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Dec 2005

Volume 17, Issue 12, Articles (12xxxx)

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Turbulent thermal convection at high Rayleigh numbers for a Boussinesq fluid of constant Prandtl number

G. Amati, K. Koal, F. Massaioli, K. R. Sreenivasan, and R. Verzicco

Phys. Fluids 17, 121701 (2005); http://dx.doi.org/10.1063/1.2140023 (4 pages) | Cited 31 times

Online Publication Date: 5 December 2005

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The results from direct numerical simulations of turbulent Boussinesq convection are briefly presented. The flow is computed for a cylindrical cell of aspect ratio 1/2 in order to compare with the results from recent experiments. The results span eight decades of Ra from 2×106 to 2×1014 and form the baseline data for a strictly Boussinesq fluid of constant Prandtl number (Pr = 0.7). A conclusion is that the Nusselt number varies nearly as the 1/3 power of Ra for about four decades towards the upper end of the Ra range covered.
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47.27.-i Turbulent flows

Evaluation of a universal transitional resistance diagram for pipes with honed surfaces

J. J. Allen, M. A. Shockling, and A. J. Smits

Phys. Fluids 17, 121702 (2005); http://dx.doi.org/10.1063/1.2145753 (4 pages) | Cited 7 times

Online Publication Date: 13 December 2005

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A method for evaluating a universal transitional resistance diagram for pipes that relates the pressure drop in the pipe to Reynolds number, as a function of relative surface roughness, is presented. The method assumes a universal wake function, a logarithmic overlap region and a power fit in the viscous and buffer layer. Estimates can be made of the friction factor–Reynolds number relationship for arbitrary relative roughness, based on a given surface geometry. The method is illustrated for a pipe with a honed surface finish and uses data of Shockling (“Turbulent flow in a rough pipe,” MSE dissertation, Princeton University, 2005). Honed roughness demonstrates an inflectional behavior in the transitionally rough regime, much like sand grain roughness [ Laws of flow in rough pipes, VDI Forschungsh, 361 (1933), 1292 (NACA TM, 1950) ], but the method proposed here can be applied to any given roughness behavior. It is suggested that the critical parameter that determines whether the resistance diagram shows inflectional characteristics is the ratio of roughness height to outer layer scale. Based on analysis of data from previous researchers it is suggested that if the relative surface roughness krms/D<0.0025, where krms is the rms amplitude of the roughness and D is the pipe diameter, inflectional relationships should be observed.
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47.60.-i Flow phenomena in quasi-one-dimensional systems

Identification method for vortex sheet structures in turbulent flows

Kiyosi Horiuti and Youhei Takagi

Phys. Fluids 17, 121703 (2005); http://dx.doi.org/10.1063/1.2147610 (4 pages) | Cited 20 times

Online Publication Date: 16 December 2005

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A new identification method was proposed for an eduction of vortex sheet structures in turbulent flows. This method took advantage of a prominent feature of a sheet, i.e., comparable dominance of both strain rate and vorticity and their strong correlation. The effectiveness of the proposed method was presented in the assessment using direct numerical simulation data for homogeneous isotropic turbulence. Both strain rate and vorticity were indeed large and correlated in the region identified using the proposed method. As a result, intense dissipation took place in the educed region. The relationship between the eigenvalue solution used in the present method and the invariants of fourth-order moments of velocity gradients was discussed. It was shown that the proposed method performed better than other invariants and previous identification methods for educing the vortex sheets.
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47.32.C- Vortex dynamics
47.27.E- Turbulence simulation and modeling
47.27.Gs Isotropic turbulence; homogeneous turbulence

Three-dimensional solitary waves on falling liquid film at low Reynolds numbers

S. V. Alekseenko, V. A. Antipin, V. V. Guzanov, S. M. Kharlamov, and D. M. Markovich

Phys. Fluids 17, 121704 (2005); http://dx.doi.org/10.1063/1.2158428 (4 pages) | Cited 11 times

Online Publication Date: 22 December 2005

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In this Letter we present novel results of the experimental study of three-dimensional waves evolving from a localized disturbance on a vertically falling film at low Reynolds numbers 1.25<Re<4.7. This range of Re is close to the values that are typical for residual layers in developed wavy film flow with moderate Reynolds numbers. A spatiotemporal evolution of three-dimensional solitary waves is investigated. Existence of the stationary horseshoe-shaped waves has been demonstrated. The measured wave characteristics are compared with the theoretical solutions.
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47.35.-i Hydrodynamic waves
47.15.G- Low-Reynolds-number (creeping) flows
68.15.+e Liquid thin films
05.45.Yv Solitons

Direct numerical simulations of shock propagation in bubbly liquids

C. F. Delale, S. Nas, and G. Tryggvason

Phys. Fluids 17, 121705 (2005); http://dx.doi.org/10.1063/1.2158431 (4 pages) | Cited 8 times

Online Publication Date: 27 December 2005

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The propagation of a pressure wave in an initially quiescent bubbly liquid of relatively high void fraction contained in a two-dimensional (2D) or three-dimensional (3D) rectangular domain is investigated by direct numerical simulations of the Navier-Stokes equations using a front-tracking/finite-volume method. The gas pressure inside the bubbles is either set equal to a constant or varied by the polytropic relation. Results obtained for 2D and 3D domains show mean shock speeds in agreement with those of one-dimensional homogeneous bubbly liquid theory.
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47.40.Nm Shock wave interactions and shock effects
47.11.Df Finite volume methods
47.55.dd Bubble dynamics
47.55.Ca Gas/liquid flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.10.ad Navier-Stokes equations
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back to top Interfacial Flows

Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems

E. I. Părău, J.-M. Vanden-Broeck, and M. J. Cooker

Phys. Fluids 17, 122101 (2005); http://dx.doi.org/10.1063/1.2140020 (9 pages) | Cited 10 times

Online Publication Date: 5 December 2005

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Numerical solutions for three-dimensional gravity capillary waves in water of finite depth are presented. The full Euler equations are used and the waves are calculated by a boundary integral equation method. The findings generalize previous results of Părău, Vanden-Broeck, and Cooker [J. Fluid Mech. 536, 99 (2005)] in water of infinite depth. It is found that there are both lumps that bifurcate from linear sinusoidal waves and other fully localized solitary waves which exist for large values of the Bond number. These findings are consistent with rigorous analytical results and asymptotic calculations. The relation between the solitary waves and free surface flows generated by moving disturbances is also explored.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.35.-i Hydrodynamic waves

Dynamics of thin free films with reaction-driven density and viscosity variations

O. K. Matar and P. D. M. Spelt

Phys. Fluids 17, 122102 (2005); http://dx.doi.org/10.1063/1.2130966 (15 pages) | Cited 1 time

Online Publication Date: 7 December 2005

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We study the dynamics of thin free viscous films in the presence of exothermic chemical reactions, which alter the film density and viscosity. We use long-wave theory and the assumption of rapid vertical diffusion to derive a coupled system of evolution equations for the film thickness, axial velocity, temperature, and reactant and product concentrations; appropriate closure relations are chosen for the dependence of the density and viscosity (both dynamic and bulk) on the product concentration and temperature. Analytical and numerical solutions of the evolution equations allow a full parametric study to be conducted. The results indicate that the film dynamics is primarily governed by density variations, which depend on competing factors: the increase in product concentration and temperature (due to the heat of reaction), which act to increase and decrease the density, respectively. Thus the film can collapse and rupture (expand) if the former (latter) effects outweigh the latter (former); here, rupture is driven by van der Waals forces.
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68.15.+e Liquid thin films
66.20.-d Viscosity of liquids; diffusive momentum transport
47.70.Fw Chemically reactive flows
82.40.-g Chemical kinetics and reactions: special regimes and techniques
66.10.C- Diffusion and thermal diffusion
82.60.Cx Enthalpies of combustion, reaction, and formation

Experiment on the dynamics of a compound drop impinging on a hot surface

Sheng-Lin Chiu and Ta-Hui Lin

Phys. Fluids 17, 122103 (2005); http://dx.doi.org/10.1063/1.2139101 (9 pages) | Cited 10 times

Online Publication Date: 8 December 2005

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A stable stream of compound drops which are composed of core fluid, water, encased by a layer of shell fluid, diesel, was utilized to investigate the dynamic behavior of a liquid-liquid compound drop impinging on a hot surface above the Leidenfrost temperature. The core-to-shell mass ratio and the modified normal Weber number, which takes into account the two interfaces involved, were taken to be the controlling parameters. The outcomes of a compound drop impacting on a hot surface consist largely of reflection with or without secondary drops. Based on energy conservation, the dissipated energy was estimated and a criterion for secondary drop formation was presented. The normal velocity after impact is reduced due to viscous dissipation while the tangential component remains almost unaffected. In addition, there is an interesting phenomenon of the core drop escaping from the compound drop. The experimental results show that an increasing core-to-shell mass ratio raises the momentum loss, reduces the number of secondary drops, and promotes core-drop escaping.
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47.55.D- Drops and bubbles

Dynamics of low capillary number interfaces moving through sharp features

Shravanthi Reddy, P. Randall Schunk, and Roger T. Bonnecaze

Phys. Fluids 17, 122104 (2005); http://dx.doi.org/10.1063/1.2140691 (6 pages) | Cited 15 times

Online Publication Date: 13 December 2005

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The success of any nanoimprint process depends upon its ability to exactly reproduce the template pattern. Thus, complete filling of recessed features in the template is an important issue that is controlled by the dynamics of the flow through these sharp structures. At these small scales, capillary forces are large and must be included in the fluid flow model. The mechanism of interface advancement at low capillary number through sharp rectangular features is useful for understanding how and why features fill or trap air. In this study we present a two-dimensional simulation of this feature filling to capture the details of the process, including the viscous and capillary effects. Fluid is injected into the channel between the template and substrate, where the fluid–air interface soon encounters a rectangular feature with some height greater than the channel gap. As the fluid advances through the channel, the shape of the interface is a circular arc due to the strong capillary forces. The interface maintains this circular arc as it negotiates the first sharp corner of the feature; the upper contact line effectively pins to the initial corner of the feature as it moves around this corner, during which time the lower contact line continues to advance forward along the substrate surface, causing the interface to stretch. For sufficiently wide or shallow features, once the upper contact line has negotiated the first corner and has moved vertically up the inner wall of the feature, it must move through the top corner of the feature. At this point the interface undergoes a rapid reconfiguration from a high surface area circular arc to a lower surface area circular arc inside the feature. Alternatively, for narrow or high features, the stretched interface can catch on the far, final corner of the feature, trapping air inside the feature and preventing filling. The conditions for filling are studied parametrically for a variety of wetting contact angles and feature dimensions with both the simulation and a simpler, successful geometric model. The dynamics of the feature filling suggest an effective boundary condition for a macroscopic lubrication model of the imprint lithography process in which a critical pressure is required to move fluid through a feature.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting

Simulations of binary drop collisions with a multiple-relaxation-time lattice-Boltzmann model

Kannan N. Premnath and John Abraham

Phys. Fluids 17, 122105 (2005); http://dx.doi.org/10.1063/1.2148987 (21 pages) | Cited 20 times

Online Publication Date: 16 December 2005

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In this paper, we report simulations of drop-drop collisions using a multi-relaxation-time multiphase flow lattice Boltzmann model. Employing a multi-relaxation-time (MRT) model in lieu of the Bhatnagar-Gross-Krook (BGK) model used in the standard lattice-Boltzmann equation enables realization of stable computations of drop collisions at relatively lower fluid viscosities without increasing the lattice resolution to prohibitive levels. Head-on and off-center computations of collisions are carried out using axisymmetric and three-dimensional (3D) versions of the MRT model, respectively. Time-resolved results showing the interactions of the interfaces of drops for different characteristic nondimensional parameters are presented. Computations show that at low Weber numbers, We, coalescence with relatively smaller deformation occurs, sometimes entrapping a stable microbubble. At higher We, head-on collisions lead to reflexive separation with or without the formation of satellite droplets. The size of the satellite droplets appears to increase with increase in the We. The Ohnesorge number, Oh, seems to modulate the transient characteristics and the outcome of collisions. It is found that the greater the Oh, the smaller is the size of the satellite droplets formed. For off-center collisions at a given We, at lower values of the impact parameter permanent coalescence is observed, while higher values result in separation by stretching action. These findings are in satisfactory agreement with experimental observations.
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47.55.Kf Particle-laden flows
47.55.D- Drops and bubbles
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.11.-j Computational methods in fluid dynamics
05.20.Dd Kinetic theory

Acoustic streaming past a vibrating wall

Paolo Luchini and François Charru

Phys. Fluids 17, 122106 (2005); http://dx.doi.org/10.1063/1.2149314 (7 pages) | Cited 4 times

Online Publication Date: 22 December 2005

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The classic phenomenon of acoustic streaming is reconsidered for the case in which the boundary layers on the vibrating and the still walls are of comparable importance, in the small-gap configuration suitable for an ultrasonic motor. The effect of temperature oscillations is included in the analysis, as well as is the impedance matching with the elastic oscillations in the vibrating wall.
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43.40.-r
47.40.-x Compressible flows; shock waves

Influence of an adsorption layer on the structure and stability of surface tension driven flows

A. Mizev

Phys. Fluids 17, 122107 (2005); http://dx.doi.org/10.1063/1.2150794 (5 pages) | Cited 6 times

Online Publication Date: 23 December 2005

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The structure and stability of thermocapillary and solutocapillary flow from a localized source has been experimentally studied in the presence of adsorption layers. It is found that the divergent flow, which is typical for this case, becomes unstable to azimuthally periodic perturbations that lead to the appearance of a surface flow with a multivortex structure. The evolution of the flow structure during an increase of concentration in the adsorption layer is shown. Two possible physical models of the observed instability are put forward.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
back to top Viscous and Non-Newtonian Flows

Transient drop deformation upon startup of shear in viscoelastic fluids

Pengtao Yue, James J. Feng, Chun Liu, and Jie Shen

Phys. Fluids 17, 123101 (2005); http://dx.doi.org/10.1063/1.2139630 (6 pages) | Cited 22 times

Online Publication Date: 6 December 2005

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Recent experiments show that upon abrupt start of a shear flow, a suspended drop undergoes an overshoot in deformation if either the drop or the matrix is a polymeric fluid. Using a diffuse-interface formulation, we carry out two-dimensional numerical simulations that trace the origin of the transient to the mismatch of two time scales: a capillary time for drop deformation and a relaxation time for the polymers in the viscoelastic component. The results are in qualitative agreement with experiments.
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47.55.-t Multiphase and stratified flows
47.50.-d Non-Newtonian fluid flows

Viscosity and slip velocity in gas flow in microchannels

M. Fichman and G. Hetsroni

Phys. Fluids 17, 123102 (2005); http://dx.doi.org/10.1063/1.2141960 (5 pages) | Cited 8 times

Online Publication Date: 13 December 2005

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It was shown that as a result of the interaction of part of the molecules with a wall, the viscosity in the Knudsen layer is lower in comparison with the viscosity in the bulk fluid. The slip condition of Maxwell depends on the normal gradient of the tangential velocity on the wall. The reduction of the viscosity increases the tangential velocity and its normal gradient, and, therefore, increases the slip. The correction factors for the Maxwell expression for one-dimensional plane and tubular isothermal and incompressible flows as a function of the Knudsen number and of the kind of interaction of molecules with the wall were derived.
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47.85.Np Fluidics
47.45.Gx Slip flows and accommodation
47.45.Dt Free molecular flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
51.20.+d Viscosity, diffusion, and thermal conductivity
85.85.+j Micro- and nano-electromechanical systems (MEMS/NEMS) and devices
back to top Particulate, Multiphase, and Granular Flows

Combustion mechanism of liquid fuel spray in a gaseous flame

Mariko Nakamura, Fumiteru Akamatsu, Ryoichi Kurose, and Masashi Katsuki

Phys. Fluids 17, 123301 (2005); http://dx.doi.org/10.1063/1.2140294 (14 pages) | Cited 17 times

Online Publication Date: 20 December 2005

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Two-dimensional direct numerical simulation is applied to spray flames stabilized in a laminar counterflow, and the detailed behavior is studied in terms of the droplet group combustion. The stretch ratio of the laminar counterflow is 40 l/s. n-decane (C10H22) is used as a liquid spray fuel, and a one-step global reaction is employed for the combustion reaction model. The results show that with increasing the issued liquid fuel mass fraction, two types of spray combustion appear in front of and inside the high gaseous temperature region, i.e., “premixed-like combustion” and “diffusion-like combustion,” respectively. A droplet group combustion behavior is observed in the diffusion-like combustion region. This diffusion-like combustion, however, disappears when the issued droplet size becomes small, because the droplets complete their evaporation before entering into the high gaseous temperature region. The droplet group combustion tends to reduce the gaseous temperature. This is caused mainly by the suppression of combustion reaction due to the lack of oxygen and partially by the energy exchange through the convective heat transfer between droplets and gaseous phase. The gaseous temperature reduction is promoted by the latent heat of vaporization of the droplets. The use of the parcel approach has a risk of causing a delay of combustion reaction, since the partial fuel vapor pressure increases at limited locations, which suppresses the global droplet evaporation rate.
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47.70.Fw Chemically reactive flows
82.33.Vx Reactions in flames, combustion, and explosions
82.70.Rr Aerosols and foams
47.15.-x Laminar flows
64.70.F- Liquid-vapor transitions
back to top Instability and Transition

Three-dimensional numerical study of natural convection in vertical cylinders partially heated from the side

D. J. Ma, D. Henry, and H. Ben Hadid

Phys. Fluids 17, 124101 (2005); http://dx.doi.org/10.1063/1.2141430 (12 pages) | Cited 6 times

Online Publication Date: 9 December 2005

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Three-dimensional steady and oscillatory flows are simulated in a vertical cylinder partially heated from the side. The vertical wall is heated in a zone at midheight and is insulated above and below this middle zone, while both ends of the cylinder are cooled. The cylinder aspect ratio (A = height/radius) ranges from 2 to 8, whereas a fixed Prandtl number, Pr = 0.021, is considered as well as a fixed length of the heated zone, equal to the cylinder radius. Three-dimensional steady and unsteady simulations as well as mode decomposition techniques and energy transfer analyses are used to characterize the flows and their transitions. The flows that develop from the steady toroidal pattern beyond the first instability threshold break the axisymmetry. At small A (2 ⩽ A ⩽ 2.5), the flow corresponds to a two-roll rotating pattern, which is triggered by a k = 2 azimuthal mode as a result of a hydrodynamic instability. At large A (3 ⩽ A ⩽ 8), the flow is steady and corresponds to a main one-roll pattern in the upper part of the cylinder. The flow is triggered by a k = 1 mode as a result of buoyancy effects affecting this unstably stratified upper part (Rayleigh-Bénard instability), but shear effects are involved in the instability for the smaller values of A. These steady flows then transit at a higher threshold to a standing-wave oscillatory one-roll pattern associated with the breaking of symmetry of the previous steady pattern. For intermediate values of A (2.7 ⩽ A ⩽ 2.9), the transition is toward an oscillatory pattern, but hysteresis phenomena with multiplicity of steady and oscillatory states have been found. Comparisons with experiments performed at aspect ratios A = 4 and 8 are then considered and discussed.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.55.Hd Stratified flows
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Splitting and merging of Görtler vortices

H. Mitsudharmadi, S. H. Winoto, and D. A. Shah

Phys. Fluids 17, 124102 (2005); http://dx.doi.org/10.1063/1.2151227 (12 pages) | Cited 2 times

Online Publication Date: 27 December 2005

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The splitting and merging of Görtler vortices are experimentally studied by varying the spacings of vertical wires located 10 mm upstream of a concave surface leading edge of 2.0 m radius of curvature subjected to a free-stream velocity of 3.0 m/s. The splitting and merging as the result of the linear instability of the vortices with respect to spanwise perturbation (Eckhaus instability), occurred when the wire spacing was set to respectively twice and half of the dominant or most amplified wavelength of Görtler vortices. These show the susceptibility of Görtler vortices to wavelengths greater and smaller than the most amplified wavelength of the vortices. The spectral study shows that the values of the dimensionless frequency parameter for the wire spacings of 7.5, 15.0, and 30.0 mm are nearly constant (of about 0.5) for the streamwise locations where the mushroom-like structures dominate the flow. It is also found that the dimensionless wavelength parameter is more sensitive than the Reynolds number of the vertical wires as a threshold identification of transition from one pair to two pairs of vortex configurations.
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47.32.C- Vortex dynamics
47.20.Lz Secondary instabilities
back to top Turbulent Flows

Effect of particle inertia and gravity on the turbulence in a suspension

G. Ooms and P. Poesio

Phys. Fluids 17, 125101 (2005); http://dx.doi.org/10.1063/1.2139683 (12 pages) | Cited 2 times

Online Publication Date: 6 December 2005

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A theoretical model is presented for the effect of particle inertia and gravity on the turbulence in a homogeneous suspension. It is an extension of the one-fluid model developed by L’vov, Ooms, and Pomyalov [Phys. Rev. E 67, 046314 (2003)] , in which the effect of gravity was not considered. In the extended model the particles are assumed to settle in the fluid under the influence of gravity due to the fact that their density is larger than the fluid density. The generation of turbulence by the settling particles is described, with special attention being paid to the turbulence intensity and spectra. A comparison is made with direct numerical simulation calculations and experimental data. Also a sensitivity study is carried out to investigate at which conditions the gravity effect becomes important.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.55.Kf Particle-laden flows

Aspect ratio effects in quasi-two-dimensional turbulence

K. Ngan, D. N. Straub, and P. Bartello

Phys. Fluids 17, 125102 (2005); http://dx.doi.org/10.1063/1.2139685 (10 pages) | Cited 6 times

Online Publication Date: 6 December 2005

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The influence of the aspect ratio on the three-dimensionalization and subsequent saturation of freely decaying two-dimensional turbulence is studied numerically. We show that the aspect ratio strongly affects the saturation level of the perturbation and its feedback on the base flow. The saturation level scales linearly with the aspect ratio, as does the total damping exerted by the perturbation. In spectral space the feedback yields a positive eddy viscosity at large scales and a small eddy viscosity at small scales. A surprising result is the persistence of coherent vortices even after the saturation of the perturbation.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Numerically induced high-pass dynamics in large-eddy simulation

Bernard J. Geurts and Fedderik van der Bos

Phys. Fluids 17, 125103 (2005); http://dx.doi.org/10.1063/1.2140022 (12 pages) | Cited 11 times

Online Publication Date: 9 December 2005

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The numerical distortion of the smallest resolved-scale dynamics in large-eddy simulation may be understood in terms of the filter that is induced by the spatial discretization. At marginal subfilter resolution r = Δ/h, with filter width Δ and grid spacing h, the character of the large-eddy closure problem is strongly influenced by the numerical method. We show that additional high-pass contributions arise from the spatial discretization. The relative importance of, on the one hand, the turbulent stresses and, on the other hand, the numerically induced contributions, is quantified for general finite differencing methods. We derive and analyze the induced filters for several popular discretization methods, including higher order central and upwind methods. The application of these induced filters to small-scale turbulent flow structures gives rise to a characteristic amplitude reduction and phase shift. Their dynamic relevance is quantified in terms of the subfilter resolution. The numerical high-pass effects are found to be negligible if the subfilter resolution is large enough (r≳4). Conversely, the numerically induced effects are comparable to, or even larger than the turbulent stresses as r = 1–2.
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02.60.Jh Numerical differentiation and integration
47.27.E- Turbulence simulation and modeling

Effects of unsteady strain rate on scalar dissipation structures in turbulent planar jets

P. S. Kothnur and N. T. Clemens

Phys. Fluids 17, 125104 (2005); http://dx.doi.org/10.1063/1.2136827 (14 pages) | Cited 2 times

Online Publication Date: 13 December 2005

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An analysis of previously acquired experimental data is performed with the objective of investigating the relationship between strain rate and scalar dissipation rate structures in gas-phase turbulent planar jet flows at local Reynolds numbers ranging from 1000 to 6100. The data analyzed were simultaneously acquired two-dimensional (2D) velocity and 2D conserved scalar fields. The measurements show that, in agreement with previous work, the scalar dissipation structures tend to align orthogonally to the axis of the principal compressive strain rate, and the magnitude of the strain rates acting on the dissipation layers is consistent with theoretical turbulent inner-scale values. Furthermore, the spatially resolved data show that profiles of scalar dissipation, taken across the sheet-like scalar dissipation structures, are approximately Gaussian, whereas the strain rate profiles across the same structures exhibit no characteristic shape, and rarely reach a maximum at the same location as the scalar dissipation. When the scalar dissipation layer thicknesses are cast in nondimensional form and plotted as a function of the instantaneous relative strain rate, the data at all Reynolds numbers exhibit similar characteristics. The measurements from the turbulent flow were compared to a simple one-dimensional (1D) unsteady strained laminar diffusion-layer model, where the imposed strain rate varied harmonically. The simplified model shows remarkable agreement with the experimental data as it predicts the correct trend of layer thickness with strain rate and captures the range of scalar dissipation layer thicknesses that are present in the turbulent flows. The model and experiments show that the layers with greater-than-average strain rate tend to be thicker than expected by steady-state theory, whereas at low strain rates the layers are significantly thinner than at steady state. The 1D model shows best agreement with the measurements when the imposed strain rates are allowed to be positive in the direction of the scalar gradient over some part of the oscillation cycle. This suggests that dissipation layers in turbulent flows experience significant positive strain over their lifetimes.
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47.20.-k Flow instabilities
47.27.wg Turbulent jets
47.35.-i Hydrodynamic waves

Anisotropy of magnetohydrodynamic turbulence at low magnetic Reynolds number

Anatoliy Vorobev, Oleg Zikanov, Peter A. Davidson, and Bernard Knaepen

Phys. Fluids 17, 125105 (2005); http://dx.doi.org/10.1063/1.2140847 (12 pages) | Cited 19 times

Online Publication Date: 13 December 2005

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Turbulent fluctuations in magnetohydrodynamic flows are known to become anisotropic under the action of a sufficiently strong magnetic field. We investigate this phenomenon in the case of low magnetic Reynolds number using direct numerical simulations and large eddy simulations of a forced flow in a periodic box. A series of simulations is performed with different strengths of the magnetic field, varying Reynolds number, and two types of forcing, one of which is isotropic and the other limited to two-dimensional flow modes. We find that both the velocity anisotropy (difference in the relative amplitude of the velocity components) and the anisotropy of the velocity gradients are predominantly determined by the value of the magnetic interaction parameter. The effects of the Reynolds number and the type of forcing are much weaker. We also find that the anisotropy varies only slightly with the length scale.
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47.27.E- Turbulence simulation and modeling
47.65.-d Magnetohydrodynamics and electrohydrodynamics

Near-field turbulent simulations of rectangular jets using lattice Boltzmann method

Huidan Yu and Sharath S. Girimaji

Phys. Fluids 17, 125106 (2005); http://dx.doi.org/10.1063/1.2140021 (17 pages) | Cited 8 times

Online Publication Date: 16 December 2005

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We perform large eddy simulation (LES) of the near field of low aspect ratio (AR) rectangular turbulent jets (RTJ) using the lattice Boltzmann method. The computational technique combines a D3Q19 multiple relaxation time (MRT) lattice Boltzmann equation (LBE) with the Smagorinsky model for the subgrid stress. First and foremost, we demonstrate that the MRT-LBE model is more suitable than the widely used single-relaxation-time LBE model for LES of turbulent flows. Then, we proceed to compute four jets with MRT-LBE: AR-1, 1.5, 2, 5; exit velocity u0 (m/s)-60, 39, 60, 23; and Reynolds number Re-184 000, 25 900, 128 000, 14 000. The investigated near-field behavior includes: (1) Decay of mean streamwise velocity (MSV) and inverse MSV; (2) spanwise and lateral profiles of MSV; (3) half-velocity width development and MSV contours; and (4) streamwise turbulence intensity distribution. The simulation results are compared against experimental data. Two unique features of RTJ—the saddle-back MSV spanwise (major axis) profile and axis switching of major axis from spanwise to lateral direction—are investigated. Our simulations show that the jet statistical behavior is more sensitive to inflow velocity and less so to the transverse boundary conditions. Overall, this work demonstrates that the MRT-LBE method is a potentially reliable computational tool for LES of turbulence even at high Reynolds numbers.
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47.27.Jv High-Reynolds-number turbulence

Statistics and geometry of passive scalars in turbulence

Jörg Schumacher and Katepalli R. Sreenivasan

Phys. Fluids 17, 125107 (2005); http://dx.doi.org/10.1063/1.2140024 (9 pages) | Cited 13 times

Online Publication Date: 16 December 2005

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We present direct numerical simulations of the mixing of the passive scalar at modest Taylor microscale (10 ⩽ Rλ ⩽ 42) and Schmidt numbers larger than unity (2 ⩽ Sc ⩽ 32). The simulations resolve below the Batchelor scale up to a factor of 4. The advecting turbulence is homogeneous and isotropic, and is maintained stationary by stochastic forcing at low wave numbers. The passive scalar is rendered stationary by a mean scalar gradient in one direction. The relation between geometrical and statistical properties of scalar field and its gradients is examined. The Reynolds numbers and Schmidt numbers are not large enough for either the Kolmogorov scaling or the Batchelor scaling to develop and, not surprisingly, we find no fractal scaling of scalar level sets, or isosurfaces, in the intermediate viscous range. The area-to-volume ratio of isosurfaces reflects the nearly Gaussian statistics of the scalar fluctuations. The scalar flux across the isosurfaces, which is determined by the conditional probability density function (PDF) of the scalar gradient magnitude, has a stretched exponential distribution towards the tails. The PDF of the scalar dissipation departs distinctly, for both small and large amplitudes, from the log-normal distribution for all cases considered. The joint statistics of the scalar and its dissipation rate, and the mean conditional moment of the scalar dissipation, are studied as well. We examine the effects of coarse-graining on the probability density to simulate the effects of poor probe-resolution in measurements.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.53.+n Fractals in fluid dynamics
02.70.Hm Spectral methods

Reynolds number dependency of the scalar flux spectrum in isotropic turbulence with a uniform scalar gradient

W. J. T. Bos, H. Touil, and J.-P. Bertoglio

Phys. Fluids 17, 125108 (2005); http://dx.doi.org/10.1063/1.2140848 (8 pages) | Cited 11 times

Online Publication Date: 16 December 2005

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In this paper, the eddy-damped quasi-normal Markovian closure is used to study the behavior of the scalar flux spectrum in isotropic turbulence as the Reynolds number Reλ varies in a range between 30 and 107. The different contributions to the evolution equation of the scalar flux spectrum are studied. One-dimensional spectra are in good agreement with direct numerical simulation (DNS) and experiments at moderate Reλ. The closure shows that at high Reynolds numbers, a K−7/3 scaling is found for the scalar flux spectrum, in agreement with Lumley’s prediction [Phys. Fluids 10, 855 (1967)] , but enormous Reλ are needed before it can be clearly observed. In the range of wind tunnel experiments, the spectral exponent for the scalar flux is closer to −2 in agreement with existing measurements [Mydlarski and Warhaft, J. Fluid Mech. 358, 135 (1998)] . The results for the molecular dissipation of scalar flux are in agreement with the DNS results of Overholt and Pope [Phys. Fluids A 8, 3128 (1996)] . The large Reλ behavior of this quantity is also addressed.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems
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