Browsing by Subject "turbulence"

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Angular Momentum Transport And Turbulence In Laboratory Models Of Keplerian Flows
(2012-11) Paoletti, M. S.; van Gils, D. P. M.; Dubrulle, B.; Sun, Chao; Lohse, Detlef; Lathrop, D. P.; Paoletti, M. S.
We present angular momentum transport (torque) measurements in two recent experimental studies of the turbulent flow between independently rotating cylinders. In addition to these studies, we reanalyze prior torque measurements to expand the range of control parameters for the experimental Taylor-Couette flows. We find that the torque may be described as a product of functions that depend only on the Reynolds number, which describes the turbulent driving intensity, and the rotation number, which characterizes the effects of global rotation. For a given Reynolds number, the global angular momentum transport for Keplerian-like flow profiles is approximately 14% of the maximum achievable transport rate. We estimate that this level of transport would produce an accretion rate of (M) over dot/(M) over dot(0) similar to 10(-3) in astrophysical disks. We argue that this level of transport from hydrodynamics alone could be significant. We also discuss the possible role of finite-size effects in triggering or sustaining turbulence in our laboratory experiments.
Angular redistribution of nonlinear perturbations: A universal feature of nonuniform flows
(2010-06) Horton, W.; Kim, J. H.; Chagelishvili, G. D.; Bowman, J. C.; Lominadze, J. G.; Horton, W.
Classically, the net action of nonlinear turbulent processes is interpreted as either a direct or inverse cascade. However, in nonuniform/shear flows the dominant process is a nonlinear redistribution over wave number angle of perturbation spatial Fourier harmonics. We call this process a nonlinear transverse redistribution (NTR). This phenomenon is demonstrated for a simple two-dimensional constant shear (non-normal) flow by numerically simulating the nonlinear dynamics of coherent and stochastic vortical perturbations in the flow. NTR is a general feature of nonlinear processes that should manifest itself in nonuniform engineering, environmental, and astrophysical flows. The conventional characterization of turbulence in terms of direct and inverse cascades, which ignores NTR, appears to be misleading for shear flow turbulence. We focus on the action of nonlinear processes on the spectral energy. NTR redistributes perturbations over different quadrants of the wave number plane and the interplay of this nonlinear redistribution with linear phenomena becomes intricate: it can realize either positive or negative feedback. In the case of positive feedback, it repopulates the quadrants in wave number space where the shear flow induces linear transient growth.
The Bolocam Galactic Plane Survey. XIII. Physical Properties And Mass Functions Of Dense Molecular Cloud Structures
(2015-06) Ellsworth-Bowers, Timothy P.; Glenn, Jason; Riley, Allyssa; Rosolowsky, Erik; Ginsburg, Adam; Evans, Neal J.; Bally, John; Battersby, Cara; Shirley, Yancy L.; Merello, Manuel; Evans, Neal J.
We use the distance probability density function formalism of Ellsworth-Bowers et al. to derive physical properties for the collection of 1,710 Bolocam Galactic Plane Survey (BGPS) version 2 sources with well-constrained distance estimates. To account for Malmquist bias, we estimate that the present sample of BGPS sources is 90% complete above 400 M-circle dot and 50% complete above 70 M-circle dot. The mass distributions for the entire sample and astrophysically motivated subsets are generally fitted well by a lognormal function, with approximately power-law distributions at high mass. Power-law behavior emerges more clearly when the sample population is narrowed in heliocentric distance (power-law index alpha = 2.0 +/- 0.1 for sources nearer than 6.5 kpc and alpha = 1.9 +/- 0.1 for objects between 2 and 10 kpc). The high-mass power-law indices are generally 1.85 <= alpha <= 2.05 for various subsamples of sources, intermediate between that of giant molecular clouds and the stellar initial mass function. The fit to the entire sample yields a high-mass power-law (alpha) over cap = 1.94(-0.10)(+0.34). Physical properties of BGPS sources are consistent with large molecular cloud clumps or small molecular clouds, but the fractal nature of the dense interstellar medium makes it difficult to map observational categories to the dominant physical processes driving the observed structure. The face-on map of the Galactic disk's mass surface density based on BGPS dense molecular cloud structures reveals the high-mass star-forming regions W43, W49, and W51 to be prominent mass concentrations in the first quadrant. Furthermore, we present a 0.25 kpc resolution map of the dense gas mass fraction across the Galactic disk that peaks around 5%.
Cluster Merger Shock Constraints On Particle Acceleration And Nonthermal Pressure In The Intracluster Medium
(2008-03) Nakar, Ehud; Milosavljevic, Milos; Nagai, Daisuke; Milosavljevic, Milos
X-ray observations of galaxy cluster merger shocks can be used to constrain nonthermal processes in the intracluster medium (ICM). The presence of nonthermal pressure components in the ICM, as well as the shock acceleration of particles and their escape, all affect shock jump conditions in distinct ways. Therefore, these processes can be constrained using X-ray surface brightness and temperature maps of merger shock fronts. Here we use these observations to place constraints on particle acceleration efficiency in intermediate Mach number ( M approximate to 2-3) shocks and explore the potential to constrain the contribution of nonthermal components ( e. g., cosmic rays, magnetic field, and turbulence) to ICM pressure in cluster outskirts. We model the hydrodynamic jump conditions in merger shocks discovered in the galaxy clusters A520 ( M approximate to 2) and 1E 0657-56 ( M approximate to 3) using a multifluid model comprising a thermal plasma, a nonthermal plasma, and a magnetic field. Based on the published X-ray spectroscopic data alone, we find that the fractional contribution of cosmic rays accelerated in these shocks is less than or similar to 10% of the shock downstream pressure. Current observations do not constrain the fractional contribution of nonthermal components to the pressure of the undisturbed shock upstream. Future X-ray observations, however, have the potential to either detect particle acceleration in these shocks through its effect on the shock dynamics, or place a lower limit on the nonthermal pressure contributions in the undisturbed ICM. We briefly discuss implications formodels of particle acceleration in collisionless shocks and the estimates of galaxy cluster masses derived from X-ray and Sunyaev-Zel'dovich effect observations.
Controlled Multi-Scale Turbulence through the Use of Laser Sintered Sierpinski Pyramids
(University of Texas at Austin, 2013) Liu, Y.; Beck, S.; Nicolleau, F.; Majewski, C.E.
The research presented here is the result of a new collaboration between the Centre for Advanced Additive Manufacturing (AdAM) and the Thermofluids group at The University of Sheffield, regarding the use of fractal geometries for the control and influence of fluid flow. It is believed that the use of multiscale objects can be used to introduce many different orders of turbulence into a flow. However, whilst substantial simulations have been carried out in this area, the complexity of the physical geometries means that to date these have not been validated via physical testing. In this work, varying orders of Sierpinski pyramids were produced using Laser Sintered PA2200 and analysed in a wind tunnel with regards to their effects on air flow through the structures. As predicted by theoretical analyses, the coarsest pyramids induced large vortices into the air-stream, whereas the more complex orders induced vortices at a number of different scales, rapidly developing into a standard turbulent flow. Further investigations are planned to isolate the effects of the smaller-scale turbulence in this situation.
Drift Wave Turbulence
(2008-05) Horton, W.; Kim, J. H.; Asp, E.; Hoang, T.; Watanabe, T. H.; Sugama, H.; Horton, W.; Kim, J. H.
Drift waves occur universally in magnetized plasmas producing the dominant mechanism for transport of particles, energy and momentum across magnetic field lines. A wealth of information obtained from laboratory experiments for plasma confinement is reviewed for drift waves driven unstable by density gradients, temperature gradients and trapped particle effects. The modern understanding of origin of the scaling laws for Bohm and gyro-Bohm transport fluxes is discussed. The role of sheared flows and magnetic shear in reducing the transport fluxes is discussed and illustrated with large scale computer simulations. Plasmas turbulence models are derived with reduced magnetized fluid descriptions. The types of theoretical descriptions reviewed include weak turbulence theory and anisotropic Kolmogorov-hke spectral indices, and the mixing length. A number of standard turbulent diffusivity formulas are given for the various space-time scales of the drift-wave turbulent mixing.
The Effect Of Turbulent Intermittency On The Deflagration To Detonation Transition In Supernova Ia Explosions
(2008-07) Pan, Lubin; Wheeler, J. Craig; Scalo, John; Pan, Lubin; Wheeler, J. Craig; Scalo, John
We examine the effects of turbulent intermittency on the deflagration to detonation transition (DDT) in Type Ia supernovae. The Zel'dovich mechanism for DDT requires the formation of a nearly isothermal region of mixed ash and fuel that is larger than a critical size. We primarily consider the hypothesis by Khokhlov et al. and Niemeyer and Woosley that the nearly isothermal, mixed region is produced when the flame makes the transition to the distributed regime. We use two models for the distribution of the turbulent velocity fluctuations to estimate the probability as a function of the density in the exploding white dwarf that a given region of critical size is in the distributed regime due to strong local turbulent stretching of the flame structure. We also estimate lower limits on the number of such regions as a function of density. We find that the distributed regime, and hence perhaps DDT, occurs in a local region of critical size at a density at least a factor of 2-3 larger than predicted for mean conditions that neglect intermittency. This factor makes the transition density much larger than the empirical value from observations in most situations. We also consider the intermittency effect on the more stringent conditions for DDT by Lisewski et al. and Woosley. We find that a turbulent velocity of 10(8) cm s(-1) in a region of size 10(6) cm, as required by Lisewski et al., is rare. We expect that intermittency has a weaker effect on the Woosley model with a stronger DDT criterion. The predicted transition density from this criterion remains below 10(7) g cm(-3) after accounting for intermittency using our intermittency models.
Electron Temperature Gradient Mode Transport
(2008-05) Horton, W.; Kim, J. H.; Hoang, G. T.; Park, H.; Kaye, S. M.; LeBlanc, B. P.; Horton, W.; Kim, J. H.
Anomalous electron thermal losses plays a central role in the history of the controlled fusion program being the first and most persistent form of anomalous transport across all toroidal magnetic confinement devices. In the past decade the fusion program has made analysis and simulations of electron transport a high priority with the result of a clearer understanding of the phenomenon, yet still incomplete. Electron thermal transport driven by the electron temperature gradient is examined in detail from theory, simulation and power balance studies in tokamaks with strong auxiliary heating.
Introduction to bifurcation-theory
(1991-10) Crawford, J. D.; Crawford, J. D.
The theory of bifurcation from equilibria based on center-manifold reductio, and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail: a Hopf bifurcation occurring in a model of three-wave mode coupling and steady-state bifurcations occurring in the real Landau-Ginzburg equation. The former provides an example of the importance of degenerate bifurcations in problems with more than one parameter and the latter illustrates new effects introduced into a bifurcation problem by a continuous symmetry.
Lagrangian Based Methods for Coherent Structure Detection
(2015-09) Allshouse, Michael R.; Peacock, Thomas; Allshouse, Michael R.
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows. (C) 2015 AIP Publishing LLC.
Macro-Turbulence from Wind Waves
(University of Texas at Austin, 1969-07) Lee, C.Y.; Masch, F.D.
Modeling The Pollution Of Pristine Gas In The Early Universe
(2013-10) Pan, Lubin B.; Scannapieco, Evan; Scalo, John; Scalo, John
We conduct a comprehensive theoretical and numerical investigation of the pollution of pristine gas in turbulent flows, designed to provide useful new tools for modeling the evolution of the first generation of stars. The properties of such Population III (Pop III) stars are thought to be very different than those of later stellar generations, because cooling is dramatically different in gas with a metallicity below a critical value Z(c), which lies between similar to 10(-6) and similar to 10(-3) Z(circle dot). The critical value is much smaller than the typical overall average metallicity, < Z >, and therefore the mixing efficiency of the pristine gas in the interstellar medium plays a crucial role in determining the transition from Pop III to normal star formation. The small critical value, Z(c), corresponds to the far left tail of the probability distribution function (PDF) of the metal abundance. Based on closure models for the PDF formulation of turbulent mixing, we derive evolution equations for the fraction of gas, P, lying below Z(c), in statistically homogeneous compressible turbulence. Our simulation data show that the evolution of the pristine fraction P can be well approximated by a generalized "self-convolution" model, which predicts that (P) over dot = -(n/tau(con))P(1 - P-1/n), where n is a measure of the locality of the mixing or PDF convolution events and the convolution timescale tau(con) is determined by the rate at which turbulence stretches the pollutants. Carrying out a suite of numerical simulations with turbulent Mach numbers ranging from M = 0.9 to 6.2, we are able to provide accurate fits to n and tau(con) as a function of M, Z(c)/< Z >, and the length scale, L-p, at which pollutants are added to the flow. For pristine fractions above P = 0.9, mixing occurs only in the regions surrounding blobs of pollutants, such that n = 1. For smaller values of P, n is larger as the mixing process becomes more global. We show how these results can be used to construct one-zone models for the evolution of Pop III stars in a single high-redshift galaxy, as well as subgrid models for tracking the evolution of the first stars in large cosmological numerical simulations.
Moment Closures for Fusion Optimization
(2020) Shukla, Akash; Hatch, David R.
Turbulent heat loss in a fusion reactor limits its ability to confine heat and produce fusion energy. Exploring tokamak parameters to find configurations that minimize turbulent trans- port will help us optimize fusion reactors. However, exploring efficiently and accurately is a challenge. Gyrokinetic models can accurately calculate turbulence but are too expensive to explore a broad parameter space with. Gyrofluid models are cheap, but they rely on moment closures that break down in the presence of turbulence. In order to develop a fast and accurate model to explore with, we will need robust closures that correctly capture nonlinear kinetic effects. As a starting point, we have developed such a closure for a simplified nonlinear gyrokinetic system, DNA (Hatch et al.), which models ITG turbulence in an unsheared slab. Numer- ical tests in the DNA simulation show that out new Dynami Multi-Mode (DMM) closure out performs standard closures and extrapolates to different parameter regimes.
Observations of the stratorotational instability in rotating concentric cylinders
(2016-09) Ibanez, Ruy; Swinney, Harry L.; Rodenborn, Bruce; Ibanez, Ruy; Swinney, Harry L.
We study the stability of density stratified flow between corotating vertical cylinders with rotation rates ohm(o) < ohm(i) and radius ratio r(i)/r(o) = 0.877, where subscripts o and i refer to the outer and inner cylinders. Just as in stellar and planetary accretion disks, the flow has rotation, anticyclonic shear, and a stabilizing density gradient parallel to the rotation axis. The primary instability of the laminar state leads not to axisymmetric Taylor vortex flow but to a nonaxisymmetric stratorotational instability (SRI). The present work extends the range of Reynolds numbers and buoyancy frequencies [N = root(-g/rho)(d rho/dz)] examined in previous experiments. We present the first experimental results for the axial wavelength. of the instability as a function of the internal Froude number, Fr = ohm(i)/ N; lambda increases by nearly an order of magnitude over the range of Fr examined. For small outer cylinder Reynolds number, the SRI occurs for inner inner Reynolds number larger than for the axisymmetric Taylor vortex flow (i.e., the SRI is more stable). For somewhat larger outer Reynolds numbers the SRI occurs for smaller inner Reynolds numbers than Taylor vortex flow and even below the Rayleigh stability line for an inviscid fluid. Shalybkov and Rudiger [Astron. Astrophys. 438, 411 (2005)] proposed that the laminar state of a stably stratified rotating shear flow should be stable for ohm(o)/ohm(i) > r(i)/r(o), but we find that this stability criterion is violated for N sufficiently large. At large Reynolds number the primary instability is not the SRI but a previously unreported nonperiodic state that mixes the fluid.
Plasma fluctuations as Markovian noise
(2007-12) Li, B.; Hazeltine, R. D.; Gentle, K. W.; Li, B.; Hazeltine, R. D.; Gentle, K. W.
Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments.
Turbulence-Induced Relative Velocity Of Dust Particles. II. The Bidisperse Case
(2014-08) Pan, Lubin B.; Padoan, Paolo; Scalo, John; Scalo, John
We extend our earlier work on turbulence-induced relative velocity between equal-size particles ( Paper I, in this series) to particles of arbitrarily different sizes. The Pan & Padoan (PP10) model shows that the relative velocity between different particles has two contributions, named the generalized shear and acceleration terms, respectively. The generalized shear term represents the particles' memory of the spatial flow velocity difference across the particle distance in the past, while the acceleration term is associated with the temporal flow velocity difference on individual particle trajectories. Using the simulation of Paper I, we compute the root-mean-square relative velocity, < w(2)>(1/2), as a function of the friction times, tau(p1) and tau(p2), of the two particles and show that the PP10 prediction is in satisfactory agreement with the data, confirming its physical picture. For a given tau(p1) below the Lagrangian correlation time of the flow, T-L, < w(2)>(1/2) as a function of tau(p2) shows a dip at tau(p2) similar or equal to tau(p1), indicating tighter velocity correlation between similar particles. Defining a ratio f equivalent to tau(p,1)/tau(p,h), with tau(p,1) and tau(p,h) the friction times of the smaller and larger particles, we find that < w(2)>(1/2) increases with decreasing f due to the generalized acceleration contribution, which dominates at f less than or similar to 1/4. At a fixed f, our model predicts that < w(2)>(1/2) scales as tau(1/2)(p,h) tau(p,h) for in the inertial range of the flow, stays roughly constant for T-L less than or similar to tau(p,h) less than or similar to T-L/f, and finally decreases as tau(-1/2)(p,h) p, h for tau(p,h) >> T-L/f. The acceleration term is independent of the particle distance, r, and reduces the r dependence of < w(2)>(1/2) in the bidisperse case.
Turbulence-Induced Relative Velocity Of Dust Particles. III. The Probability Distribution
(2014-09) Pan, Lubin B.; Padoan, Paolo; Scalo, John; Scalo, John
Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, tau(p1) and tau(p2), of two particles of arbitrary sizes. The friction time of the particles included in the simulation ranges from 0.1 tau(eta) to 54T(L), where tau(eta) and T-L are the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of tau(p1), the PDF shape is the fattest for equal-size particles (tau(p2) = tau(p1)), and becomes thinner at both tau(p2) < tau(p1) and tau(p2) > tau(p1). Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in (1/2) less than or similar to f less than or similar to 1, the PDF fatness first increases with the friction time tau(p,h) of the larger particle, peaks at tau(p,h) similar or equal to tau(eta), and then decreases as tp, h increases further. For 0 <= f less than or similar to (1/4), the PDF becomes continuously thinner with increasing tau(p,h). The PDF is nearly Gaussian only if tau(p,h) is sufficiently large (>> T-L). These features are successfully explained by the Pan & Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanetary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem.
Turbulent Clustering Of Protoplanetary Dust And Planetesimal Formation
(2011-10) Pan, Lubin B.; Padoan, Paolo; Scalo, John; Kritsuk, Alexei G.; Norman, Michael L.; Scalo, John
We study the clustering of inertial particles in turbulent flows and discuss its applications to dust particles in protoplanetary disks. Using numerical simulations, we compute the radial distribution function (RDF), which measures the probability of finding particle pairs at given distances, and the probability density function of the particle concentration. The clustering statistics depend on the Stokes number, St, defined as the ratio of the particle friction timescale, tau(p), to the Kolmogorov timescale in the flow. In agreement with previous studies, we find that, in the dissipation range, the clustering intensity strongly peaks at St similar or equal to 1, and the RDF for St similar to 1 shows a fast power-law increase toward small scales, suggesting that turbulent clustering may considerably enhance the particle collision rate. Clustering at inertial-range scales is of particular interest to the problem of planetesimal formation. At these large scales, the strongest clustering is from particles with tau(p) in the inertial range. Clustering of these particles occurs primarily around a scale where the eddy turnover time is similar to tau(p). We find that particles of different sizes tend to cluster at different locations, leading to flat RDFs between different particles at small scales. In the presence of multiple particle sizes, the overall clustering strength decreases as the particle size distribution broadens. We discuss particle clustering in two recent models for planetesimal formation. We argue that, in the model based on turbulent clustering of chondrule-size particles, the probability of finding strong clusters that can seed planetesimals may have been significantly overestimated. We discuss various clustering mechanisms in simulations of planetesimal formation by gravitational collapse of dense clumps of meter-size particles, in particular the contribution from turbulent clustering due to the limited numerical resolution.