Small-scale Turbulent Motions Research Articles

CORONAL MASS EJECTION INITIATION BY CONVERGING PHOTOSPHERIC FLOWS: TOWARD A REALISTIC MODEL

In the context of coronal mass ejections triggering, we reconsider the class of models in which the evolution of an active region (AR) is driven by imposed boundary motions converging toward the polarity inversion line (PIL). We introduce a new model problem in which there is a large-scale flow with a diverging structure on the photosphere. This flow is reminiscent of that of the well-known moat flow around each of the two spots of a bipolar AR and transports only part of the magnetic flux toward the PIL. It is thus more compatible with observations than the one used in our previous study, which forced the whole positive and negative polarity parts of the AR approaching each other. We also include a diffusion term associated with small-scale turbulent photospheric motions, but keep the associated diffusivity at a low value in the particular study described here. We show that the evolution of an initial sheared force-free field first leads to the formation of a twisted flux rope which stays in equilibrium for some time. Eventually, however, the configuration suffers a global disruption whose underlying mechanism is found by energetic considerations to be nonequilibrium. It begins indeed when the magnetic energy becomes of the order of the energy of an accessible partially open field. For triggering an eruption by converging flows, it is thus not necessary to advect the whole AR toward the PIL, but only its central part.

An Integrated TKE-Based Eddy Diffusivity/Mass Flux Boundary Layer Closure for the Dry Convective Boundary Layer

Abstract This study presents a new approach to the eddy diffusivity/mass flux (EDMF) framework for the modeling of convective boundary layers. At the root of EDMF lies a decomposition of turbulent transport mechanisms into strong ascending updrafts and smaller-scale turbulent motions. The turbulent fluxes can be therefore described using two conventional approaches: mass flux (MF) for the organized thermals and eddy diffusivity (ED) for the remaining turbulent field. Since the intensities of both MF and ED transports depend on the kinetic energy of the turbulent motions, it seems reasonable to formulate an EDMF framework based on turbulent kinetic energy (TKE). Such an approach allows for more physical and less arbitrary formulations of parameters in the model. In this study the EDMF–TKE coupling is achieved through the use of (i) a new parameterization for the lateral entrainment coefficient ɛ and (ii) the MF contribution to the buoyancy source of TKE. Some other important features of the EDMF parameterization presented here include a revised mixing length formulation and Monin–Obukhov stability scaling for the surface layer. The scheme is implemented in a one-dimensional (1D) model. Several cases of dry convective boundary layers (CBL) with different surface sensible heat fluxes in the free-convection limit are investigated. Results are compared to large-eddy simulation (LES). Good agreement between LES and the 1D model is achieved with respect to mean profiles, boundary layer evolution, and updraft characteristics. Some disagreements between the models are found to most likely relate to deficiencies in the TKE simulation in the 1D model. Comparison with other previously established ɛ parameterizations shows that the new TKE-based formulation leads to equally accurate, and in many respects better, simulation of the CBL. The encouraging results obtained with the proposed EDMF framework indicate that full integration of EDMF with higher-order closures is possible and can further improve boundary layer simulations.

Structure identification in turbulent flows for feedback flow control

Feedback flow control strategies have traditionally been developed by focusing on prototype laminar flows such as the wake behind a cylinder or a free shear layer. Many strategies rely on some form of proper orthogonal decomposition (POD) of the velocity field to identify the flow structures that need to be mitigated. However, in turbulent flows, POD does not readily identify the large, coherent motion targeted by flow control. Ongoing research at the US Air Force Academy is focused on developing feedback flow control strategies for the turbulent shear layer behind a backward facing step. POD of the velocity and density fields showed that the density is a better marker of the coherent structures in the shear layer and nearly completely eliminates the contribution of the small-scale turbulent motion to the POD spatial modes, allowing for a focused development of strategies to control the coherent motion in the shear layer.

THE FRACTAL DIMENSION OF STAR-FORMING REGIONS AT DIFFERENT SPATIAL SCALES IN M33

We study the distribution of stars, HII regions, molecular gas, and individual giant molecular clouds in M33 over a wide range of spatial scales. The clustering strength of these components is systematically estimated through the fractal dimension. We find scale-free behavior at small spatial scales and a transition to a larger correlation dimension (consistent with a nearly uniform distribution) at larger scales. The transition region lies in the range 500-1000 pc. This transition defines a characteristic size that separates the regime of small-scale turbulent motion from that of large-scale galactic dynamics. At small spatial scales, bright young stars and molecular gas are distributed with nearly the same three-dimensional fractal dimension (Df <= 1.9), whereas fainter stars and HII regions exhibit higher values (Df = 2.2-2.5). Our results indicate that the interstellar medium in M33 is on average more fragmented and irregular than in the Milky Way.

Sedimentation of particles in a vigorously convecting fluid

The sedimentation of particles in a vigorously convecting fluid is a process of great interest in various geophysical and industrial settings. Using a classical Rayleigh-Bénard setup with salty water as a working fluid and PMMA particles, we systematically quantify the progressive settling of a large number of heavy particles initially distributed homogeneously through the tank. Our two control parameters are the Rayleigh number Ra characterizing the vigor of convection and the density ratio between the particles and the fluid Deltarho/rho. In all our experiments, the time evolution of the solid fraction of suspended particles is correctly described by a diffusion-convection equation, taking into account a constant settling velocity given by the classical Stoke's law with an apparent viscosity due to small-scale turbulent motions, as well as a time-independent diffusive flux of particles from the bottom of the tank. We define scaling laws for this diffusive flux as well as for the equilibrium value of the suspended particles solid fraction as a function of Ra and Deltarho/rho, in agreement with the experimental results.

INFLUENCE OF DOPPLER WIDTH FLUCTUATIONS ON THE SHAPE OF SPECTRAL LINES

We investigate the influence of stochastic Doppler width fluctuations on the shape of spectral lines. The photospheres and atmospheres of stars, and the interstellar medium, possess stochastic behavior especially near nonstationary objects such as active galactic nuclei, quasars, flare stars, and regions of star formation. In reality, we observe the mean values of intensities from these objects. In most situations, the spectral line extinction coefficient has a Gaussian shape with the stochastic Doppler width determined by thermal and small-scale turbulent motions of atoms or molecules. For small-scale turbulent motions (short-correlated turbulence) the propagation of radiation is described by the average extinction factor. This coefficient depends on the level of the Doppler width fluctuations {eta}. We show that these fluctuations change both the value of intensity and the shape of spectral lines. We consider distortions of the spectral line shapes for the absorption and emission lines for various values of the parameter {eta}. For a number of H{sub 2}O maser sources we estimate the values of this parameter, the optical depths of the inverted media, and the mean effective Doppler velocities. Maser emission lines with non-Gaussian shape can serve as an additional method for the investigation of the physical parameters inmore » maser 'spots'.« less

A study of the asymmetry in the H2O maser line atλ= 1.35 cm on the base of the hyperfine structure

The results of analyzing asymmetry in the H2O maser lines at λ = 1.35 cm are presented. We investigated in detail the known mechanism of the asymmetry origin due to the hyperfine structure of the 616 523 transition and different (not equidistant) positions of the corresponding triplet components. The triplet of the lines is characterized by the sum of extinction factors that are continuously transformed into a single-peaked asymmetric extinction coefficient, with the increase in the Doppler widths (characterizing by effective Doppler velocity uD). A noticeable asymmetry corresponds to 0.5-1 km s-1. For higher values of uD the extinction factor approaches a Gaussian shape with the decreasing magnitude of the profile asymmetry. An appreciable asymmetry in unsaturated maser lines can only arise at 0.5 km s-1, if there are very narrow linewidths (≈ 0.2-0.4 km s-1). But observed saturated masers possess a fairly high degree of the line asymmetry, 10-40%. Most probably, this asymmetry is a result of rebroadening of the linewidth up to the value that is comparable to the width of the asymmetric extinction coefficient.

A mesoscale vortex in a small stratified lake

A mesoscale vortex structure in the small stratified Lake Stechlin has been revealed by field experiments with satellite-tracked quasi-lagrangian drifters. The vortex with a radius of about 200 m drifted at 300 m/day along the western bight of the lake with nearly constant rotation speed of 3 cpd. Analysis of kinematical properties of the vortex motion demonstrates solid body character of rotation. Extrapolation of the vortex drift trajectory over the period preceding the observations combined with data on local winds and seiche dynamics has allowed tracing the vortex fate from its generation point. The normal modes analysis of the internal seiching in the lake reveals the vortex generation mechanism to be the interaction of certain seiche modes with local bottom topography and suggests generation of the mesoscale vortices to be the a regular feature of the lake circulation. Analysis of vorticity suggests additional energy supply to rotational flow, possibly from inverse cascading of small-scale turbulent motions—a feature typical for quasi-2D turbulence. The vortices can play an important role in the energy transport from basin-scale motions to small-scale boundary mixing. They can also contribute significantly to the horizontal heterogeneity of phyto- and zooplankton distribution as well as to the transport of dissolved matter such as nutrients between littoral and profundal areas. The topographically generated traveling vortices represent an analog of the synoptic eddies in the Ocean and in the Atmosphere, whereas their role in the lake hydrodynamics is practically unknown.

Simulation of Turbulent Flow Around a Bluff Body Using a Combined Model of Random Fourier Modes and Rapid Distortion Theory (1st Report, Description of the Combined Model and Its Application to Turbulent Flow Around a Cylinder)

A new simulation method to predict turbulence quantities around a bluff body has been developed using a combined model of the random Fourier modes and rapid distortion theory (RDT). In the proposed method, both large- and small-scale turbulent motions are simulated using the random Fourier modes varying in space and time, and the change of vorticity field around the body is modeled by the RDT. The novel advantage of the present method is as follows : 1. we can simulate a high-Reynolds-number turbulent flow around a bluff body, 2. we can obtain a time dependent fluctuating velocity field at arbitrary points around a body, 3. low computational cost compared with DNS and LES. The method is applied to turbulent flow around a cylinder and the results are compared with the previous measurement. The computational results are in agreements with the previous measurements in the front region of the cylinder. It is concluded that the present method is useful to simulate the turbulence fields where the effects of distortion of eddies and blocking by the wall are dominant.

An H2O maser in the infrared source IRAS 20126+4104

Results of monitoring of H2O maser in the infrared source IRAS 20126+4104, which is associated with a cool molecular cloud, are presented. The observations were carried out on the 22-meter radio telescope of the Pushchino Radio Astronomy Observatory (Russia) between June 1991 and January 2006. The spectrum of the H2O maser emission extends from − 16.7 to 4.8 km/s and splits into separate groups of emission features. Cyclic variations of the integrated maser flux with a period from 3.4 to 5.5 years were detected, together with strong flares of up to 220 Jy in individual emission features. It is shown that large linewidths in periods of high maser activity are due to small-scale turbulent motions of the material. An expanding envelope around a young star is accepted as a model for the source. The protostar has a small peculiar velocity with respect to the molecular cloud (∼2 km/s). Individual emission features form organized structures, including multi-link chains.

Experimental investigation of a blunt trailing edge flow field with application to sound generation

The unsteady lift generated by turbulence at the trailing edge of an airfoil is a source of radiated sound. The objective of the present research was to measure the velocity field in the near wake region of an asymmetric beveled trailing edge in order to determine the flow mechanisms responsible for the generation of trailing edge noise. Two component velocity measurements were acquired using particle image velocimetry. The chord Reynolds number was 1.9 × 106. The data show velocity field realizations that were typical of a wake flow containing an asymmetric periodic vortex shedding. A phase average decomposition of the velocity field with respect to this shedding process was utilized to separate the large scale turbulent motions that occurred at the vortex shedding frequency (i.e., those responsible for the production of tonal noise) from the smaller scale turbulent motions, which were interpreted to be responsible for the production of broadband sound. The small scale turbulence was found to be dependent on the phase of the vortex shedding process implying a dependence of the broadband sound generated by the trailing edge on the phase of the vortex shedding process.

Mixing of cloud and clear air in centimeter scales observed in laboratory by means of Particle Image Velocimetry

Cloudy air, containing small (∅ 14 μm) water droplets, undergoes mixing with the unsaturated environment inside the cloud chamber in the process resembling smallest scales of entrainment and mixing in real clouds. Particle Image Velocimetry (PIV) applied to images from the chamber interior is used to investigate dynamics of the process in scales from 1.2 mm to few centimeters. A special algorithm, allowing for investigation of droplets motion, is developed, tested and adapted to the experimental data. Two velocity components retrieved in the vertical cross-section through the chamber interior indicate anisotropy of small-scale turbulent motions, with the preferred vertical direction. This result confirms earlier numerical studies, indicating that evaporation of cloud droplets at the cloud–clear air interface may substantially influence the small-scale turbulence in clouds.

Radiated sound and turbulent motions in a blunt trailing edge flow field

The dipole sound produced by edge scattering of pressure fluctuations at a trailing edge is most often an undesirable effect in turbomachinery and control surface flows. The ability to model the flow mechanisms associated with the production of trailing edge acoustics is important for the quiet design of such devices. The objective of the present research was to experimentally measure flow field and acoustic variables in order to develop an understanding of the mechanisms that generate trailing edge noise. The results of these experiments have provided insight into the causal relationships between the turbulent flow field, unsteady surface pressure, and radiated far field acoustics. Experimental methods used in this paper include particle image velocimetry (PIV), unsteady surface pressures, and far field acoustic pressures. The model investigated had an asymmetric 45° beveled trailing edge. Reynolds numbers based on chord ranged from 1.2 × 10 6 to 1.9 × 10 6. It was found that the small-scale turbulent motions in the vicinity of the trailing edge were modulated by a large scale von Karman wake instability. The broadband sound produced by these motions was also found to be dependant on the “phase” of the wake instability.

LES benchmark study of high cycle temperature fluctuations caused by thermal striping in a mixing tee

Thermal striping is identified as one of the causes of thermal fatigue failure in nuclear power plants. Numerical studies of thermal striping require three-dimensional, unsteady turbulent modeling that resolves both large and small-scale turbulent motions. Benchmark studies were carried out using the LES turbulence model solved by the commercial CFD code FLUENT. Two types of mixing tee configurations were modeled to evaluate the performance of the CFD code. The simulation results presented in normalized average temperature and normalized fluctuating temperatures are in good agreement with measurements.

On the Mechanism Responsible for Turbulent Drag Reduction by Dilute Addition of High Polymers: Theory, Experiments, Simulations, and Predictions

Abstract Turbulent drag reduction by dilute addition of high polymers is studied by considering local stretching of the molecular structure of a polymer by small-scale turbulent motions in the region very close to the wall. The stretching process is assumed to restructure turbulence at small scales by forcing these to satisfy local axisymmetry with invariance under rotation about the axis aligned with the main flow. It can be shown analytically that kinematic constraints imposed by local axisymmetry force turbulence near the wall to tend towards the one-component state and when turbulence reaches this limiting state it must be entirely suppressed across the viscous sublayer. For the limiting state of wall turbulence, the statistical dynamics of the turbulent stresses, constructed by combining the two-point correlation technique and invariant theory, suggest that turbulent drag reduction by homogeneously distributed high polymers, cast into the functional space which emphasizes the anisotropy of turbulence, resembles the process of reverse transition from the turbulent state towards the laminar flow state. These findings are supported by results of direct numerical simulations of wall-bounded turbulent flows of Newtonian and non-Newtonian fluids and by experiments carried out, under well-controlled laboratory conditions, in a refractive index-matched pipe flow facility using state-of-the art laser-Doppler anemometry. Theoretical considerations based on the elastic behavior of a polymer and spatial intermittency of turbulence at small scales enabled quantitative estimates to be made for the relaxation time of a polymer and its concentration that ensure maximum drag reduction in turbulent pipe flows, and it is shown that predictions based on these are in very good agreement with available experimental data.

Leaking method approach to surface transport in the Mediterranean Sea from a numerical ocean model

We use Lagrangian diagnostics (the leaking and the exchange methods) to characterize surface transport out of and between selected regions in the Western Mediterranean. Velocity fields are obtained from a numerical model. Residence times of water of Atlantic origin in the Algerian subbasin, with a strong seasonal dependence, are calculated. Exchange rates between these waters and the ones occupying the northern basin are also evaluated. At surface, northward transport is dominant, and involves filamental features and eddy structures that can be identified with the Algerian eddies. The impact on these results of the presence of small scale turbulent motions is evaluated by adding Lagrangian diffusion.

The effect of polymers on the dynamics of turbulence in a drag reduced flow

An experimental investigation of a polymer drag reduced flow using state-of-the-art laser-Doppler anemometry in a refractive index-matched pipe flow facility is reported. The measured turbulent stresses deep in the viscous sublayer are analyzed using the tools of invariant theory. It is shown that with higher polymer concentration the anisotropy of the Reynolds stresses increases. This trend is consistent with the trends extracted from DNS data of non-Newtonian fluids yielding different amounts of drag reduction. The interaction between polymer and turbulence is studied by considering local stretching of the molecular structure of a polymer by small-scale turbulent motions in the region very close to the wall. The stretching process is assumed to re-structure turbulence at small scales by forcing these to satisfy local axisymmetry with invariance under rotation about the axis aligned with the main flow. It is shown analytically that kinematic constraints imposed by local axisymmetry farce turbulence near the wall to tend towards the one-component state and when turbulence reaches this limiting state it must be entirely suppressed across the viscous sublayer. Based on this consideration it is suggested that turbulent drag reduction by high polymers resembles the reverse transition process from turbulent to laminar. Theoretical considerations based on the elastic behavior of a polymer and spatial intermittency of turbulence at small scales enabled quantitative estimates to be made for the relaxation time of a polymer and its concentration that ensure maximum drag reduction in turbulent pipe flows, and it is shown that predictions based on these are in very good agreement with available experimental data.

Lagrangian Methods for Climatological Analysis of Regional Atmospheric Transport

A quantitative climatological analysis of regional-scale atmospheric transport in Texas is developed using previously described Lagrangian (kinematic) trajectory methods. The trajectories are computed using resolved winds from 1979 to 2001 from the National Centers for Environmental Prediction‐National Center for Atmospheric Research reanalysis project dataset. The wind data do not include small-scale turbulent atmospheric motion. The probability distributions of particle trajectories can be used to estimate the climatological (ensemble mean) Green’s function for the mass conservation equation for a passive trace substance. A discrete approximation of the Green’s function is computed for low-level summertime atmospheric flow over Texas. Examples are provided of the use of the Green’s function to estimate both forward and backward transport properties. The Green’s function can be used to evaluate the climatological probability of transport by the resolved flow to or from a given location.

Effects of small-scale turbulent motions on the filtered velocity gradient tensor as deduced from holographic particle image velocimetry measurements

The effects of small-scale motions on the inertial range structure of turbulence are investigated by considering the dynamics of the velocity gradient tensor (Ãij) filtered at scale Δ. In addition to self-interactions and the filtered pressure Hessian, the evolution of Ãij is determined by the subgrid-scale stress tensor. As in the so-called restricted Euler dynamics, the evolution equations can be simplified by considering the invariants RΔ and QΔ of Ãij. The effects of the subgrid-scale stress tensor on RΔ and QΔ can be quantified unambiguously by evaluating conditional averages that appear in the evolution equation for the joint probability distribution function of these invariants. The required conditional averages are computed from three-dimensional measurements of fully developed turbulence in a square duct, at Reτ≈2360. The measurements are performed using holographic particle image velocimetry [Tao et al., Phys. Fluids 12, 941 (2000); Tao et al., J. Fluid Mech. 457, 35 (2002)]. The velocity distributions are spatially filtered in the inertial range using a box filter at about 30 Kolmogorov scales to separate large from small scales. The results show that the subgrid scale (SGS) stresses have significant effect on the evolution of filtered velocity gradients. In particular, along the so-called Vieillefosse tail at RΔ&amp;gt;0 and QΔ&amp;lt;0, they oppose the formation of a finite-time singularity that occurs in restricted Euler dynamics. Various other trends are quantified in different parts of the (RΔ,QΔ) plane. Included are the SGS dissipation rate of kinetic energy, and the effect of the SGS stress in modifying the so-called “discriminant,” which is a conserved quantity in restricted Euler dynamics. A priori tests of the Smagorinsky, nonlinear, and mixed models show that all reproduce the real SGS stress effect along the Vieillefosse tail, but that they fail in several other regions. An attempt is made to optimize the mixed model by letting the two coefficients be functions of RΔ and QΔ.

Polarization of resonance X-ray lines from clusters of galaxies

It is known that resonant scattering can distort the surface brightness profiles of clusters of galaxies in X-ray lines. We demonstrate that the scattered line emission should be polarized and possibly detectable with future X-ray polarimeters. Spectrally resolved mapping of a galaxy cluster in polarized X-rays could provide valuable independent information on the physical conditions, in particular element abundances and the characteristic velocity of small-scale turbulent motions, in the intracluster gas. The expected degree of polarization is of the order of 10 per cent for the richest regular clusters (e.g. Coma) and clusters whose X-ray emission is dominated by a central cooling flow (such as Perseus and M87/Virgo).