POF Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Search Issue | RSS Feeds RSS
Previous Issue Next Issue

May 1999

Volume 11, Issue 5, pp. 949-1278

Page 1 of 2 Pages Next Page | Jump to Page
back to top
RSS Feeds

Nonlinear interactions of chemical reactions and viscous fingering in porous media

A. De Wit and G. M. Homsy

Phys. Fluids 11, 949 (1999); http://dx.doi.org/10.1063/1.869988 (3 pages) | Cited 26 times

Full Text: | Download PDF

Show Abstract
Nonlinear interactions of chemical reactions and viscous fingering are studied in porous media by direct numerical simulations of Darcy’s law coupled to the evolution equation for the concentration of a chemically reacting solute controlling the viscosity of miscible solutions. Chemical kinetics introduce important topological changes in the fingering pattern: new robust pattern formation mechanisms such as droplet formation and enhanced tip splitting are evidenced and analyzed. © 1999 American Institute of Physics.
Show PACS
47.70.Fw Chemically reactive flows
47.56.+r Flows through porous media
47.54.-r Pattern selection; pattern formation
82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer
02.60.Cb Numerical simulation; solution of equations
47.55.D- Drops and bubbles
47.55.Hd Stratified flows

Stability of a growing end rim in a liquid sheet of uniform thickness

José Maria Fullana and Stéphane Zaleski

Phys. Fluids 11, 952 (1999); http://dx.doi.org/10.1063/1.869989 (3 pages) | Cited 15 times

Full Text: | Download PDF

Show Abstract
We study the stability of a viscous liquid layer of uniform thickness subject only to viscous stresses and surface tension. We show that the growing cylindrical end rim does not typically break into droplets for moderate wavelengths. Thus, other mechanisms are needed to cause the instabilities, which, for instance, lead to the famous milk crown. The problem remains open for very large wavelengths. © 1999 American Institute of Physics.
Show PACS
47.20.-k Flow instabilities
68.03.Cd Surface tension and related phenomena
47.55.D- Drops and bubbles
66.20.-d Viscosity of liquids; diffusive momentum transport

Stability of periodically compressed vortices at low Mach number

Stéphane Leblanc and Lionel Le Penven

Phys. Fluids 11, 955 (1999); http://dx.doi.org/10.1063/1.869990 (3 pages)

Full Text: | Download PDF

Show Abstract
Stability analysis of circular and elliptical vortices periodically compressed axially in their plane reveals, at low Mach number, two distinct mechanisms of three-dimensional instability. The first one is a manifestation of the elliptical instability, modified by compression. The second one, which exists also in the circular case, is a resonance between the frequency of compression and the intrinsic rotation rate of the uncompressed vortex. © 1999 American Institute of Physics.
Show PACS
47.32.C- Vortex dynamics
47.20.Cq Inviscid instability
47.40.-x Compressible flows; shock waves
back to top
RSS Feeds

Blade coating of a power-law fluid

A. B. Ross, S. K. Wilson, and B. R. Duffy

Phys. Fluids 11, 958 (1999); http://dx.doi.org/10.1063/1.869968 (13 pages) | Cited 9 times

Full Text: | Download PDF

Show Abstract
In this paper we re-examine the problem of applying a thin layer of a power-law fluid to a solid substrate by means of a simple blade coater. Specifically we use lubrication theory to examine steady plane flow of a power-law fluid in the narrow nonuniform channel formed between a fixed blade of prescribed shape and a plane substrate moving parallel to itself. The first-order asymptotic solution for the case of a weakly non-Newtonian fluid is presented. An explicit expression is obtained for the first-order pressure gradient from which the first-order contributions to several important physical quantities including the thickness of the applied fluid layer and the forces on the blade are calculated for both plane and exponentially shaped blades. In particular, we find that, depending on the shape and height ratio of the coater, the effect of weakly non-Newtonian behavior can be either to increase or to decrease both the pressure and the load from their Newtonian values. We also re-examine the approximate solutions of Hwang [Trans. ASME J. Fluids Eng. 104, 469 (1982)] and Dien and Elrod [Trans. ASME J. Lubrication Technol. 105, 385 (1983)] and make a detailed comparison between their predictions and those of the exact solution in the weakly non-Newtonian limit. We find that in this limit the Dien and Elrod approximation is usually in significantly better agreement with the exact solution than Hwang’s approximation. In the Appendix we re-examine the Dien and Elrod approximate solution for the flow of a generalized Newtonian fluid. © 1999 American Institute of Physics.
Show PACS
46.55.+d Tribology and mechanical contacts

Experimental trajectories of two drops in planar extensional flow

Derek C. Tretheway, Masahiro Muraoka, and L. Gary Leal

Phys. Fluids 11, 971 (1999); http://dx.doi.org/10.1063/1.869969 (11 pages) | Cited 11 times

Full Text: | Download PDF

Show Abstract
In this paper we map the experimental trajectories of two deformable drops in planar extensional flow and compare the experimental results with theoretical calculations for spherical drops. We examine the effects that deformation, initial position, and viscosity ratio have on the interaction of two drops and the necessity of incorporating deformation into trajectory calculations, which can be used to estimate the collision rates, the collision efficiencies, and the collision interaction times. For drops which do not come into close contact, the existing theoretical calculations for spherical drops accurately predict the symmetric trajectories and capture the increased hydrodynamic interaction for higher viscosity ratios. For drops which come into close contact, the spherical drop theory accurately predicts the approach and exit trajectories and with a slight empirical modification adequately predicts the interaction times for deformable drops with a Taylor deformation parameter up to 0.22. The experimental results show that for drops with close contact, the collision trajectories are asymmetric and irreversible with a minimum separation between the centers of mass that is less than the minimum separation of two spheres. This minimum separation corresponds to the minor axis of the deformed drop and is not captured by the spherical theory. However, overall, the modified trajectory theory based upon the hydrodynamic mobility for spherical drops does provide a reasonable estimate for the trajectories and the interaction times for two deformable drops in planar extensional flow. © 1999 American Institute of Physics.
Show PACS
47.55.D- Drops and bubbles
47.55.Kf Particle-laden flows

The spreading of a non-isothermal liquid droplet

Steven W. Benintendi and Marc K. Smith

Phys. Fluids 11, 982 (1999); http://dx.doi.org/10.1063/1.869970 (8 pages) | Cited 8 times

Full Text: | Download PDF

Show Abstract
The effect of the slip coefficient and the mobility capillary number on the spreading of a thin axisymmetric liquid droplet with uniform heating/cooling of the solid surface is examined. The results show that increasing the slip coefficient reduces the spreading/shrinking behavior of the droplet and that the final equilibrium states are slip dependent. These results are explained by the development of a return flow inside the droplet. We show how a speed-dependent slip coefficient can be used to remove the dependence of the final state on the slip coefficient. It is also shown that increasing the mobility capillary number decreases the spreading/shrinking rate of the droplet. For thermocapillary-driven droplets, there is a capillary-number-dependent time delay for the onset of motion. The entire effect of the mobility capillary number on the spreading process is explained in terms of the deformability of the free surface.© 1999 American Institute of Physics.
Show PACS
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting

Critical behavior of drop breakup in axisymmetric viscous flow

Yiftah Navot

Phys. Fluids 11, 990 (1999); http://dx.doi.org/10.1063/1.869971 (7 pages) | Cited 17 times

Full Text: | Download PDF

Show Abstract
The critical behavior of a liquid droplet immersed in a host fluid under external axisymmetric viscous flow is studied. It is well known that when the external extensional flow is weak the system approaches a steady-state flow, but when the shear rate is increased beyond some critical value a steady state is never attained and the droplet is stretched to infinity. This behavior is explained qualitatively by a simple semianalytic argument. The critical power law behavior of the droplet shape and its time dependence when the shear rate approaches the critical value is studied and is verified by numerical simulations for linear axisymmetric flows. For biaxial extensional flow (negative elongational flow) it is known that another critical point appears, and the droplet goes over into a toroidal shape. Similar critical behavior is predicted at that point also. © 1999 American Institute of Physics.
Show PACS
01.50.-i Educational aids
47.55.D- Drops and bubbles

Effects of insoluble surfactants on the nonlinear deformation and breakup of stretching liquid bridges

Bala Ambravaneswaran and Osman A. Basaran

Phys. Fluids 11, 997 (1999); http://dx.doi.org/10.1063/1.869972 (19 pages) | Cited 23 times

Full Text: | Download PDF

Show Abstract
During the emission of single drops and the atomization of a liquid from a nozzle, threads of liquid are stretched and broken. A convenient setup for studying in a controlled manner the dynamics of liquid threads is the so-called liquid bridge, which is created by holding captive a volume of liquid between two solid disks and pulling apart the two disks at a constant velocity. Although the stability of static bridges and the dynamics of stretching bridges of pure liquids have been extensively studied, even a rudimentary understanding of the dynamics of the stretching and breakup of bridges of surfactant-laden liquids is lacking. In this work, the dynamics of a bridge of a Newtonian liquid containing an insoluble surfactant are analyzed by solving numerically a one-dimensional set of equations that results from a slender-jet approximation of the Navier–Stokes system that governs fluid flow and the convection-diffusion equation that governs surfactant transport. The computational technique is based on the method-of-lines, and uses finite elements for discretization in space and finite differences for discretization in time. The computational results reveal that the presence of an insoluble surfactant can drastically alter the physics of bridge deformation and breakup compared to the situation in which the bridge is surfactant free. They also make clear how the distribution of surfactant along the free surface varies with stretching velocity, bridge geometry, and bulk and surface properties of the liquid bridge. Gradients in surfactant concentration along the interface give rise to Marangoni stresses which can either retard or accelerate the breakup of the liquid bridge. For example, a high-viscosity bridge being stretched at a low velocity is stabilized by the presence of a surfactant of low surface diffusivity (high Peclet number) because of the favorable influence of Marangoni stresses on delaying the rupture of the bridge. This effect, however, can be lessened or even negated by increasing the stretching velocity. Large increases in the stretching velocity result in interesting changes in their own right regardless of whether surfactants are present or not. Namely, it is shown that whereas bridges being stretched at low velocities rupture near the bottom disk, those being stretched at high velocities rupture near the top disk. © 1999 American Institute of Physics.  
Show PACS
68.03.Cd Surface tension and related phenomena
83.50.-v Deformation and flow

Buoyancy-driven viscous interaction of a rising drop with a smaller trailing drop

Robert H. Davis

Phys. Fluids 11, 1016 (1999); http://dx.doi.org/10.1063/1.869973 (13 pages) | Cited 18 times

Full Text: | Download PDF

Show Abstract
An axisymmetric boundary-integral method was developed and used to study the interaction of two deformable drops (or bubbles) rising (or settling) due to gravity in a viscous medium under conditions of small Reynolds number. The focus is on cases where the smaller drop trails behind the larger drop. When the Bond number is small, interfacial tension keeps the drops nearly spherical, and they separate with time. At higher Bond numbers, however, deformation is significant and the trailing drop is stretched due to the flow created by the leading drop; it may form one or more necks and break when one of these pinches off. The leading drop is flattened due to the flow created by the trailing drop; it may form a depression on its underside which evolves into a plume that rises through its center. Moreover, at sufficiently high Bond numbers, the larger leading drop does not leave the trailing drop behind, but instead may entrain and engulf it within the depression or plume. Systematic results for the parameter ranges which demarcate impending breakup and coalescence are presented. © 1999 American Institute of Physics.
Show PACS
47.55.D- Drops and bubbles
45.70.Mg Granular flow: mixing, segregation and stratification
47.55.Hd Stratified flows
47.55.Kf Particle-laden flows

Fluid dynamics of a double emulsion droplet in an electric field

Jong-Wook Ha and Seung-Man Yang

Phys. Fluids 11, 1029 (1999); http://dx.doi.org/10.1063/1.869974 (13 pages) | Cited 7 times

Full Text: | Download PDF

Show Abstract
One of general free boundary problems concerning the electrohydrodynamic effects on a concentric double emulsion drop is studied theoretically for the three constituent phases of leaky dielectric fluids. In order to proceed the problem analytically, the domain perturbation procedure is utilized in the small deformation limit. The patterns of electric-field-driven flow are successfully characterized by examining the distribution of induced surface charges at the inner and outer drop interfaces. The second recirculating flow is generated in the annular phase when the inner and outer interfaces are charged with the same sense. The deformation type of inner and outer interfaces can be roughly interpreted by the flow patterns, although the exact description on the deformation requires consideration of the combined contributions from both electric and flow fields. In addition, the presence of double emulsion droplets alters the stress field of the continuous phase. The electric-field-induced “particle stress” not only changes the effective viscosity of dispersion of the double emulsion droplets but yields the normal stress difference, which is typical of a viscoelastic fluid. Finally, the heat transfer rate enhanced by the electric-field-driven flow is also considered. © 1999 American Institute of Physics.
Show PACS
47.55.D- Drops and bubbles
47.27.T- Turbulent transport processes
47.65.-d Magnetohydrodynamics and electrohydrodynamics

Dynamic generation of capillary waves

Hector D. Ceniceros and Thomas Y. Hou

Phys. Fluids 11, 1042 (1999); http://dx.doi.org/10.1063/1.869975 (9 pages) | Cited 13 times

Full Text: | Download PDF

Show Abstract
We investigate the dynamic generation of capillary waves in two-dimensional, inviscid, and irrotational water waves with surface tension. It is well known that short capillary waves appear in the forward front of steep water waves. Although various experimental and analytical studies have contributed to the understanding of this physical phenomenon, the precise mechanism that generates the dynamic formation of capillary waves is still not well understood. Using a numerically stable and spectrally accurate boundary integral method, we perform a systematic study of the time evolution of breaking waves in the presence of surface tension. We find that the capillary waves originate near the crest in a neighborhood, where both the curvature and its derivative are maximum. For fixed but small surface tension, the maximum of curvature increases in time and the interface develops an oscillatory train of capillary waves in the forward front of the crest. Our numerical experiments also show that, as time increases, the interface tends to a possible formation of trapped bubbles through self-intersection. On the other hand, for a fixed time, as the surface tension coefficient τ is reduced, both the capillary wavelength and its amplitude decrease nonlinearly. The interface solutions approach the τ = 0 profile. At the onset of the capillaries, the derivative of the convection is comparable to that of the gravity term in the dynamic boundary condition and the surface tension becomes appreciable with respect to these two terms. We find that, based on the τ = 0 wave, it is possible to estimate a threshold value τ0 such that if τ ⩽ τ0 then no capillary waves arise. On the other hand, for τ sufficiently large, breaking is inhibited and pure capillary motion is observed. The limiting behavior is very similar to that in the classical KdV equation. We also investigate the effect of viscosity on the generation of capillary waves. We find that the capillary waves still persist as long as the viscosity is not significantly greater than surface tension. © 1999 American Institute of Physics.
Show PACS
47.35.-i Hydrodynamic waves
68.03.Cd Surface tension and related phenomena
92.10.Hm Ocean waves and oscillations

Branching behavior of standing waves—The signatures of resonance

D. H. Smith and A. J. Roberts

Phys. Fluids 11, 1051 (1999); http://dx.doi.org/10.1063/1.869976 (14 pages)

Full Text: | Download PDF

Show Abstract
Arclength continuation methods are used to conduct a detailed branching study of standing wave solutions for fluids in a rectangular container, using depth and crest acceleration as control parameters. At each depth the applicable acceleration range extends between zero and one, and a number of multiple solution structures are uncovered. An intimate connection is established between these structures and the phenomenon of harmonic resonance. © 1999 American Institute of Physics.
Show PACS
47.35.-i Hydrodynamic waves
47.60.-i Flow phenomena in quasi-one-dimensional systems

Determination of particle size distributions from acoustic wave propagation measurements

Peter D. M. Spelt, Michael A. Norato, Ashok S. Sangani, and Lawrence L. Tavlarides

Phys. Fluids 11, 1065 (1999); http://dx.doi.org/10.1063/1.869977 (16 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
The wave equations for the interior and exterior of the particles are ensemble averaged and combined with an analysis by Allegra and Hawley [J. Acoust. Soc. Am. 51, 1545 (1972)] for the interaction of a single particle with the incident wave to determine the phase speed and attenuation of sound waves propagating through dilute slurries. The theory is shown to compare very well with the measured attenuation. The inverse problem, i.e., the problem of determining the particle size distribution given the attenuation as a function of frequency, is examined using regularization techniques that have been successful for bubbly liquids. It is shown that, unlike the bubbly liquids, the success of solving the inverse problem is limited since it depends strongly on the nature of particles and the frequency range used in inverse calculations. © 1999 American Institute of Physics.
Show PACS
82.70.-y Disperse systems; complex fluids
62.60.+v Acoustical properties of liquids

Propagation and reflection of internal waves

B. R. Sutherland

Phys. Fluids 11, 1081 (1999); http://dx.doi.org/10.1063/1.869978 (10 pages) | Cited 8 times

Full Text: | Download PDF

Show Abstract
Fully nonlinear numerical simulations are performed to examine the behavior of large-amplitude internal gravity waves incident upon a level where the Doppler-shifted frequency of the waves is comparable to the background buoyancy frequency. Although linear theory predicts that the waves should reflect if the Doppler-shifted frequency is greater than the buoyancy frequency, it is found that nonlinear effects may greatly enhance the transmission of a wave packet across a reflecting level. If the Doppler-shifted frequency is moderately less than the buoyancy frequency, then nonlinear effects may greatly enhance the reflection of waves. A range of simulations is performed to characterize the reflection coefficient as a function of the amplitude and spatial extent of the wave packet. In comparison with horizontally periodic wave packets, it is found that the nonlinearly enhanced transmission of wave packets is more significant if they are horizontally compact. This occurs because the wave-induced mean flow effectively increases and decreases the horizontal phase speed of the waves on the incident and trailing flank of the wave packets, respectively, and this significantly broadens the frequency spectrum of the waves. © 1999 American Institute of Physics.
Show PACS
47.35.-i Hydrodynamic waves
47.11.-j Computational methods in fluid dynamics

Time-dependent simulations of point explosions with heat conduction

A. I. Shestakov

Phys. Fluids 11, 1091 (1999); http://dx.doi.org/10.1063/1.869979 (5 pages) | Cited 8 times

Full Text: | Download PDF

Show Abstract
A hydrodynamic-diffusion code is used to simulate a point explosion. The gas motion is governed by both hydrodynamics and nonlinear heat conduction and is a combination of the well-known, self-similar Taylor–Sedov spherically expanding shock wave and the spherically expanding thermal wave. Two problems are discussed. In the first problem, a similarity solution exists if the diffusion coefficient is given in terms of powers of density and temperature which also define the ambient spatial density profile. If the initial explosion energy is small, the diffusive effect is limited to a region behind the shock. However, if the explosion energy is large, the thermal front precedes the hydrodynamic front, which is then an isothermal shock. In the second problem, the initial density is constant and the diffusion coefficient depends on only a power of the temperature. In this case, the solution is not self-similar; in early times, heat conduction dominates; in late times—hydrodynamics. The problems were previously analyzed by Reinicke and Meyer-ter-Vehn in terms of similarity variables. © 1999 American Institute of Physics.
Show PACS
47.40.-x Compressible flows; shock waves
82.33.Vx Reactions in flames, combustion, and explosions
47.27.T- Turbulent transport processes
05.60.-k Transport processes
47.11.-j Computational methods in fluid dynamics

The stability of steady, helical vortex filaments in a tube

L. G. Sarasúa, A. C. Sicardi Schifino, and R. González

Phys. Fluids 11, 1096 (1999); http://dx.doi.org/10.1063/1.869980 (8 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
The nonlinear conditions for the development of helical vortex filaments in a circular tube are considered. The helical flow is assumed to be irrotational, except in a vortex filament of infinitesimal core area. By introducing an appropriate image for this helical vortex filament, the boundary condition on the material frontier is satisfied. By assuming an axisymmetric flow upstream and imposing the conservation laws, a dependence between the helix pitch and the nonlinear amplitude of the helical vortex developed downstream is obtained. Our results show that only helical flows with the pitch in a certain range of values are allowed. The dependence of this range on the swirl ratio and on the tube cross section is considered. We discuss the usefulness of the nonlinear analysis of the allowed flows to explain experimental results and to complement the usual linear study of stability. © 1999 American Institute of Physics.  
Show PACS
47.20.Cq Inviscid instability
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.32.C- Vortex dynamics
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Pulsed gradient spin echo nuclear magnetic resonance measurements of hydrodynamic instabilities with coherent structure: Taylor vortices

Joseph D. Seymour, Bertram Manz, and Paul T. Callaghan

Phys. Fluids 11, 1104 (1999); http://dx.doi.org/10.1063/1.869981 (10 pages) | Cited 10 times

Full Text: | Download PDF

Show Abstract
Pulsed gradient spin echo (PGSE) nuclear magnetic resonance (NMR) is applied to the characterization of hydrodynamic instabilities. It is demonstrated theoretically and experimentally that for Taylor vortex flow in a Couette cell the PGSE NMR data is coherently modulated in an interference pattern dependent upon the vortex size, or wavelength, and velocity intensity. Spatially resolved NMR velocity images of all three velocity components for water in supercritical Taylor number flow and NMR velocity image data of the axial disturbance velocity for pentane at three supercritical values of the Taylor number are presented. For the short column used the NMR velocity data clearly show axial asymmetry with maximum velocities and the center (eye) of the vortex drawn toward the radial outflow boundary. © 1999 American Institute of Physics.
Show PACS
47.32.C- Vortex dynamics
47.15.Fe Stability of laminar flows
47.15.ki Inviscid flows with vorticity

Nonparallel linear stability analysis of Long’s vortex

R. Fernandez-Feria

Phys. Fluids 11, 1114 (1999); http://dx.doi.org/10.1063/1.869982 (13 pages) | Cited 5 times

Full Text: | Download PDF

Show Abstract
A nonparallel linear stability analysis of a family of self-similar vortex cores which includes Long’s vortex as a particular member is performed using parabolized stability equations (PSE). The resulting streamwise variation of both the spatial growth rate and the axial wave number of the different unstable modes is compared with the results from a local spatial stability analysis which also takes into account the effects of viscosity and of the streamwise variation of the basic flow, so that the effect of the history of the disturbances on their stability is quantified. It is shown that this last effect is negligible for high Reynolds numbers, but becomes increasingly important as the Reynolds number decreases, especially for very small growth rates. The marching method used to solve the PSE is computationally much faster than the standard methods for solving the nonlinear eigenvalue problem resulting from the local stability equations. As a new result, the local spatial calculations reveal the existence of unstable counter-rotating spiral modes with negative group velocities for Type II Long’s vortices (that is, vortices with negative streamwise velocity at the axis), thus showing that these flows are subcritical in Benjamin’s sense. This kind of instability does not appear for Type I vortices, which can only sustain non-axisymmetric convective instabilities, and are therefore supercritical. Thus, the spatial stability analysis establishes a fundamental distinction between Type I and Type II Long’s vortices. © 1999 American Institute of Physics.
Show PACS
47.32.C- Vortex dynamics
47.20.-k Flow instabilities

Experiments on the Richtmyer–Meshkov instability: Wall effects and wave phenomena

M. Brouillette and R. Bonazza

Phys. Fluids 11, 1127 (1999); http://dx.doi.org/10.1063/1.869983 (16 pages) | Cited 4 times

Full Text: | Download PDF

Show Abstract
Experiments examining the interaction of shock waves with an interface separating two gases of different densities are reported. Flow visualization by the schlieren method and x-ray densitometry reveals that important secondary effects are introduced by the experimental apparatus, especially at the walls of the shock tube from shock wave/boundary layer interaction below, above, and at the interface itself. These effects can impair the observation of the primary phenomenon under study and can lead to the overall deformation of the interface. In particular, the thickness of the viscous boundary layer at the interface is computed using a familiar shock tube turbulent boundary layer model and the occurrence of bifurcation of reflected waves below and above the interface is successfully predicted based on classical bifurcation arguments. The formation of wall vortical structures at the interface is explained in terms of baroclinic vorticity deposition resulting from the interaction of reflected waves with the interface distorted by the boundary layer. This mechanism of wall vortex formation can also explain observed test gas contamination in reflected shock tunnels when shock wave bifurcation is absent. In general, it is found that most of the side effects of the experimental investigation of the Richtmyer–Meshkov instability can be alleviated by performing experiments in large test sections near atmospheric initial pressure. © 1999 American Institute of Physics.
Show PACS
47.40.Nm Shock wave interactions and shock effects
47.20.Lz Secondary instabilities
47.20.Gv Viscous and viscoelastic instabilities
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.52.+j Chaos in fluid dynamics
47.32.C- Vortex dynamics
47.27.nb Boundary layer turbulence
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.55.Hd Stratified flows

On the three-dimensional Rayleigh–Taylor instability

Xiaoyi He, Raoyang Zhang, Shiyi Chen, and Gary D. Doolen

Phys. Fluids 11, 1143 (1999); http://dx.doi.org/10.1063/1.869984 (10 pages) | Cited 50 times

Full Text: | Download PDF

Show Abstract
The three-dimensional Rayleigh–Taylor instability is studied using a lattice Boltzmann scheme for multiphase flow in the nearly incompressible limit. This study focuses on the evolution of the three-dimensional structure of the interface. In addition to the bubble and spike fronts, a saddle point is found to be another important landmark on the interface. Two layers of heavy-fluid roll-ups, one at the spike tip and the other at the saddle point, were observed. The secondary instability in the horizontal planes entangles the already complicated structure of the interface. Parallel computations are utilized to accommodate the massive computational requirements of the simulations. © 1999 American Institute of Physics.
Show PACS
47.20.-k Flow instabilities
47.55.Kf Particle-laden flows
47.55.D- Drops and bubbles
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.60.Cd Classical transport

Asymptotic growth of disturbances from spatially compact source in a skewed mixing layer

Ganyu Lu and Sanjiva K. Lele

Phys. Fluids 11, 1153 (1999); http://dx.doi.org/10.1063/1.869985 (8 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
The growth of disturbances in a skewed mixing layer, i.e., the shear layer between two streams with different velocity magnitudes and directions, is examined. Due to the three-dimensionality of the mean flow, the natural amplification direction for spatially amplifying waves needs to be determined. This issue can be resolved through investigation of the asymptotic growth of disturbances from a spatially compact source. The results show that the disturbances grow in a wedge-shaped region centered at the mean convection direction for both incompressible and compressible mixing layers. For incompressible unskewed mixing layers, the normal to the instability wave fronts is parallel to the amplification direction. The wave front normal is oblique to the amplification direction for skewed mixing layers and/or mixing layers with moderate compressibility. © 1999 American Institute of Physics.
Show PACS
47.10.-g General theory in fluid dynamics
64.75.-g Phase equilibria
47.35.-i Hydrodynamic waves
47.40.-x Compressible flows; shock waves

Sheared salt fingers: Instability in a truncated system

Francesco Paparella and Edward A. Spiegel

Phys. Fluids 11, 1161 (1999); http://dx.doi.org/10.1063/1.869890 (8 pages) | Cited 3 times

Full Text: | Download PDF

Show Abstract
We derive a model for fingering doubly diffusive convection from a truncated expansion in horizontal planform functions with the inclusion of a large-scale shearing mode. This produces nonlinear partial differential equations in time and in vertical coordinate. At a high enough Rayleigh number, both convection and shear modes are sustained and their interaction produces rich cyclic dynamics with the fingering layer dividing into two distinct finger layers that engender steps in the mean salinity before being disrupted by the beginning of a new cycle. © 1999 American Institute of Physics.
Show PACS
47.55.Hd Stratified flows
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.27.T- Turbulent transport processes
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)

Linear control and estimation of nonlinear chaotic convection: Harnessing the butterfly effect

Thomas R. Bewley

Phys. Fluids 11, 1169 (1999); http://dx.doi.org/10.1063/1.869986 (18 pages) | Cited 7 times

Full Text: | Download PDF

Show Abstract
This paper examines the application of linear optimal/robust control theory to a low-order nonlinear chaotic convection problem. Linear control feedback is found to be fully effective only when it is switched off while the state is far from the desired equilibrium point, relying on the attractor of the system to bring the state into a neighborhood of the equilibrium point before control is applied. Linear estimator feedback is found to be fully effective only when (a) the Lyapunov exponent of the state estimation error is negative, indicating that the state estimate converges to the uncontrolled state, and (b) the estimator is stable in the vicinity of the desired equilibrium point. The aim in studying the present problem is to understand better some possible pitfalls of applying linear feedback to nonlinear systems in a low-dimensional framework. Such an exercise foreshadows problems likely to be encountered when applying linear feedback to infinite-dimensional nonlinear systems such as turbulence. It is important to understand these problems and the remedies available in a low-dimensional framework before moving to more complex systems. © 1999 American Institute of Physics.
Show PACS
47.27.T- Turbulent transport processes
47.52.+j Chaos in fluid dynamics
47.85.L- Flow control

Stability analysis of perturbed plane Couette flow

Dwight Barkley and Laurette S. Tuckerman

Phys. Fluids 11, 1187 (1999); http://dx.doi.org/10.1063/1.869987 (9 pages) | Cited 11 times

Full Text: | Download PDF

Show Abstract
Plane Couette flow perturbed by a spanwise oriented ribbon, similar to a configuration investigated experimentally at the Centre d’Etudes de Saclay, is investigated numerically using a spectral-element code. Two-dimensional (2-D) steady states are computed for the perturbed configuration; these differ from the unperturbed flows mainly by a region of counter-circulation surrounding the ribbon. The 2-D steady flow loses stability to three-dimensional (3-D) eigenmodes at Rec = 230, βc = 1.3 for ρ = 0.086 and Rec ≈ 550, βc ≈ 1.5 for ρ = 0.043, where β is the spanwise wave number and 2ρ is the height of the ribbon. For ρ = 0.086, the bifurcation is determined to be subcritical by calculating the cubic term in the normal form equation from the time series of a single nonlinear simulation; steady 3-D flows are found for Re as low as 200. The critical eigenmode and nonlinear 3-D states contain streamwise vortices localized near the ribbon, whose streamwise extent increases with Re. All of these results agree well with experimental observations. © 1999 American Institute of Physics.
Show PACS
47.15.Fe Stability of laminar flows
47.32.C- Vortex dynamics

Velocity fluctuations in a turbulent soap film: The third moment in two dimensions

A. Belmonte, W. I. Goldburg, H. Kellay, M. A. Rutgers, B. Martin, and X. L. Wu

Phys. Fluids 11, 1196 (1999); http://dx.doi.org/10.1063/1.869891 (5 pages) | Cited 22 times

Full Text: | Download PDF

Show Abstract
Quasi-two-dimensional decaying turbulence is studied in a flowing soap film by measuring the moments of the probability density function P(δv(r)) for the longitudinal velocity differences δv(r) on a scale r. As in three-dimensional (3-D) turbulence, P becomes non-Gaussian with decreasing r. The third moment S3(r) ≡ 〈(δv(r))3〉 is small and negative at small scales, but becomes positive at larger scales. The exact calculation of S3(r) for 2-D homogeneous isotropic turbulence relates this change in sign to the development of the velocity correlation function as the turbulence decays. © 1999 American Institute of Physics.
Show PACS
68.15.+e Liquid thin films
Page 1 of 2 Pages Next Page | Jump to Page
Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. Direct numerical simulation of turbulent channel flow up to Reτ = 590
  2. The formation and evolution of synthetic jets
  3. Experimental study of the kinematic mixing of two fluids in a 2D enclosure
  4. Bifurcation analysis of double-diffusive convection with opposing horizontal thermal and solutal gradients
  5. Discontinuous behavior of liquids between parallel and tilted plates
Go to AIP Home
Copyright © American Institute of Physics
close