the velocity power spectrum, for instance, is -1:95 compared to -5=3 in the incompressible case. The exponent of the third-order velocity structure function is 1:28, while in incompressible turbulence it is known to be unity. We propose a natural extension of Kolmogorov’s phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the Kolmogorov scaling of the power spectrum and structure functions of the density-weighted velocity v 1=3 u. The low-order statistics of v appear to be invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of v v is -1:69, and the exponent of the third-order structure function of v v is unity. We also directly measure the mass dimension of the ifractali density distribution in the inertial subrange, Dm 2:4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology. Subject headings: hydrodynamics o instabilities o ISM: structure o methods: numerical o turbulence

Evaluation of Various Turbulence Models in Predicting Airflow and Turbulence in Enclosed Environments by CFD: Part 2—Comparison with Experimental Data from Literature

Abstract: Numerous turbulence models have been developed in the past two decades, and many of them can be used in predicting airflows and turbulence in enclosed environments. It is important to evaluate the generality and robustness of the turbulence models for various indoor airflow scenarios. This study evaluated the performance of eight turbulence models, potentially suitable for indoor airflow, in terms of accuracy and computing cost. These models cover a wide range of computational fluid dynamics (CFD) approaches, including Reynolds averaged Navier-Stokes (RANS) modeling, hybrid RANS and large-eddy simulation (or detached-eddy simulation [DES]), and large-eddy simulation (LES). The RANS turbulence models tested include the indoor zero-equation model, three two-equation models (the RNG k-∊, low Reynolds number k-∊, and SST k-ω models), a three-equation model ( model), and a Reynolds-stress model (RSM). The investigation tested these models for representative airflows in enclosed environments, such as forced con...

Review of atmospheric turbulence over cities

Abstract: This paper provides a comprehensive, critical review of turbulence observations over cities. More than fifty studies are analysed with their experimental conditions summarized in an appendix. The main results are based on 14 high-quality experiments which met criteria based on stringent experimental requirements. The observations are presented as non-dimensional statistics to facilitate comparison between urban studies and work conducted over other rough, inhomogeneous surfaces. Wake production associated with bluff bodies, and the inhomogeneous distribution of sources and sinks of scalars, result in a roughness sub-layer which for the studies reviewed extends to about 2.5 to 3 times the height of the buildings. It is shown that within this region the basis of several traditional micrometeorological approaches to describe the turbulent exchange is in doubt. There are strong similarities to flow over plant canopies, and many of the turbulence characteristics can be interpreted in the framework of a plane mixing layer. Future field observations should concentrate on the turbulent exchange near the top and within the urban canopy as well as within the urban boundary layer.

Turbulence transition in pipe flow

Abstract: Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile. Experiments on pipe flow, as well as plane Couette and plane Poiseuille flow, show that triggering turbulence depends sensitively on initial conditions, that between the laminar and the turbulent states there exists no intermediate state with simple spatial or temporal characteristics, and that turbulence is not persistent, i.e., it can decay again, if the observation time is long enough. All these features can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space. The goal of this review is to explain this concept, summarize the numerical and experimental evidence for pipe flow, and outline the consequences for related flows.

Air–Sea Exchange in Hurricanes: Synthesis of Observations from the Coupled Boundary Layer Air–Sea Transfer Experiment

Abstract: The Coupled Boundary Layer Air–Sea Transfer (CBLAST) field program, conducted from 2002 to 2004, has provided a wealth of new air–sea interaction observations in hurricanes. The wind speed range for which turbulent momentum and moisture exchange coefficients have been derived based upon direct flux measurements has been extended by 30% and 60%, respectively, from airborne observations in Hurricanes Fabian and Isabel in 2003. The drag coefficient (CD) values derived from CBLAST momentum flux measurements show CD becoming invariant with wind speed near a 23 m s−1 threshold rather than a hurricane-force threshold near 33 m s−1 . Values above 23 m s−1 are lower than previous open-ocean measurements. The Dalton number estimates (CE) derived from CBLAST moisture flux measurements are shown to be invariant with wind speeds up to 30 m s −1 which is in approximate agreement with previous measurements at lower winds. These observations imply a CE/CD ratio of approximately 0.7, suggesting that additional energy sour...

Protoplanetary Disk Turbulence Driven by the Streaming Instability: Nonlinear Saturation and Particle Concentration

Abstract: We present simulations of the nonlinear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag forces. We find that the initially laminar equilibrium flow spontaneously develops into turbulence in our unstratified local model. Marginally coupled solids (that couple to the gas on a Keplerian timescale) trigger an upward cascade to large particle clumps with peak overdensities above 100. The clumps evolve dynamically by losing material downstream to the radial drift flow while receiving recycled material from upstream. Smaller, more tightly coupled solids produce weaker turbulence with more transient overdensities on smaller length scales. The net inward radial drift is decreased for marginally coupled particles, whereas the tightly coupled particles migrate faster in the saturated turbulent state. The turbulent diffusion of solid particles, measured by their random walk, depends strongly on their stopping time and on the solids-to-gas ratio of the background state, but diffusion is generally modest, particularly for tightly coupled solids. Angular momentum transport is too weak and of the wrong sign to influence stellar accretion. Self-gravity and collisions will be needed to determine the relevance of particle overdensities for planetesimal formation.

Effective Inflow Conditions for Turbulence Models in Aerodynamic Calculations

Abstract: The selection of inflow values at boundaries far upstream of an aircraft is considered, for one- and two-equation turbulence models. Inflow values are distinguished from the ambient values near the aircraft, which may be much smaller. Ambient values should be selected first, and inflow values that will lead to them after the decay second; this is not always possible, especially for the time scale. The two-equation decay during the approach to the aircraft is shown; often, the time scale has been set too short for this decay to be calculated accurately on typical grids. A simple remedy for both issues is to impose floor values for the turbulence variables, outside the viscous sublayer, and it is argued that overriding the equations in this manner is physically justified. Selecting laminar ambient values is easy, if the boundary layers are to be tripped, but a more common practice is to seek ambient values that will cause immediate transition in boundary layers. This opens up a wide range of values, and selection criteria are discussed. The turbulent Reynolds number, or ratio of eddy viscosity to laminar viscosity has a huge dynamic range that makes it unwieldy; it has been widely mis-used, particularly by codes that set upper limits on it. The value of turbulent kinetic energy in a wind tunnel or the atmosphere is also of dubious value as an input to the model. Concretely, the ambient eddy viscosity must be small enough to preserve potential cores in small geometry features, such as flap gaps. The ambient frequency scale should also be small enough, compared with shear rates in the boundary layer. Specific values are recommended and demonstrated for airfoil flows

Large- and very-large-scale motions in channel and boundary-layer flows

Abstract: Large-scale motions (LSMs; having wavelengths up to 2–3 pipe radii) and very-LSMs (having wavelengths more than 3 pipe radii) have been shown to carry more than half of the kinetic energy and Reynolds shear stress in a fully developed pipe flow. Studies using essentially the same methods of measurement and analysis have been extended to channel and zero-pressure-gradient boundary-layer flows to determine whether large structures appear in these canonical wall flows and how their properties compare with that of the pipe flow. The very large scales, especially those of the boundary layer, are shorter than the corresponding scales in the pipe flow, but otherwise share a common behaviour, suggesting that they arise from similar mechanism(s) aside from the modifying influences of the outer geometries. Spectra of the net force due to the Reynolds shear stress in the channel and boundary layer flows are similar to those in the pipe flow. They show that the very-largescale and main turbulent motions act to decelerate the flow in the region above the maximum of the Reynolds shear stress.

In situ evidence of magnetic reconnection in turbulent plasma

Abstract: Magnetic reconnection is a universal process leading to energy conversion in plasmas1. It occurs in the Solar System2,3,4,5,6,7, in laboratory plasmas 8 and is important in astrophysics 9,10. Reconnection has been observed so far only at large-scale boundaries between different plasma environments 4,5,6,7,8. It is not known whether reconnection occurs and is important in turbulent plasmas where many small-scale boundaries can form. Solar11 and laboratory12 measurements as well as numerical simulations 13,14,15,16 indicate such possibility. Here we report, for the first time, in situ evidence of reconnection in a turbulent plasma. The turbulent environment is the solar wind downstream of the Earth’s bow shock. We show that reconnection is fast and electromagnetic energy is converted into heating and acceleration of particles. This has significant implications for laboratory and astrophysical plasmas where both turbulence and reconnection should be common.

A turbulent jet in crossflow analysed with proper orthogonal decomposition

Abstract: Detailed instantaneous velocity fields of a jet in crossflow have been measured with stereoscopic particle image velocimetry (PIV). The jet originated from a fully developed turbulent pipe flow and entered a crossflow with a turbulent boundary layer. The Reynolds number based on crossflow velocity and pipe diameter was 2400 and the jet to crossflow velocity ratios were R=3.3 and R=1.3. The experimental data have been analysed by proper orthogonal decomposition (POD). For R=3.3, the results in several different planes indicate that the wake vortices are the dominant dynamic flow structures and that they interact strongly with the jet core. The analysis identifies jet shear-layer vortices and finds that these vortical structures are more local and thus less dominant. For R=1.3, on the other hand, jet shear-layer vortices are the most dominant, while the wake vortices are much less important. For both cases, the analysis finds that the shear-layer vortices are not coupled to the dynamics of the wake vortices. Finally, the hanging vortices are identified and their contribution to the counter-rotating vortex pair (CVP) and interaction with the newly created wake vortices are described.

Turbulent convection in stellar interiors. I. Hydrodynamic simulation

Abstract: We describe the results of 3D numerical simulations of oxygen shell burning and hydrogen core burning in a 23 M☉ stellar model. A detailed comparison is made to stellar mixing-length theory (MLT) for the shell-burning model. Simulations in 2D are significantly different from 3D, in terms of both flow morphology and velocity amplitude. Convective mixing regions are better predicted using a dynamic boundary condition based on the bulk Richardson number than by purely local, static criteria like Schwarzschild or Ledoux. MLT gives a good description of the velocity scale and temperature gradient for shell convection; however, there are other important effects that it does not capture, mostly related to the dynamical motion of the boundaries between convective and nonconvective regions. There is asymmetry between upflows and downflows, so the net kinetic energy flux is not zero. The motion of convective boundaries is a source of gravity waves; this is a necessary consequence of the deceleration of convective plumes. Convective overshooting is best described as an elastic response by the convective boundary, rather than ballistic penetration of the stable layers by turbulent eddies. The convective boundaries are rife with internal and interfacial wave motions, and a variety of instabilities arise that induce mixing through a process best described as turbulent entrainment. We find that the rate at which material entrainment proceeds at the boundaries is consistent with analogous laboratory experiments and simulation and observation of terrestrial atmospheric mixing. In particular, the normalized entrainment rate E = uE/σH is well described by a power-law dependence on the bulk Richardson number RiB = ΔbL/σ for the conditions studied, 20 RiB 420. We find E = ARi, with best-fit values log A = 0.027 ± 0.38 and n = 1.05 ± 0.21. We discuss the applicability of these results to stellar evolution calculations.

Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium.

Abstract: We report the observation of dynamo action in the von Karman sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R-m similar to 30. A mean magnetic field of the order of 40 G is observed 30\% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.

Compressible turbulence in galaxy clusters: physics and stochastic particle re-acceleration

Abstract: We attempt to explain the non-thermal emission arising from galaxy clusters as a result of the re-acceleration of electrons by compressible turbulence induced by cluster mergers. On the basis of the available observational facts we put forward a simplified model of turbulence in clusters of galaxies focusing our attention on the compressible motions. In our model intracluster medium (ICM) is represented by a high-beta plasma in which turbulent motions are driven at large scales. The corresponding injection velocities are higher than the Alfven velocity. As a result, the turbulence is approximately isotropic up to the scale at which the turbulent velocity gets comparable with the Alfven velocity. These motions are most important for the energetic particle acceleration, but at the same time they are subjected to most of the plasma damping. Under the hypothesis that turbulence in the ICM is highly super-Alfvenic the magnetic field is passively advected and the field lines are bended on scales smaller than that of the classical, unmagnetized, ion-ion mean free path. This affects ion diffusion and the strength of the effective viscosity. Under these conditions the bulk of turbulence in hot (5-10 keV temperature) galaxy clusters is likely to be dissipated at collisionless scales via resonant coupling with thermal and fast particles. We use collisionless physics to derive the amplitude of the different components of the energy of the compressible modes, and review and extend the treatment of plasma damping in the ICM. We calculate the acceleration of both protons and electrons taking into account both transit time damping acceleration and non-resonant acceleration by large-scale compressions. We find that relativistic electrons can be re-accelerated in the ICM up to energies of several GeV provided that the rms velocity of the compressible turbulent-eddies is (V L /c s ) 2 ≈ 0.15-0.3; c s is the sound speed in the ICM. We find that under typical conditions ≈2-5 per cent of the energy flux of the cascading of compressible motions injected at large scales goes into the acceleration of fast particles and that this may explain the observed non-thermal emission from merging galaxy clusters.

A quarter-century of H-mode studies

Abstract: The H-mode is a confinement mode of toroidal plasmas, which may make the goals of fusion possible—the development of a clean energy source at competitive electricity costs. The most challenging aspect of the H-mode physics is the sudden disappearance of the edge turbulence whereas its driving forces—the gradients—increase. As the physics behind the H-mode is subtle many features are not yet clarified. There is, however, substantial experimental and theoretical evidence that turbulent flows, which normally limit the confinement, are diminished by sheared poloidal flow residing at the plasma edge. There are many conceivable mechanisms giving rise to sheared flow. The most intriguing of these is that fluctuations themselves induce the flow, which acts back to its generating origin and annihilates the turbulence. This review concentrates mostly on the transition physics, describes one line of understanding the H-mode in more detail, recalls some of the older observations and summarizes the achievements in the H-mode for both tokamaks and stellarators. (Some figures in this article are in colour only in the electronic version)

Protoplanetary Disk Turbulence Driven by the Streaming Instability: Non-Linear Saturation and Particle Concentration

Abstract: We present simulations of the non-linear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag forces. We find that the initially laminar equilibrium flow spontaneously develops into turbulence in our unstratified local model. Marginally coupled solids (that couple to the gas on a Keplerian time-scale) trigger an upward cascade to large particle clumps with peak overdensities above 100. The clumps evolve dynamically by losing material downstream to the radial drift flow while receiving recycled material from upstream. Smaller, more tightly coupled solids produce weaker turbulence with more transient overdensities on smaller length scales. The net inward radial drift is decreased for marginally coupled particles, whereas the tightly coupled particles migrate faster in the saturated turbulent state. The turbulent diffusion of solid particles, measured by their random walk, depends strongly on their stopping time and on the solids-to-gas ratio of the background state, but diffusion is generally modest, particularly for tightly coupled solids. Angular momentum transport is too weak and of the wrong sign to influence stellar accretion. Self-gravity and collisions will be needed to determine the relevance of particle overdensities for planetesimal formation.

Large-scale features in turbulent pipe and channel flows

Abstract: In recent years there has been significant progress made towards understanding the large-scale structure of wall-bounded shear flows. Most of this work has been conducted with turbulent boundary layers, leaving scope for further work in pipes and channels. In this article the structure of fully developed turbulent pipe and channel flow has been studied using custom-made arrays of hot-wire probes. Results reveal long meandering structures of length up to 25 pipe radii or channel half-heights. These appear to be qualitatively similar to those reported in the log region of a turbulent boundary layer. However, for the channel case, large-scale coherence persists further from the wall than in boundary layers. This is expected since these large-scale features are a property of the logarithmic region of the mean velocity profile in boundary layers and it is well-known that the mean velocity in a channel remains very close to the log law much further from the wall. Further comparison of the three turbulent flows shows that the characteristic structure width in the logarithmic region of a boundary layer is at least 1.6 times smaller than that in a pipe or channel.

Heavy particle concentration in turbulence at dissipative and inertial scales.

Abstract: Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale � � . In the inertial range, the particle distribution is no longer scale invariant. It is, however, shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.

Structure of a spatially developing turbulent lean methane–air Bunsen flame

Abstract: Direct numerical simulation of a three-dimensional spatially developing turbulent slot-burner Bunsen flame has been performed with a new reduced methane–air mechanism. The mechanism, derived from sequential application of directed relation graph theory, sensitivity analysis and computational singular perturbation over the GRI-1.2 detailed mechanism is non-stiff and tailored to the lean conditions of the DNS. The simulation is performed for three flow through times, long enough to achieve statistical stationarity. The turbulence parameters have been chosen such that the combustion occurs in the thin reaction zones regime of premixed combustion. The data is analyzed to study possible influences of turbulence on the structure of the preheat and reaction zones. The results show that the mean thickness of the turbulent flame, based on progress variable gradient, is greater than the corresponding laminar flame. The effects of flow straining and flame front curvature on the mean flame thickness are quantified through conditional means of the thickness and by examining the balance equation for the evolution of the flame thickness. Finally, conditional mean reaction rate of key species compared to the laminar reaction rate profiles show that there is no significant perturbation of the heat release layer.

Scaling analysis and simulation of strongly stratified turbulent flows

Abstract: Direct numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re >> 1 and horizontal Froude number F-h > 1, viscous forces are unimportant and l(v) scales as l ...

Recurrent motions within plane Couette turbulence

Abstract: The phenomenon of bursting, in which streaks in turbulent boundary layers oscillate and then eject low-speed fluid away from the wall, has been studied experimentally, theoretically and computationally for more than 50 years because of its importance to the three-dimensional structure of turbulent boundary layers. Five new three-dimensional solutions of turbulent plane Couette flow are produced, one of which is periodic while the other four are relative periodic. Each of these five solutions demonstrates the breakup and re-formation of near-wall coherent structures. Four of our solutions are periodic, but with drifts in the streamwise direction. More surprisingly, two of our solutions are periodic, but with drifts in the spanwise direction, a possibility that does not seem to have been considered in the literature. It is argued that a considerable part of the streakiness observed experimentally in the near-wall region could be due to spanwise drifts that accompany the breakup and re-formation of coherent structures. A new periodic solution of plane Couette flow is also computed that could be related to transition to turbulence. The violent nature of the bursting phenomenon implies the need for good resolution in the computation of periodic and relative periodic solutions within turbulent shear flows. This computationally demanding requirement is addressed with a new algorithm for computing relative periodic solutions one of whose features is a combination of two well-known ideas – namely the Newton–Krylov iteration and the locally constrained optimal hook step. Each of the six solutions is accompanied by an error estimate. Dynamical principles are discussed that suggest that the bursting phenomenon, and more generally fluid turbulence, can be understood in terms of periodic and relative periodic solutions of the Navier–Stokes equation.

Edge turbulence measurements in toroidal fusion devices

Abstract: This paper reviews measurements of edge plasma turbulence in toroidal magnetic fusion devices with an emphasis on recent results in tokamaks. The dominant feature of edge turbulence is a high level of broadband density fluctuations with a relative amplitude δn/n ~ 5–100%, accompanied by large potential and electron temperature fluctuations. The frequency range of this turbulence is ~10 kHz–1 MHz, and the size scale is typically ~0.1–10 cm perpendicular to the magnetic field but many metres along the magnetic field, i.e. the structure is nearly that of 2D 'filaments'. Large intermittent bursts or 'blobs' are usually observed in the scrape-off layer. Diagnostic and data analysis techniques are reviewed and the main experimental results are summarized. Recent comparisons of experimental results with edge turbulence theory are discussed, and some directions for future experiments are suggested.

Protostellar Turbulence Driven by Collimated Outflows

Abstract: We investigate the global properties of the outflow-driven protostellar turbulence through 3D MHD simulations The simulations show that the turbulence in regions of active cluster formation is quickly transformed by the forming stars through protostellar outflows, and that strongly influences and perhaps controls protostellar turbulence cluster formation We find that collimated outflows are more efficient in driving turbulence than spherical outflows that carry the same amounts of momentum This is because collimated outflows can propagate farther away from their sources, effectively increasing the turbulence driving length; turbulence driven on a larger scale decays more slowly Gravity plays an important role in shaping the turbulence, generating infall motions that balance the outward motions driven by outflows The resulting quasi-equilibrium state is maintained through a slow rate of star formation, with a fraction of the total mass converted into stars per free-fall time as low as a few percent Magnetic fields are dynamically important even in magnetically supercritical clumps, provided that their initial strengths are not far below the critical value for static cloud support They contain an energy comparable to the turbulent energy and can significantly reduce the rate of star formation The mass-weighted probability distribution function (PDF) of the volume density of the protostellar turbulence is often, although not always, approximately lognormal The PDFs of the column density deviate more strongly from lognormal distributions There is a prominent break in the power spectrum, which may provide a way to distinguish it from other types of turbulence

Density Fluctuations in MHD Turbulence: Spectra, Intermittency and Topology

Abstract: We perform three-dimensional (3D) compressible MHD simulations over many dynamical times for an extended range of sonic and Alfven Mach numbers and analyze the statistics of 3D density and 2D column density, which include probability distribution functions, spectra, skewness, kurtosis, She-Leveque exponents, and genus. In order to establish the relation between the statistics of the observables, i.e., column densities, and the underlying 3D statistics of density, we analyze the effects of cloud boundaries. We define the parameter space for 3D measures to be recovered from column densities. In addition, we show that for subsonic turbulence the spectra of density fluctuations are consistent with k-7/3 in the case of a strong magnetic field and k-5/3 in the case of a weak magnetic field. For supersonic turbulence we confirm the earlier findings of the shallow spectra of density and Kolmogorov spectra of the logarithm of density. We find that the intermittencies of the density and velocity are very different.