Phys. Fluids (1994-Present) - Physics of Fluids

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Dynamics of freely swimming flexible foils

Silas Alben, Charles Witt, T. Vernon Baker, Erik Anderson, and George V. Lauder

Phys. Fluids 24, 051901 (2012); http://dx.doi.org/10.1063/1.4709477 (25 pages)

Online Publication Date: 1 May 2012

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We use modeling and simulations guided by initial experiments to study thin foils which are oscillated at the leading edge and are free to move unidirectionally under the resulting fluid forces. We find resonant-like peaks in the swimming speed as a function of foil length and rigidity. We find good agreement between the inviscid model and the experiment in the foil motions (particularly the wavelengths of their shapes), the dependences of their swimming speeds on foil length and rigidity, and the corresponding flows. The model predicts that the foil speed is proportional to foil length to the −1/3 power and foil rigidity to the 2/15 power. These scalings give a good collapse of the experimental data.

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47.11.-j

Computational methods in fluid dynamics

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New exact solutions for Hele-Shaw flow in doubly connected regions

Michael C. Dallaston and Scott W. McCue

Phys. Fluids 24, 052101 (2012); http://dx.doi.org/10.1063/1.4711274 (13 pages)

Online Publication Date: 4 May 2012

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Radial Hele–Shaw flows are treated analytically using conformal mapping techniques. The geometry of interest has a doubly connected annular region of viscous fluid surrounding an inviscid bubble that is either expanding or contracting due to a pressure difference caused by injection or suction of the inviscid fluid. The zero-surface-tension problem is ill-posed for both bubble expansion and contraction, as both scenarios involve viscous fluid displacing inviscid fluid. Exact solutions are derived by tracking the location of singularities and critical points in the analytic continuation of the mapping function. We show that by treating the critical points, it is easy to observe finite-time blow-up, and the evolution equations may be written in exact form using complex residues. We present solutions that start with cusps on one interface and end with cusps on the other, as well as solutions that have the bubble contracting to a point. For the latter solutions, the bubble approaches an ellipse in shape at extinction.

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47.55.dd	Bubble dynamics
68.03.Cd	Surface tension and related phenomena
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Experimental investigation of convective structure evolution and heat transfer in quasi-steady evaporating liquid films

J. T. Kimball, J. C. Hermanson, and J. S. Allen

Phys. Fluids 24, 052102 (2012); http://dx.doi.org/10.1063/1.4711368 (16 pages)

Online Publication Date: 4 May 2012

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The stability, convective structure, and heat transfer characteristics of upward-facing, evaporating, thin liquid films were studied experimentally. Dichloromethane, chloroform, methanol, and acetone films with initial thicknesses of 2–5 mm were subjected to constant levels of superheating until film rupture occurred (typically at a thickness of around 50 μm). The films resided on a temperature controlled, polished copper plate incorporated into a closed pressure chamber free of non-condensable gasses. The dynamic film thickness was measured at multiple points using a non-intrusive ultrasound ranging system. Instability wavelength and convective structure information was obtained using double-pass schlieren imaging. The sequence of the convective structures as the film thins due to evaporation is observed to be as follows: (1) large, highly variable cells, (2) concentric rings and spirals, and (3) apparent end of convection. The transition from large, variable cells to concentric rings and spirals occurs at a Rayleigh number of 4800 ± 960. The apparent end of convection occurs at a Rayleigh number of 1580 ± 180. At the cessation of convection, the Nusselt number is nearly unity, indicating that there is little heat transfer in the film due to convection. In films where the Rayleigh number is above this transitional value, the Nusselt number increases with increasing Rayleigh number. The current results suggest that the equilibrium condition at the evaporating surface suppresses surface temperature variation, effectively eliminating thermocapillary-driven instability.

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47.80.Jk	Flow visualization and imaging
68.15.+e	Liquid thin films
47.20.-k	Flow instabilities
47.60.Dx	Flows in ducts and channels
68.03.Fg	Evaporation and condensation of liquids

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Landau-Levich flow visualization: Revealing the flow topology responsible for the film thickening phenomena

H. C. Mayer and R. Krechetnikov

Phys. Fluids 24, 052103 (2012); http://dx.doi.org/10.1063/1.4703924 (33 pages)

Online Publication Date: 4 May 2012

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An extensive body of experimental work has proven the validity of the analysis of Landau and Levich, who were the first to determine theoretically the thickness of the film deposited by the withdrawal of a flat substrate from a bath of liquid with a clean interface. However, there are a number of experimental investigations that have shown that surfactants in the liquid may result in a thickening of the deposited film. Marangoni phenomena have usually been considered responsible for this effect. However, some careful experiments and numerical simulations reported in the literature seemed to rule out this view as the cause of the observed behavior. Despite all these studies and the number of reports of film thickening, an experimental study of the flow field close to the coated substrate in the presence of surfactants has never been undertaken. In this paper we will present a set of flow visualization experiments on coating of a planar substrate in the range of capillary numbers 10⁻⁴ ≲ Ca ≲ 10⁻³ for sodium dodecyl sulfate solutions with bulk concentrations of 0.25 CMC ⩽ C ⩽ 5.0 CMC (critical micelle concentration). It was evident during experiments that the flow field near the meniscus region exhibits patterns that can only be explained with a stagnation point residing in the bulk and not at the interface. As opposed to patterns with an interfacial stagnation point, the observed flow fields allow for the increase in film thickness due to the presence of surfactants compared to the clean interface case.

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47.55.nd	Spreading films
47.55.nb	Capillary and thermocapillary flows
47.80.Jk	Flow visualization and imaging
68.15.+e	Liquid thin films
68.55.jd	Thickness
82.70.Uv	Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems, (hydrophilic and hydrophobic interactions)

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Internal dynamics of Newtonian and viscoplastic fluid avalanches down a sloping bed

Nicolas Andreini, Gaël Epely-Chauvin, and Christophe Ancey

Phys. Fluids 24, 053101 (2012); http://dx.doi.org/10.1063/1.4718018 (20 pages)

Online Publication Date: 14 May 2012

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We experimentally investigated the spreading of fluid avalanches (i.e., fixed volumes of fluid) down an inclined flume. Emphasis was given to the velocity field within the head. Using specific imaging techniques, we were able to measure velocity profiles within the flowing fluid far from the sidewalls. We studied the behavior of Newtonian and viscoplastic fluids for various flume inclinations and initial masses. For the Newtonian fluids tested (glycerol and Triton X100), we compared the measured velocity field with that predicted by lubrication theory. Provided that the flow Reynolds number Re was sufficiently low (typically Re < 1), there was excellent agreement between theory and experiment except for the very thin region just behind the contact line. For higher Reynolds numbers (typically Re ∼ 10), the discrepancy between theory and experiment was more marked (relative errors up to 17% for the body). As viscoplastic materials, we used Carbopol ultrez 10. For the body, agreement between theoretical and measured velocity profiles was fairly satisfactory whereas it was very poor for the tip region as the curvature of the free surface became more pronounced: the velocities were not only much lower than those predicted by lubrication theory, but there was also evidence of slipping in the flow part adjacent to the contact line.

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47.15.G-	Low-Reynolds-number (creeping) flows
47.80.Jk	Flow visualization and imaging
47.15.Cb	Laminar boundary layers

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Flow properties of particles in a model annular shear cell

X. Wang, H. P. Zhu, and A. B. Yu

Phys. Fluids 24, 053301 (2012); http://dx.doi.org/10.1063/1.4710539 (18 pages)

Online Publication Date: 4 May 2012

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In order to quantitatively investigate the mechanical and rheological properties of solid flow in a shear cell under conditions relevant to those in an annular cell, we performed a series of discrete particle simulations of slightly polydispersed spheres from quasi-static to intermediate flow regimes. It is shown that the average values of stress tensor components are uniformly distributed in the cell space away from the stationary walls; however, some degree of inhomogeneity in their spatial distributions does exist. A linear relationship between the (internal/external) shear and normal stresses prevails in the shear cell and the internal and external friction coefficients can compare well with each other. It is confirmed that annular shear cells are reasonably effective as a method of measuring particle flow properties. The so-called I-rheology proposed by Jop et al. [Nature (London) 441, 727 (2006)] is rigorously tested in this cell system. The results unambiguously display that the I-rheology can effectively describe the intermediate flow regime with a high correlation coefficient. However, significant deviations take place when it is applied to the quasi-static regime, which corresponds to very small values of inertial number.

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47.57.Gc	Granular flow
47.57.Qk	Rheological aspects
45.70.Mg	Granular flow: mixing, segregation and stratification
47.11.-j	Computational methods in fluid dynamics

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Transition due to base roughness in a dense granular flow down an inclined plane

V. Kumaran and S. Maheshwari

Phys. Fluids 24, 053302 (2012); http://dx.doi.org/10.1063/1.4710543 (23 pages)

Online Publication Date: 15 May 2012

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Particle simulations based on the discrete element method are used to examine the effect of base roughness on the granular flow down an inclined plane. The base is composed of a random configuration of fixed particles, and the base roughness is decreased by decreasing the ratio of diameters of the base and moving particles. A discontinuous transition from a disordered to an ordered flow state is observed when the ratio of diameters of base and moving particles is decreased below a critical value. The ordered flowing state consists of hexagonally close packed layers of particles sliding over each other. The ordered state is denser (higher volume fraction) and has a lower coordination number than the disordered state, and there are discontinuous changes in both the volume fraction and the coordination number at transition. The Bagnold law, which states that the stress is proportional to the square of the strain rate, is valid in both states. However, the Bagnold coefficients in the ordered flowing state are lower, by more than two orders of magnitude, in comparison to those of the disordered state. The critical ratio of base and moving particle diameters is independent of the angle of inclination, and varies very little when the height of the flowing layer is doubled from about 35 to about 70 particle diameters. While flow in the disordered state ceases when the angle of inclination decreases below 20°, there is flow in the ordered state at lower angles of inclination upto 14°.

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47.57.Gc	Granular flow
02.50.-r	Probability theory, stochastic processes, and statistics
45.70.Mg	Granular flow: mixing, segregation and stratification
47.11.-j	Computational methods in fluid dynamics

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Low-dimensional modeling of streaks in a wedge flow boundary layer

María Higuera and José M. Vega

Phys. Fluids 24, 053601 (2012); http://dx.doi.org/10.1063/1.4711371 (14 pages)

Online Publication Date: 4 May 2012

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This paper is concerned with the low dimensional structure of optimal streaks in a wedge flow boundary layer, which have been recently shown to consist of a unique (up to a constant factor) three-dimensional streamwise evolving mode, known as the most unstable streaky mode. Optimal streaks exhibit a still unexplored/unexploited approximate self-similarity (not associated with the boundary layer self-similarity), namely the streamwise velocity re-scaled with their maximum remains almost independent of both the spanwise wavenumber and the streamwise coordinate; the remaining two velocity components instead do not satisfy this property. The approximate self-similar behavior is analyzed here and exploited to further simplify the description of optimal streaks. In particular, it is shown that streaks can be approximately described in terms of the streamwise evolution of the scalar amplitudes of just three one-dimensional modes, providing the wall normal profiles of the streamwise velocity and two combinations of the cross flow velocity components; the scalar amplitudes obey a singular system of three ordinary differential equations (involving only two degrees of freedom), which approximates well the streamwise evolution of the general streaks.

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47.60.Dx	Flows in ducts and channels
47.53.+n	Fractals in fluid dynamics
02.30.Hq	Ordinary differential equations
47.20.-k	Flow instabilities

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An efficient approach for eigenmode analysis of transient distributive mixing by the mapping method

O. Gorodetskyi, M. F. M. Speetjens, and P. D. Anderson

Phys. Fluids 24, 053602 (2012); http://dx.doi.org/10.1063/1.4712133 (16 pages)

Online Publication Date: 9 May 2012

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The mapping method is an efficient tool to investigate distributive mixing induced by periodic flows. Computed only once, the mapping matrix can be applied a number of times to determine the distribution of concentration inside the flow domain. Spectral analysis of the mapping matrix reveals detailed properties of the distributive mixing as all relevant information is stored in its eigenmodes. Any vector that describes a distribution of concentration can be expanded in the complete system of linearly independent eigenvectors of the mapping matrix. The rapid decay of the contribution of each mode in the eigenmode decomposition allows for a truncation of the eigenmode expansion from the whole spectrum to only the dominant eigenmodes (characterized by a decay rate significantly lower than the duration of the mixing process). This truncated decomposition adequately represents the distribution of concentration inside the flow domain already after a low number of periods, because contributions of all non-dominant eigenmodes rapidly become insignificant. The truncation is determined independently of the initial distribution of concentration and based on the decay rates of the eigenmodes, which are inversely proportional to the corresponding eigenvalues. Only modes with eigenvalues above a certain threshold are retained. The key advantage of the proposed compact eigenmode representation of the mapping method is that it includes practically relevant transient states and not just the asymptotic one. As such the method enables an eigenmode analysis of realistic problems yet with a substantial reduction in computational effort compared to the conventional approach.

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47.11.-j	Computational methods in fluid dynamics
47.51.+a	Mixing
02.10.Ud	Linear algebra
02.10.Yn	Matrix theory

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Two regimes of self-propelled motion of a torus rotating about its centerline in a viscous incompressible fluid at intermediate Reynolds numbers

N. P. Moshkin and Pairin Suwannasri

Phys. Fluids 24, 053603 (2012); http://dx.doi.org/10.1063/1.4717760 (11 pages)

Online Publication Date: 14 May 2012

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In the present work, the problem of the motion of a self-propelled torus in a viscous incompressible fluid is investigated numerically. The surface of the torus rotates with constant velocity around its centerline. The rotating boundary of a torus generates inertia in the surrounding fluid. The outer and inner surfaces produce inertia in opposite directions. There are two self-motion regimes. In one of them, the torus moves in the direction of the inner surface motion due to the larger production of inertia by the outer portion of the torus boundary. The direction of propulsion is the same as in the case of a zero Reynolds number. In the other regime the torus moves in opposite direction due to the high momentum flux associated with the jet of fluid expelled from the hole. The drag coefficients and flow patterns are analyzed at Reynolds numbers Re = 20 − 60, (Reynolds number defined by velocity of a uniform stream and a smaller diameter of torus), the aspect ratios Ar = 2, 3 (aspect ratio defined as ratio of torus diameter to cross-section diameter), and a range of rotational rate −5.6 ⩽ α ⩽ 2.5 (α defined as ratio of tangential tank-treading motion of torus surface to the uniform far-field velocity).

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47.50.Cd	Modeling
47.11.Bc	Finite difference methods
47.15.-x	Laminar flows
47.15.Uv	Laminar jets
47.32.Ef	Rotating and swirling flows

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Experimental investigation of reshocked spherical gas interfaces

Ting Si, Zhigang Zhai, Jiming Yang, and Xisheng Luo

Phys. Fluids 24, 054101 (2012); http://dx.doi.org/10.1063/1.4711866 (17 pages)

Online Publication Date: 8 May 2012

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The evolution of a spherical gas interface under reshock conditions is experimentally studied using the high-speed schlieren photography with high time resolutions. A number of experimental sets of helium or SF₆ bubble surrounded by air for seven different end wall distances have been performed. Distinct flow structures are observed due to the additional vorticity and wave configuration caused by the reshock. In the air/helium case, the deformation of the reshocked bubble is dependent on the development of the penetrating air jet along the symmetry axis of the bubble. In general, two separate vortex rings can be observed, i.e., one develops slowly, and the other approaches and eventually impinges on the shock tube end wall. In the air/SF₆ case, two SF₆ jets moving in opposite directions are generated and the oscillation of the interface is observed for small end wall distances, while small scale vortex morphologies on the gas interface are found for large end wall distances. The physical mechanisms of the baroclinic vorticity generation and the pressure perturbation are highlighted in the interface evolution process. Based on the sequence of the schlieren images obtained during a single run for each case, the x-t diagrams of the shock and reshock interacting with the helium or SF₆ bubble are plotted and the velocities estimated in linear stages are compared with those calculated from one-dimensional gas dynamics. The changes with time in the characteristic bubble sizes including the interface length, height, and vortex diameter are also measured.

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47.55.db	Drop and bubble formation
47.80.Jk	Flow visualization and imaging
47.40.Nm	Shock wave interactions and shock effects
47.32.cf	Vortex reconnection and rings
47.32.Ff	Separated flows
47.55.dd	Bubble dynamics

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Effects of axial flow on the stability of a helical vortex tube

Y. Hattori and Y. Fukumoto

Phys. Fluids 24, 054102 (2012); http://dx.doi.org/10.1063/1.4717769 (15 pages)

Online Publication Date: 15 May 2012

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The effects of axial flow on the stability of a helical vortex tube are studied by short-wavelength stability analysis. By axial flow we mean the flow along the helical tube inside the vortex core. At the leading order the base flow is set to the Rankine vortex with uniform velocity along the helical tube. The exponential growth rate is obtained analytically as the magnitude of the sum of three O(ε) and five O(ε²) complex numbers, where ε is the ratio of the core to curvature radius. At O(ε) the effect of axial flow can be regarded as the effect of the Coriolis force; as a result the instability is the superposition of the curvature instability and the Coriolis or precessional instability since the two instabilities occur under the same resonance condition. At O(ε²) combined effects of the axial flow and the torsion appear; the maximum growth rate increases when the period of particle motion increases.

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47.32.cd

Vortex stability and breakdown

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Spatio-temporal linear stability of double-diffusive two-fluid channel flow

Kirti Chandra Sahu and Rama Govindarajan

Phys. Fluids 24, 054103 (2012); http://dx.doi.org/10.1063/1.4718775 (10 pages)

Online Publication Date: 15 May 2012

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Absolute instabilities in shear flows can cause a catastrophic breakdown into a new unsteady state, or even into turbulence. We demonstrate that in a double-diffusive channel flow with a viscosity stratification across the channel, rapidly growing absolute instability may be obtained at Reynolds numbers of a few hundreds. The instability is much weaker in an equivalent single solute fluid with the same viscosity contrast, or even in one which is made up only of the more dangerous of the two diffusing species. This is a novel characteristic of double-diffusive systems driven by viscosity, rather than density variations. Convective instabilities too are stronger in the double-diffusive case.

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47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.55.Hd	Stratified flows
47.55.pd	Multidiffusive convection
47.60.Dx	Flows in ducts and channels

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Mixing properties of coaxial jets with large velocity ratios and large inverse density ratios

S. Alexander Schumaker and James F. Driscoll

Phys. Fluids 24, 055101 (2012); http://dx.doi.org/10.1063/1.4711396 (21 pages)

Online Publication Date: 8 May 2012

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An experimental study was conducted to better understand the mixing properties of coaxial jets as several parameters were systematically varied, including the velocity ratio, density ratio, and the Reynolds number. Diameters of the inner and outer jet were also varied. Coaxial jets are commonly used to mix fluids due to the simplicity of their geometry and the rapid mixing that they provide. A measure of the overall mixing efficiency is the stoichiometric mixing length (L_s), which is the distance along the jet centerline where the two fluids have mixed to some desired concentration, which was selected to be the stoichiometric concentration for H₂/O₂ and CH₄/O₂ in this case. For 56 cases, the profiles of mean mixture fraction, rms mixture fraction fluctuations (unmixedness), and L_s were measured using acetone planar laser induced fluorescence diagnostics. Results were compared to three mixing models. The entrainment model of Villermaux and Rehab showed good agreement with the data, indicating that the proper non-dimensional scaling parameter is the momentum flux ratio M. The work extends the existing database of coaxial jet scalar mixing properties because it considers the specific regime of large values of both the velocity ratio and the inverse density ratio, which is the regime in which rocket injectors operate. Also the work focuses on the mixing up to L_s where previous work focused on the mixing up to the end of the inner core. The Reynolds numbers achieved for a number of cases were considerably larger than previous gas mixing studies, which insures that the jet exit boundary conditions are fully turbulent.

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47.85.Np	Fluidics
89.20.Kk	Engineering
05.40.-a	Fluctuation phenomena, random processes, noise, and Brownian motion
47.80.Jk	Flow visualization and imaging

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On Lagrangian single-particle statistics

Gregory Falkovich, Haitao Xu, Alain Pumir, Eberhard Bodenschatz, Luca Biferale, Guido Boffetta, Alessandra S. Lanotte, and Federico Toschi

Phys. Fluids 24, 055102 (2012); http://dx.doi.org/10.1063/1.4711397 (8 pages)

Online Publication Date: 14 May 2012

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In turbulence, ideas of energy cascade and energy flux, substantiated by the exact Kolmogorov relation, lead to the determination of scaling laws for the velocity spatial correlation function. Here we ask whether similar ideas can be applied to temporal correlations. We critically review the relevant theoretical and experimental results concerning the velocity statistics of a single fluid particle in the inertial range of statistically homogeneous, stationary and isotropic turbulence. We stress that the widely used relations for the second structure function, D₂(t) ≡ ⟨[v(t) − v(0)]²⟩∝εt, relies on dimensional arguments only: no relation of D₂(t) to the energy cascade is known, neither in two- nor in three-dimensional turbulence. State of the art experimental and numerical results demonstrate that at high Reynolds numbers, the derivative math

has a finite non-zero slope starting from t ≈ 2τ_η. The analysis of the acceleration spectrum Φ_A(ω) indicates a possible small correction with respect to the dimensional expectation Φ_A(ω) ∼ ω⁰ but present data are unable to discriminate between anomalous scaling and finite Reynolds effects in the second order moment of velocity Lagrangian statistics.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
02.50.-r	Probability theory, stochastic processes, and statistics
02.60.-x	Numerical approximation and analysis

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Modeling scalar dissipation and scalar variance in large eddy simulation: Algebraic and transport equation closures

E. Knudsen, E. S. Richardson, E. M. Doran, H. Pitsch, and J. H. Chen

Phys. Fluids 24, 055103 (2012); http://dx.doi.org/10.1063/1.4711369 (24 pages)

Online Publication Date: 15 May 2012

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Scalar dissipation rates and subfilter scalar variances are important modeling parameters in large eddy simulations (LES) of reacting flows. Currently available models capture the general behavior of these parameters, but these models do not always perform with the degree of accuracy that is needed for predictive LES. Here, two direct numerical simulations (DNS) are used to analyze LES dissipation rate and variance models, and to propose a new model for the dissipation rate that is based on a transport equation. The first DNS that is considered is a non-premixed auto-igniting C₂H₄ jet flame simulation originally performed by Yoo et al. [Proc. Combust. Inst. 33, 1619–1627 (2011)]10.1016/j.proci.2010.06.147. A LES of this case is run using algebraic models for the dissipation rate and subfilter variance. It is shown that the algebraic models fail to adequately reproduce the DNS results. This motivates the introduction of a transport equation model for the LES dissipation rate. Closure of the equation is addressed by formulating a new adapted dynamic approach. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside on the smallest flow length scales. The adapted dynamic approach is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Data from this second DNS are used to confirm that the adapted dynamic approach successfully closes the dissipation rate equation over a wide range of LES filter widths. The first reacting jet case is then returned to and used to test the LES transport equation models. The transport equation model for the dissipation rate is shown to be more accurate than its algebraic counterpoint, and the dissipation rate is eliminated as a source of error in the transported variance model.

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47.70.Fw	Chemically reactive flows
47.70.Pq	Flames; combustion
47.27.ek	Direct numerical simulations
47.27.ep	Large-eddy simulations
47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.27.wg	Turbulent jets

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Maximum entropy states of quasi-geostrophic point vortices

Takeshi Miyazaki, Tomoyoshi Sato, and Naoya Takahashi

Phys. Fluids 24, 056601 (2012); http://dx.doi.org/10.1063/1.4711393 (15 pages)

Online Publication Date: 4 May 2012

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The statistical equilibrium state of quasi-geostrophic point vortices is investigated theoretically, based on the maximum entropy theory. We search for the state of maximum Shannon entropy under the constraints of the vertical vorticity distribution P(z), the angular momentum I, and the energy of the vortex system E. Solutions of the mean field equation are obtained by the numerical procedure proposed by Turkington and Whittaker. The most probable state in an infinite fluid domain is axisymmetric, whose radial distribution depends both on the vertical vortex distribution P(z) and the total energy of the vortex system E. At a certain critical energy value E_c, the number of microscopic state of fixed angular momentum becomes largest (zero-inverse temperature state), where the radial distribution is Gaussian at any vertical height. When the energy is smaller (E < E_c: positive temperature), the radial distribution becomes flatter than the Gaussian. In contrast, if the energy is higher (E > E_c: negative temperature), the radial distribution becomes sharper showing tighter concentration near the axis of symmetry. In order to compare with these theoretical results, very long numerical computations are performed using the fast special-purpose computer for molecular dynamics simulations (GRAPE-DR). Quantitative agreements between the theoretical and numerical results are found for any cases considered.

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47.32.Ef	Rotating and swirling flows
05.70.Ce	Thermodynamic functions and equations of state
47.11.Mn	Molecular dynamics methods
02.50.Ng	Distribution theory and Monte Carlo studies

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Large bubble entrapment during drop impacts on a restricted liquid surface

Jun Zou, Chen Ji, BaoGang Yuan, YuLiang Ren, XiaoDong Ruan, and Xin Fu

Phys. Fluids 24, 057101 (2012); http://dx.doi.org/10.1063/1.3703674 (7 pages)

Online Publication Date: 4 May 2012

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The behavior of millimetric drops impacting on a gas-liquid interface restricted by surrounding walls is studied using a high-speed video camera. A novel phenomenon of large bubble entrapment is observed in experiments. It is found that the large bubble formation is not only dependent on the impact velocity of the drop, but also the shape of drop at the moment of contact with the liquid surface and the distance from the impact point to surrounding walls.

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