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

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Re-examining the logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flow

C. M. White, Y. Dubief, and J. Klewicki

Phys. Fluids 24, 021701 (2012); http://dx.doi.org/10.1063/1.3681862 (6 pages)

Online Publication Date: 3 February 2012

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A re-examination of the logarithmic dependence of the mean velocity distribution in polymer drag reduced flows shows that drag reducing polymers modify the von Kármán coefficient and, in channel flow, eradicate the log-layer at high drag reductions. It is also found that the “ultimate profile,” corresponding to the state of maximum drag reduction is not logarithmic.

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47.27.nb	Boundary layer turbulence
47.57.Ng	Polymers and polymer solutions
47.27.nd	Channel flow
47.50.Cd	Modeling
47.27.E-	Turbulence simulation and modeling
47.60.Dx	Flows in ducts and channels

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Oscillatory bubbles induced by geometrical constraint

M. Pailha, A. L. Hazel, P. A. Glendinning, and A. Juel

Phys. Fluids 24, 021702 (2012); http://dx.doi.org/10.1063/1.3682772 (7 pages)

Online Publication Date: 9 February 2012

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We show that a simple change in pore geometry can radically alter the behavior of a fluid-displacing air finger, indicating that models based on idealized pore geometries fail to capture key features of complex practical flows. In particular, partial occlusion of a rectangular cross section can force a transition from a steadily propagating centered finger to a state that exhibits spatial oscillations formed by periodic sideways motion of the interface at a fixed distance behind the moving finger tip. We characterize the dynamics of the oscillations, which suggest that they arise from a global homoclinic connection between the stable and unstable manifolds of a steady, symmetry-broken solution.

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47.55.dd	Bubble dynamics
47.54.De	Experimental aspects

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Clouds of particles in a periodic shear flow

Bloen Metzger and Jason E. Butler

Phys. Fluids 24, 021703 (2012); http://dx.doi.org/10.1063/1.3685537 (6 pages)

Online Publication Date: 14 February 2012

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We have investigated the time evolution of a cloud of non-Brownian particles subjected to a periodic shear flow in an otherwise pure liquid at low Reynolds number. This experiment illustrates the irreversible nature of particulate systems submitted to a shear. When repeating the cycles of shear, we have found that clouds of particles progressively disperse in the flow direction until reaching a threshold critical volume fraction that depends upon the strain amplitude; this critical volume fraction coincides with measurements of the threshold for reversibility found from experiments on homogeneous suspensions in periodic shear. Two distinct patterns, including a “galaxy-like” shape, are observed for the evolution of the clouds and the transition between the patterns is identified using a simple scaling analysis. Movies are available with the online version of the paper.

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47.55.Kf	Particle-laden flows
47.57.E-	Suspensions
47.54.De	Experimental aspects
47.60.-i	Flow phenomena in quasi-one-dimensional systems

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Velocity slip coefficients based on the hard-sphere Boltzmann equation

Livio Gibelli

Phys. Fluids 24, 022001 (2012); http://dx.doi.org/10.1063/1.3680873 (14 pages)

Online Publication Date: 3 February 2012

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We present a kinetic theory derivation of higher-order slip boundary conditions. The situation studied is that of a pressure driven isothermal gas flowing through a plane microchannel. The distribution function is expanded in terms of half-range Hermite polynomials and the system of moment equations in the expansion coefficients is analytically solved. The velocity slip coefficients, as well as their Knudsen-layer corrections, are obtained by evaluating the solution in the near continuum limit. The proposed approach is accurate and easy to implement. The results are presented for the hard-sphere Boltzmann equation and Maxwell's diffuse-specular boundary conditions, but can be extended to arbitrary intermolecular interactions and more general scattering kernels.

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47.45.Gx	Slip flows and accommodation
47.60.Dx	Flows in ducts and channels
47.11.-j	Computational methods in fluid dynamics
47.15.Rq	Laminar flows in cavities, channels, ducts, and conduits
47.40.-x	Compressible flows; shock waves
47.45.Ab	Kinetic theory of gases

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Bouncing, coalescence, and separation in head-on collision of unequal-size droplets

Chenglong Tang, Peng Zhang, and Chung K. Law

Phys. Fluids 24, 022101 (2012); http://dx.doi.org/10.1063/1.3679165 (15 pages)

Online Publication Date: 1 February 2012

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The dynamics of head-on collision of unequal-size droplets were experimentally and theoretically investigated, with emphasis on identifying distinct collision outcomes and interpreting the size-ratio dependence. A unified regime diagram in terms of bouncing, permanent coalescence, and separation after coalescence was identified for hydrocarbon and water droplets in the parameter space of the size ratio and a collision Weber number. Experimental results show that the transition Weber number, We_b-c, that separates the bouncing and permanent coalescence regimes, weakly depends on the size ratio, while the transition Weber number, We_c-s, that separates permanent coalescence and separation regimes, significantly increases with the size ratio. A theoretical model based on energy balance and scaling analysis was developed to explain the size-ratio dependence of We_c-s. The theoretical results show good agreement with the experimental data for tetradecane and decane droplets, with a moderate discrepancy for water droplets.

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47.55.df	Breakup and coalescence
47.32.Ff	Separated flows

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Thermocapillary motion of a slender viscous droplet in a channel

E. Katz, M. Haj, A. M. Leshansky, and A. Nepomnyashchy

Phys. Fluids 24, 022102 (2012); http://dx.doi.org/10.1063/1.3681813 (11 pages)

Online Publication Date: 7 February 2012

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We extend the previously developed low-capillary-number asymptotic theory of thermocapillary motion of a long bubble and a moderately viscous droplet in a channel [S. K. Wilson, “The effect of an axial temperature gradient on the steady motion of a large droplet in a tube,” J. Eng. Math. 29, 205 (1995)10.1007/BF00042854; A. Mazouchi and G. M. Homsy, “Thermocapillary migration of long bubbles in cylindrical capillary tubes,” Phys. Fluids 12, 542 (2000)10.1063/1.870260] toward droplets with an arbitrary viscosity. A generalized modified Landau-Levich-Bretherton equation, governing the thickness of the carrier liquid film entrained between the droplet and the channel wall in the transition region between constant thickness film and constant curvature cap, is solved numerically. The resulting droplet velocity is determined applying the mass balance and it is a function of two dimensionless parameters, the modified capillary number, Δσ*, equal to the surface tension variance over a distance of channel half-width scaled with the mean surface tension, and the inner-to-outer liquid viscosity ratio, λ. It is found that the droplet speed decreases with the increase in droplet viscosity, as expected, while this retardation becomes more operative upon the increase in Δσ*.

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47.55.dm	Thermocapillary effects
47.60.Dx	Flows in ducts and channels
47.10.A-	Mathematical formulations

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Observation of collision and oscillation of microdroplets with extremely large shear deformation

Tatsuya Yamada and Keiji Sakai

Phys. Fluids 24, 022103 (2012); http://dx.doi.org/10.1063/1.3681810 (9 pages)

Online Publication Date: 8 February 2012

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We measured the viscosity and surface tension of various liquids under large (∼10⁶ s⁻¹) shear deformation. Oscillation of a 10-μm size microdroplet is brought about by the head-on collision of two droplets. Since the Reynolds number is as small as 100, the motion of the liquid is stable and the dynamic image is obtained with high reproducibility by the stroboscopic method. By observing and evaluating the mechanical oscillation of the microdroplet, of which frequency ranges typically in 100 – 300 kHz, we found that the viscosity of ethylene glycol and diethylene glycol is smaller than the known literature value, which is considered to be the viscosity at zero-frequency. This phenomena can be attributed to the slow viscous relaxation of associated liquids due to the re-combination dynamics of the network of H-bonds.

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47.55.D-	Drops and bubbles
61.20.Qg	Structure of associated liquids: electrolytes, molten salts, etc.
68.03.Cd	Surface tension and related phenomena
66.20.Ej	Studies of viscosity and rheological properties of specific liquids
62.10.+s	Mechanical properties of liquids
47.80.Jk	Flow visualization and imaging

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The physics of aerobreakup. II. Viscous liquids

T. G. Theofanous, V. V. Mitkin, C. L. Ng, C-H. Chang, X. Deng, and S. Sushchikh

Phys. Fluids 24, 022104 (2012); http://dx.doi.org/10.1063/1.3680867 (39 pages)

Online Publication Date: 14 February 2012

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We extend the work of Theofanous and Li [“On the physics of aerobreakup,” Phys. Fluids 20, 052103 (2008)] on aerobreakup physics of water-like, low viscosity liquid drops, to Newtonian liquids of any viscosity. The scope includes the full range of aerodynamics from near incompressible to high Mach number flows. The key physics of Rayleigh–Taylor piercing (RTP, first criticality) and of shear-induced entrainment (SIE, second and terminal criticality) are verified and quantified by new viscosity- and capillarity-based scalings for fluids of any viscosity. The relevance and predictive power of linear stability analysis of the Rayleigh–Taylor and Kelvin–Helmholtz problems (both including viscosity) is demonstrated for the RTP and the SIE regimes, respectively. The advanced stages of breakup and of the resulting particle-clouds are observed and clear definition and quantification of breakup times are offered.

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47.55.df	Breakup and coalescence
47.55.Hd	Stratified flows
47.55.nb	Capillary and thermocapillary flows
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.20.Ma	Interfacial instabilities (e.g., Rayleigh-Taylor)
47.40.-x	Compressible flows; shock waves

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Thin films flowing down inverted substrates: Three-dimensional flow

T.-S. Lin, L. Kondic, and A. Filippov

Phys. Fluids 24, 022105 (2012); http://dx.doi.org/10.1063/1.3682001 (18 pages)

Online Publication Date: 14 February 2012

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We study contact line induced instabilities for a thin film of fluid under destabilizing gravitational force in three-dimensional setting. In the previous work [T.-S. Lin and L. Kondic, Phys. Fluids 22, 052105 (2010)], we considered two-dimensional flow, finding formation of surface waves whose properties within the implemented long-wave model depend on a single parameter, D = (3Ca)^1/3cotα, where Ca is the capillary number and α is the inclination angle. In the present work we consider fully 3D setting and discuss the influence of the additional dimension on stability properties of the flow. In particular, we concentrate on the coupling between the surface instabilities and the transverse (fingering) instabilities of the film front. We furthermore consider these instabilities in the setting where fluid viscosity varies in the transverse direction. It is found that the flow pattern strongly depends on the inclination angle and the viscosity gradient.

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47.55.nd	Spreading films
68.15.+e	Liquid thin films
47.55.nb	Capillary and thermocapillary flows
47.54.Bd	Theoretical aspects
47.35.-i	Hydrodynamic waves
47.55.np	Contact lines

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Measurements of liquid film thickness for a droplet at a two-fluid interface

G. Oldenziel, R. Delfos, and J. Westerweel

Phys. Fluids 24, 022106 (2012); http://dx.doi.org/10.1063/1.3684706 (18 pages)

Online Publication Date: 14 February 2012

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Coalescence of a droplet at a two-fluid interface is studied at Bond numbers larger than one and at three different values of the viscosity ratio. Both the thickness of the liquid film between the rising droplet and the two-fluid interface, and the location of film rupture are measured using laser induced fluorescence. Particle image velocimetry was applied to the flow in the film. It is found that the film thins asymetrically, and that the time interval between collision and film rupture is shorter than predicted by commonly used models. The film ruptures at an off-center location. It can be concluded that asymmetric film drainage speeds up coalescence.

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47.55.df	Breakup and coalescence
47.55.nd	Spreading films
47.80.Jk	Flow visualization and imaging
66.20.-d	Viscosity of liquids; diffusive momentum transport
68.15.+e	Liquid thin films

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Dip coating with an interaction potential normal to the substrate

C. Vannozzi

Phys. Fluids 24, 022107 (2012); http://dx.doi.org/10.1063/1.3680872 (13 pages)

Online Publication Date: 16 February 2012

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Dip coating in the presence of a substrate-liquid interaction potential normal to the substrate, previously theoretically investigated by R. Krechetnikov and G. M. Homsy [Phys. Fluids 17, 038101 (2005)], was revisited. Their solution procedure leads to predictions of the entrained film thickness h∞* that deviate substantially from the classical Landau-Levich law because of the impossibility to identify meniscus solutions satisfying the proper boundary conditions of zero thickness and zero apparent contact angle on the solid substrate (L-L BC’s). In contrast, in the present analysis, by choosing a different method of integration and requiring the satisfaction of the boundary condition of flat bath for large, but finite, meniscus thickness, we obtain solutions subject to L-L BC's for the same parameter range studied in Krechetnikov and Homsy's paper. Thus, the matching follows a modified Landau-Levich law, where h∞* is inversely proportional to the meniscus curvature at the substrate. Since the interaction potential changes considerably this curvature, the entrained film significantly thickens for attractive interactions or thins for repulsive ones. Similar results are also found for a potential of the Debye-Hückel form.

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47.55.nd	Spreading films
68.03.Cd	Surface tension and related phenomena
47.11.-j	Computational methods in fluid dynamics
47.55.Hd	Stratified flows

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Analytical study in the mechanism of flame movement in horizontal tubes

Kirill A. Kazakov

Phys. Fluids 24, 022108 (2012); http://dx.doi.org/10.1063/1.3684712 (34 pages)

Online Publication Date: 16 February 2012

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The problem of premixed flame propagation in wide horizontal tubes is revisited. Employing the on-shell description of flames with arbitrary gas expansion, a nonlinear second-order differential equation for the front position of steady flame is derived. Solutions to this equation, obtained numerically, reveal two distinct physical regimes of laminar flame propagation controlled by the strong baroclinic effect. They differ by the front shape and flame speed, the ratio of the total consumption rates in the two regimes being 1.4 to 1.8, depending on the value of the gas expansion coefficient. Comparison with the existing experimental data on methane-air flames is made, and explanation of the main trends in the observed flame behavior is given. It is shown, in particular, that the faster (slower) regime of combustion is realized in mixtures close to (far from) the stoichiometric composition, with pronounced changeover in between.

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47.70.Pq	Flames; combustion
47.70.Fw	Chemically reactive flows
47.60.Dx	Flows in ducts and channels
47.40.-x	Compressible flows; shock waves
47.15.Rq	Laminar flows in cavities, channels, ducts, and conduits
47.11.-j	Computational methods in fluid dynamics

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The final stages of capillary break-up of polymer solutions

R. Sattler, S. Gier, J. Eggers, and C. Wagner

Phys. Fluids 24, 023101 (2012); http://dx.doi.org/10.1063/1.3684750 (21 pages)

Online Publication Date: 14 February 2012

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The capillary break-up of a polymer solution evolves via a series of stages. After the initial instability a long-lived cylindrical filament is formed, which thins exponentially in time, while the flow is purely extensional. During the final stages of the thinning process, at which the polymers are stretched sufficiently for the filament to become unstable to a Rayleigh–Plateau-like instability, a complex flow pattern develops, which we describe here. Achieving a high spatial resolution well below the optical Rayleigh limit, we describe both the formation of individual droplets as well as that of periodic patterns. Following the periodic instability, a blistering pattern appears, with different generations of smaller droplets. At sufficiently high polymer concentrations, the filament does not break at all, but a solid polymeric fiber with a thickness well below a micron remains. The experiments were performed for various polymer and solvent systems, all of which showed the same qualitative behavior for most of the observed features.

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47.50.Gj	Instabilities
47.57.Ng	Polymers and polymer solutions
47.55.df	Breakup and coalescence
47.55.nb	Capillary and thermocapillary flows

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Strain-vorticity induced secondary motion in shallow flows

Leon P. J. Kamp

Phys. Fluids 24, 023601 (2012); http://dx.doi.org/10.1063/1.3682097 (12 pages)

Online Publication Date: 6 February 2012

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Deviations from two-dimensionality of a shallow flow that is dominated by bottom friction are quantified in terms of the spatial distribution of strain and vorticity as described by the Okubo-Weiss function. This result is based on a Poisson equation for the pressure in a quasi-horizontal (primary) flow. It is shown that the Okubo-Weiss function specifies vertical pressure gradients, which for their part drive vertical (secondary) motion. An asymptotic expansion of these gradients based on the smallness of the vertical to horizontal scale ratio demonstrates that the sign and magnitude of secondary circulation inside the fluid layer is dictated by the signs and magnitude of the Okubo-Weiss function. As a consequence of this, secondary motion as well as nonzero horizontal divergence do also depend on the strength, i.e., the Reynolds number of the primary flow. The theory is exemplified by two generic vortical structures (monopolar and dipolar structures). Most importantly, the theory can be applied to more complicated turbulent shallow flows in order to assess the degree of two-dimensionality using measurements of the free-surface flow only.

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47.32.C-	Vortex dynamics
02.30.Jr	Partial differential equations
47.27.E-	Turbulence simulation and modeling

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Draining of a thin film on the wall of a conical container set into rapid rotation about its vertical axis

Marius Ungarish and John D. Sherwood

Phys. Fluids 24, 023602 (2012); http://dx.doi.org/10.1063/1.3682714 (21 pages)

Online Publication Date: 14 February 2012

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A theory for how rotation modifies the draining of a thin fluid film on the surface of a conical container is developed. Rapid rotation, imposed instantaneously, creates an Ekman layer that pumps fluid to the outer edge of the container. This fluid is flung out of the vessel, rather than being transferred to the interior of the container. In consequence, fluid in the vessel but outside the Ekman layer does not spin up and continues to drain towards the container base. The net result is that draining is enhanced by the outward Ekman flux and finishes in finite time (when only the thin Ekman layer remains). The governing equations can be solved by the method of characteristics, to within numerical quadrature. The amount of fluid pumped outwards (rather than draining towards the base of the container) depends upon a single parameter that characterizes the ratio of the Ekman flux to gravitational draining.

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47.32.Ef	Rotating and swirling flows
68.15.+e	Liquid thin films
47.60.Dx	Flows in ducts and channels
02.60.Jh	Numerical differentiation and integration

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Simulation of the flow around an upstream transversely oscillating cylinder and a stationary cylinder in tandem

Sheng Bao, Sheng Chen, Zhaohui Liu, Jing Li, Hanfeng Wang, and Chuguang Zheng

Phys. Fluids 24, 023603 (2012); http://dx.doi.org/10.1063/1.3683565 (20 pages)

Online Publication Date: 22 February 2012

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The flow around a transversely oscillating cylinder in tandem with a stationary cylinder was studied using the lattice Boltzmann method at Re = 100. The influences of spacing, oscillation frequency, and amplitude on the flow field were investigated in detail. It was found that, when the upstream cylinder oscillates with small amplitude, the flow pattern can be changed significantly from that of its fixed counterpart. First, the stagnation region ceases to exist. Second, the transition from the vortex suppression (VS) regime to the vortex formation (VF) regime appears earlier than when both cylinders are fixed. Moreover, the system has a wider frequency range of lock-in for both tandem cylinders in the VS regime, while the locked frequency range is slightly increased in the VF regime. The locked region of the tandem-paired cylinders is only slightly wider than that of a single oscillating cylinder. When the system is unlocked, different responses occur in the wakes of the two cylinders. Analysis of the power spectral of lift forces, lift phase portraits, and vorticity contours shows that the wake is regular under conditions of small spacing and small oscillating amplitude. However, with larger spacing, higher oscillating frequency or larger amplitude, the oscillation is powerful enough to dominate the flow field, inducing chaotic flow. The drag and lift forces of both oscillating and stationary cylinders are also discussed. The results reveal large differences between the case of one oscillating cylinder and that of two stationary tandem cylinders.

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47.15.Rq	Laminar flows in cavities, channels, ducts, and conduits
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.52.+j	Chaos in fluid dynamics
47.15.Tr	Laminar wakes
47.15.ki	Inviscid flows with vorticity
47.11.Qr	Lattice gas

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Study of instabilities and transitions for a family of quasi-two-dimensional magnetohydrodynamic flows based on a parametrical model

S. Smolentsev, N. Vetcha, and R. Moreau

Phys. Fluids 24, 024101 (2012); http://dx.doi.org/10.1063/1.3680864 (21 pages)

Online Publication Date: 7 February 2012

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In this study, flow phenomena associated with inflectional and boundary-layer instabilities, as well as a mixed instability mode in quasi-two-dimensional magnetohydrodynamic flows in a rectangular duct are accessed with the help of a parametrical model, where the basic velocity profile with near-wall jets and associated points of inflection are produced by imposing an external flow-opposing force. By varying this force, various instability modes and transition scenarios are reproduced. First, linear stability analysis is performed and then nonlinear effects are studied using direct numerical simulation for Hartmann numbers 100 and 200 and Reynolds numbers from 1800 to 5000. A special attention is paid to the location of the inflection point with respect to the duct wall. A more complex flow dynamics, including various vortex-wall and vortex-vortex interactions, and even negative turbulence production are observed and analyzed as the inflection point approaches the wall. The analysis of obtained results and their comparison with relevant data for magnetohydrodynamic duct flows gain an insight into what is typically called “jet instability,” including linear and nonlinear mechanisms.

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47.27.Cn	Transition to turbulence
47.27.nb	Boundary layer turbulence
47.27.nf	Flows in pipes and nozzles
47.27.wg	Turbulent jets
47.60.Dx	Flows in ducts and channels
47.20.Ib	Instability of boundary layers; separation

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Secondary instability in the near-wake past two tandem square cylinders

Choon-Bum Choi, Yong-Jun Jang, and Kyung-Soo Yang

Phys. Fluids 24, 024102 (2012); http://dx.doi.org/10.1063/1.3682373 (22 pages)

Online Publication Date: 8 February 2012

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Floquet stability analysis has been carried out to detect the onset of the secondary instability in the laminar flow past two identical square cylinders in tandem. Presence of a neighbouring cylinder alters flow topology, leading to change of stability characteristics. A parametric study has been performed with the gap between the two square cylinders as the key parameter. Three distinct patterns of base flow are found depending on the gap, and distinctive modes of the secondary instability are identified for each pattern of the base flow. The modes exhibit either odd reflection-translation symmetry or even RT symmetry. The critical Reynolds number and the corresponding dominant spanwise wavelength are presented for a wide range of the gap. Temporal and spatial characteristics of the dominant Floquet modes are described in detail. A hysteresis is also noticed in a certain range of the gap. Neutral stability curves are presented for some selected values of the gap. The averaged in-plane vorticity of the dominant normalized Floquet mode is depicted as a function of the downstream distance from the rear face of the cylinder that sheds vortices. Comparison of stability characteristics is also made between the current flow and the flow past two circular cylinders in tandem arrangements.

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47.15.Fe	Stability of laminar flows
47.15.Tr	Laminar wakes
47.54.Bd	Theoretical aspects
47.32.cd	Vortex stability and breakdown

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Transition between turbulent magnetically driven flow states in a Rayleigh-Bénard cell

I. Grants and G. Gerbeth

Phys. Fluids 24, 024103 (2012); http://dx.doi.org/10.1063/1.3682374 (15 pages)

Online Publication Date: 14 February 2012

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Transition between turbulent flow regimes is studied experimentally in a cylinder of liquid mercury heated from below under the influence of a rotating magnetic field. The latter creates a rotating flow which almost completely suppresses the temperature fluctuation near horizontal boundaries at a much lower angular velocity than a simple mechanical rotation. Our experiment confirms that this effect persists in the deep turbulent range to Grashof numbers as high as about 10⁹. An intermediate range is observed for Gr > 2 × 10⁸ with the temperature fluctuation suppressed in the core but near the sidewall. This is explained by turbulent friction replacing the Coriolis force as the leading retarding force. The linear instability of a simplified model is studied numerically. The model considers a base flow consisting of a uniform rotation and a formally independent uniform meridional flow in a cylinder with an adverse vertical temperature gradient. The model shows that the bulk meridional flow being itself much slower than the rotation is able to delay the Rayleigh-Bénard instability.

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47.27.Cn	Transition to turbulence
47.32.Ef	Rotating and swirling flows
05.40.-a	Fluctuation phenomena, random processes, noise, and Brownian motion
47.27.nb	Boundary layer turbulence
47.27.te	Turbulent convective heat transfer
47.65.-d	Magnetohydrodynamics and electrohydrodynamics

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The three-dimensional transition stages over the NACA-0009 airfoil at Reynolds numbers of several ten thousand

Y. Elimelech, R. Arieli, and G. Iosilevskii

Phys. Fluids 24, 024104 (2012); http://dx.doi.org/10.1063/1.3682377 (14 pages)

Online Publication Date: 14 February 2012

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This experimental study addresses late transition stages over a conventional airfoil at Reynolds numbers of several ten thousands. The study is based on extensive volumetric flow measurements using constant temperature anemometry. This technique provided both the time-averaged description of the flow field in the vicinity of the wing and the high fidelity spectral analysis inside the separated boundary layer. Large cellular flow structures were observed above the wing. They resemble the stall cells at Reynolds numbers of a few hundred thousands and separation cells at Reynolds numbers of a few hundred. It is shown that most of the energy of the velocity fluctuations within the boundary layer over the forward half of the wing is concentrated in the low-frequency range of the spectrum, where the chord-based Strouhal number is small as compared with unity.

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47.85.Np	Fluidics
47.27.nb	Boundary layer turbulence
47.80.Jk	Flow visualization and imaging
47.32.Ff	Separated flows
05.40.-a	Fluctuation phenomena, random processes, noise, and Brownian motion

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Inertial-range anisotropy in Rayleigh-Taylor turbulence

Olivier Soulard and Jérôme Griffond

Phys. Fluids 24, 025101 (2012); http://dx.doi.org/10.1063/1.3680871 (25 pages)

Online Publication Date: 14 February 2012

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In this work, the spectral equilibrium theory of Ishihara et al. [Phys. Rev. Lett. 88, 154501 (2002)10.1103/PhysRevLett.88.154501] is applied to Rayleigh-Taylor turbulence. With the help of Canuto and Dubovikov's model [V. Canuto and M. Dubovikov, Phys. Fluids 8, 571 (1996)10.1063/1.868842] closed expressions for the anisotropic spectra of velocity and density, valid in the inertial range, are derived. Based on this result, the main properties of Rayleigh-Taylor turbulence at small scales are discussed. These theoretical results are compared against a direct numerical simulation of a Rayleigh-Taylor mixing zone.

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47.20.Ma	Interfacial instabilities (e.g., Rayleigh-Taylor)
47.27.E-	Turbulence simulation and modeling
47.51.+a	Mixing
02.60.Cb	Numerical simulation; solution of equations
45.70.Mg	Granular flow: mixing, segregation and stratification

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Wavelet decomposition of forced turbulence: Applicability of the iterative Donoho-Johnstone threshold

Jesse W. Lord, Mark P. Rast, Christopher Mckinlay, John Clyne, and Pablo D. Mininni

Phys. Fluids 24, 025102 (2012); http://dx.doi.org/10.1063/1.3683556 (14 pages)

Online Publication Date: 14 February 2012

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We examine the decomposition of forced Taylor-Green and Arn'old-Beltrami-Childress (ABC) flows into coherent and incoherent components using an orthonormal wavelet decomposition. We ask whether wavelet coefficient thresholding based on the Donoho-Johnstone criterion can extract a coherent vortex signal while leaving behind Gaussian random noise. We find that no threshold yields a strictly Gaussian incoherent component, and that the most Gaussian incoherent flow is found for data compression lower than that achieved with the fully iterated Donoho-Johnstone threshold. Moreover, even at such low compression, the incoherent component shows clear signs of large-scale spatial correlations that are signatures of the forcings used to drive the flows.

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47.27.De	Coherent structures
02.60.-x	Numerical approximation and analysis
47.11.-j	Computational methods in fluid dynamics
47.32.C-	Vortex dynamics

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Parametric study of cylindrical converging shock waves generated based on shock dynamics theory

Zhigang Zhai, Ting Si, Xisheng Luo, Jiming Yang, Cangli Liu, Duowang Tan, and Liyong Zou

Phys. Fluids 24, 026101 (2012); http://dx.doi.org/10.1063/1.3682376 (13 pages)

Online Publication Date: 8 February 2012

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In our previous work, the technique of generating cylindrical converging shock waves based on shock dynamics theory was proposed. In the present work, a further study is carried out to assess the influence of several parameters including the converging angle θ₀, the incident planar shock Mach number M₀, and the shock tube height h on the wall profile and the converging shock wave. Combining the high-speed schlieren photography and the numerical simulation with the shock dynamics theory, the characteristics of wall profiles, cylindrical converging shock waves, and thermodynamic properties for different controllable parameters are analyzed. It is found that these parameters have great effects on shapes of the wall profile and experimental investigation favors large values of M₀ and h and moderate θ₀. The experimental sequences of schlieren images indicate that the shocks moving in the converging part are of circular shapes, which further verifies the method in our previous work. In addition, the changes of the shock Mach number, pressure, temperature, and density are obtained quantitatively. The results show that higher pressure and temperature can be reached in the converging part at the same distance to the center of convergence for larger incident shock Mach numbers, larger shock tube heights, or smaller converging angles. All the database will be useful for understanding the shock focusing and further investigating the Richtmyer-Meshkov instability induced by the converging shock waves.

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47.40.Nm	Shock wave interactions and shock effects
02.60.Cb	Numerical simulation; solution of equations
47.60.Dx	Flows in ducts and channels

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Gravity currents in a two-layer stratified ambient: The theory for the steady-state (front condition) and lock-released flows, and experimental confirmations

M. R. Flynn, M. Ungarish, and A. W. Tan

Phys. Fluids 24, 026601 (2012); http://dx.doi.org/10.1063/1.3680260 (26 pages)

Online Publication Date: 1 February 2012

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We consider the propagation of a gravity current of density ρ_c at the bottom of a two-layer stratified ambient in a horizontal channel of height H, in the high-Reynolds number Boussinesq domain. The study emphasizes theoretical-analytical modeling, however, experimental and Navier-Stokes simulation data are also presented and their comparison with theory is discussed. The stratification parameters are S = (ρ₁ − ρ₂)/(ρ_c − ρ₂) where ρ is the fluid density, and φ = h_1R/H where h_1R is the (unperturbed) ambient interface height. Here, 1 and 2 denote, respectively, the lower and upper layer and c denotes the gravity current. The reduced gravity is defined as g^′ = (ρ_c/ρ₂ − 1)g. Rigorous results are obtained for the steady-state analogue of the classical problem of Benjamin [J. Fluid Mech. 31, 209 (1968)]10.1017/S0022112068000133, in which the half-infinite gravity current has thickness h and speed U. We thereby demonstrate that the Froude number F = U/(g′h)^1/2 is a function of a = h/H, S, and φ. In general, two solutions (or modes) may be realized. Issues of energy dissipation, sub- vs. supercriticality with respect to long internal waves and, more generally, the influence of upstream-propagating disturbances are discussed. For a gravity current released from a lock of height h₀ and length x₀, we derive an approximate shallow-water model and show that the motion is in this case governed by Ξ = H/h₀, S, and φ. Although the shallow-water model neglects motion in the ambient layers and ignores the impact of propagation on stratification, the gravity current front speed in the slumping stage is in excellent agreement with measured data. Our theoretical solutions are consistent with previous results (in particular, Holyer and Huppert [J. Fluid Mech. 100, 739 (1980)] and Tan et al. [Environ. Fluid Mech. 11, 203 (2011)]), but have the advantages of being (i) derived without reliance on adjustable constants and ad hoc closures; (ii) applicable to a significantly broader range of dimensionless parameters; and (iii) better assessed by comparison against measured data. The present one-layer shallow-water approximation turns out to be a simple and versatile extension of existing models for homogeneous and linearly stratified ambients, and can be straightforwardly incorporated into the available prediction tools for gravity currents.

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47.55.Hd	Stratified flows
47.60.Dx	Flows in ducts and channels
47.10.ad	Navier-Stokes equations
47.27.nb	Boundary layer turbulence
47.35.Bb	Gravity waves

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Dipole evolution in rotating two-dimensional flow with bottom friction

V. G. Makarov

Phys. Fluids 24, 026602 (2012); http://dx.doi.org/10.1063/1.3680870 (19 pages)

Online Publication Date: 3 February 2012

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The evolution of a dipolar vortex in a quasi-two-dimensional rotating flow of barotropic fluid over a flat surface with a no-slip condition in the Ekman bottom layer is considered. The vorticity equation in this case becomes nonlinear. An effect of bottom friction is displayed mainly in cyclone-anticyclone asymmetry, which results in the expansion (diminution) of cyclonic (anticyclonic) local structures and in the stronger decay of positive vorticity. When a lateral viscosity is omitted, the vorticity equation has a solution in the form of vortex patches and hence a contour dynamics method may be used for numerical simulation. An approach of point vortices with decaying strengths is also discussed. In an approximation of two patches of opposite uniform vorticity, a three-parameter family of stationary (in an ideal fluid) orbital dipoles [V. G. Makarov and Z. Kizner, “Stability and evolution of uniform-vorticity dipoles,” J. Fluid Mech. 672, 307 (2011)]10.1017/S0022112010006026 consisting of patches with unequal areas and absolute values of vorticity is considered. A three-dimensional domain of instability for this family is numerically constructed. It is shown that the evolution of such dipoles in a flow with bottom friction is described with good accuracy by a properly matched trajectory in parameter space of ideal-fluid steady states. Explicit time-dependent formulae for this phase trajectory are obtained. All characteristics (including the patch's shapes) of the evolutionary dipole, and the same characteristics for the corresponding ideal-fluid stationary dipole, almost completely coincide, at least while the phase trajectory remains in the stability region. The evolution of stationary translating dipoles (with zero net circulation) that have continuously distributed vorticity inside a quasi-elliptical finite region is also examined. When the circular Lamb dipole is used as the initial condition, good qualitative agreement is observed between the asymmetric dipoles obtained during evolution and the chain of the exact solutions from the known one-parameter family of non-symmetrical Chaplygin dipoles.

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