Showing papers in "Physics of Fluids in 1996"

Capillary effects during droplet impact on a solid surface

Abstract: Impact of water droplets on a flat, solid surface was studied using both experiments and numerical simulation. Liquid–solid contact angle was varied in experiments by adding traces of a surfactant to water. Impacting droplets were photographed and liquid–solid contact diameters and contact angles were measured from photographs. A numerical solution of the Navier–Stokes equation using a modified SOLA‐VOF method was used to modeldroplet deformation. Measured values of dynamic contact angles were used as a boundary condition for the numerical model. Impacting droplets spread on the surface until liquid surface tension and viscosity overcame inertial forces, after which they recoiled off the surface. Adding a surfactant did not affect droplet shape during the initial stages of impact, but did increase maximum spread diameter and reduce recoil height. Comparison of computer generated images of impacting droplets with photographs showed that the numerical model modeled droplet shape evolution correctly. Accurate predictions were obtained for droplet contact diameter during spreading and at equilibrium. The model overpredicted droplet contact diameters during recoil. Assuming that dynamic surface tension of surfactant solutions is constant, equaling that of pure water, gave predicted droplet shapes that best agreed with experimental observations. When the contact angle was assumed constant in the model, equal to the measured equilibrium value, predictions were less accurate. A simple analytical model was developed to predict maximum droplet diameter after impact. Model predictions agreed well with experimental measurements reported in the literature. Capillary effects were shown to be negligible during droplet impact when We≫Re1/2.

On boundary conditions in lattice Boltzmann methods

Abstract: A lattice Boltzmann boundary condition for simulation of fluid flow using simple extrapolation is proposed. Numerical simulations, including two‐dimensional Poiseuille flow, unsteady Couette flow, lid‐driven square cavity flow, and flow over a column of cylinders for a range of Reynolds numbers, are carried out, showing that this scheme is of second order accuracy in space discretization. Applications of the method to other boundary conditions, including pressure condition and flux condition are discussed.

Control of laminar vortex shedding behind a circular cylinder using splitter plates

Abstract: Laminar vortex shedding behind a circular cylinder and its control using splitter plates attached to the cylinder are simulated. The vortex shedding behind a circular cylinder completely disappears when the length of the splitter plate is larger than a critical length, and this critical length is found to be proportional to the Reynolds number. The Strouhal number of the vortex shedding is rapidly decreasing with the increased plate length until the plate length (l) is nearly the same as the cylinder diameter (d). On the other hand, at 1

Large eddy simulation of particle‐laden turbulent channel flow

Abstract: Particle transport in fully‐developed turbulent channel flow has been investigated using large eddy simulation (LES) of the incompressible Navier–Stokes equations. Calculations were performed at channel flow Reynolds numbers, Reτ, of 180 and 644 (based on friction velocity and channel half width); subgrid‐scale stresses were parametrized using the Lagrangian dynamic eddy viscosity model. Particle motion was governed by both drag and gravitational forces and the volume fraction of the dispersed phase was small enough such that particle collisions were negligible and properties of the carrier flow were not modified. Material properties of the particles used in the simulations were identical to those in the DNS calculations of Rouson and Eaton [Proceedings of the 7th Workshop on Two‐Phase Flow Predictions (1994)] and experimental measurements of Kulick et al. [J. Fluid Mech. 277, 109 (1994)]. Statistical properties of the dispersed phase in the channel flow at Reτ=180 are in good agreement with the DNS; reas...

Transient growth in compressible boundary layer flow

Abstract: The potential for transient growth in compressible boundary layers is studied. Transient amplification is mathematically associated with a non‐orthogonal eigenvector basis, and can amplify disturbances although the spectrum of the linearized evolution operator is entirely confined to the stable half‐plane. Compressible boundary layer flow shows a large amount of transient growth over a wide range of parameter values. The disturbance size is here measured by a positive definite energy like quantity that has been derived such that pressure‐related transfer terms in its evolution equation mutually cancel. The maximum of the transient growth is found for structures which are independent of the streamwise direction and is found to scale with R2. This suggests that the transient growth originates from the same lift‐up mechanism found to give large growth in incompressible shear flows. The maximum growth is also found to increase with Mach number. In compressible flow, disturbances that experience optimal transi...

Boundary conditions for the lattice Boltzmann method

Abstract: When the Lattice Boltzmann Method (LBM) is used for simulating continuum fluid flow, the discrete mass distribution must satisfy imposed constraints for density and momentum along the boundaries of the lattice. These constraints uniquely determine the three‐dimensional (3‐D) mass distribution for boundary nodes only when the number of external (inward‐pointing) lattice links does not exceed four. We propose supplementary rules for computing the boundary distribution where the number of external links does exceed four, which is the case for all except simple rectangular lattices. Results obtained with 3‐D body‐centered‐cubic lattices are presented for Poiseuille flow, porous‐plate Couette flow, pipe flow, and rectangular duct flow. The accuracy of the two‐dimensional (2‐D) Poiseuille and Couette flows persists even when the mean free path between collisions is large, but that of the 3‐D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3‐D low‐Reynolds‐number flow.

Numerical simulation of particle interactions with wall turbulence

Abstract: This paper presents the results of a numerical investigation of the effects of near‐neutral density solid particles on turbulent liquid flow in a channel. Interactions of particles, in a size range about the dissipative length scale, with wall turbulence have been simulated at low volume fractions (average volume fraction less than 4×10−4). Fluid motion is calculated by directly solving the Navier‐Stokes equations by a pseudo‐spectral method and resolving all scales of motion. Particles are moved in a Lagrangian frame through the action of forces imposed by the fluid and gravity. Particle effects on fluid motion are fed back at each time step by calculating the velocity disturbance caused by the particles assuming the flow around them is locally Stokesian. Particle‐particle interactions are not considered. The slightly heavier‐than‐fluid particles of the size range considered are found to preferentially accumulate in the low‐speed streaks, as reported in several other investigations. It is also found that particles smaller than the dissipative length scale reduce turbulence intensities and Reynolds stress, whereas particles that are somewhat larger increase intensities and stress. By examining higher order turbulence statistics and doing a quadrant analysis of the Reynolds stress, it is found that the ejection‐sweep cycle is affected—primarily through suppression of sweeps by the smaller particles and enhancement of sweep activity by the larger particles. A preliminary assessment of the impact of these findings on scalar transfer is made, as enhancement of transfer rate is a motivation of the overall work on this subject. For the case investigated, comparison of the calculations with an existing experiment was possible, and shows good agreement.

The passive scalar spectrum and the Obukhov–Corrsin constant

Abstract: It is pointed out that, for microscale Reynolds numbers less than about 1000, the passive scalar spectrum in turbulent shear flows is less steep than anticipated and that the Obukhov–Corrsin constant can be defined only if the microscale Reynolds number exceeds this value In flows where the large‐scale velocity field is essentially isotropic (as in grid turbulence), the expected 5/3 scaling is observed even at modest Reynolds numbers All known data on the Obukhov–Corrsin constant are collected The support for the notion of a ‘‘universal’’ constant is shown to be reasonable Its value is about 04

Phase diagrams for sonoluminescing bubbles

Abstract: Sound driven gas bubbles in water can emit light pulses This phenomenon is called sonoluminescence (SL) Two different phases of single bubble SL have been proposed: diffusively stable and diffusively unstable SL We present phase diagrams in the gas concentration versus forcing pressure state space and also in the ambient radius versus gas concentration and versus forcing pressure state spaces These phase diagrams are based on the thresholds for energy focusing in the bubble and two kinds of instabilities, namely (i) shape instabilities and (ii) diffusive instabilities Stable SL only occurs in a tiny parameter window of large forcing pressure amplitude Pa~12?15 atm and low gas concentration of less than 04% of the saturation The upper concentration threshold becomes smaller with increased forcing Our results quantitatively agree with experimental results of Putterman's UCLA group on argon, but not on air However, air bubbles and other gas mixtures can also successfully be treated in this approach if in addition (iii) chemical instabilities are considered All statements are based on the Rayleigh?Plesset ODE approximation of the bubble dynamics, extended in an adiabatic approximation to include mass diffusion effects This approximation is the only way to explore considerable portions of parameter space, as solving the full PDEs is numerically too expensive Therefore, we checked the adiabatic approximation by comparison with the full numerical solution of the advection diffusion PDE and find good agreemen

Energy balance for turbulent flow around a surface mounted cube placed in a channel

Abstract: Results of an experimental investigation of the inhomogeneous, three‐dimensional flow around a surface mounted cube in a channel are presented. LDA measurements of single‐point velocity correlations are used to determine the production, convection and transport of the turbulence kinetic energy, k, in the obstacle wake. The turbulence dissipation rate is obtained as a closing term to the balance of the k‐transport equation. The results provide some insight to the evolution of the turbulence dissipation rate from the near field recirculation zone to the asymptotic wake. Also presented is a comparison between measured and modeled transport terms.

The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere

Abstract: Results from a series of simulations of unforced turbulence evolving within a shallow layer of fluid on a rotating sphere are presented. Simulations show that the turbulent evolution in the spherical domain is strongly dependent on numerical and physical conditions. The independent effects of (1) (hyper)dissipation and initial spectrum, (2) rotation rate, and (3) Rossby deformation radius are carefully isolated and studied in detail. In the nondivergent and nonrotating case, an initially turbulent flow evolves into a vorticity quadrupole at long times, a direct consequence of angular momentum conservation. In the presence of sufficiently strong rotation, the nondivergent long‐time behavior yields a field dominated by polar vortices—as previously reported by Yoden and Yamada. In contrast, the case with a finite deformation radius (i.e., the full spherical shallow‐water system) spontaneously evolves toward a banded configuration, the number of bands increasing with the rotation rate. A direct application of...

Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence

Abstract: Mixing of a passive scalar in statistically homogeneous, isotropic, and stationary turbulence with a mean scalar gradient is investigated via direct numerical simulation, for Taylor‐scale Reynolds numbers, Rλ, from 28 to 185. Multiple independent simulations are performed to get confidence intervals, and local regression smoothing is used to further reduce statistical fluctuations. The scalar fluctuation field, φ(x,t), is initially zero, and develops to a statistically stationary state after about four eddy turnover times. Quantities investigated include the dissipation of scalar flux, which is found to be significant; probability density functions (pdfs) and joint‐pdfs of the scalar, its derivatives, scalar dissipation, and mechanical dissipation; and conditional expectations of scalar mixing, ∇2φ. A linear model for scalar mixing jointly conditioned on the scalar and v‐velocity is developed, and reproduces the data quite well. Also considered is scalar mixing jointly conditioned on the scalar and scalar...

Stability of Newtonian and viscoelastic dynamic contact lines

Abstract: The stability of the moving contact line is examined for both Newtonian and viscoelastic fluids. Two methods for relieving the contact line singularity are chosen: matching the free surface profile to a precursor film of thickness b, and introducing slip at the solid substrate. The linear stability of the Newtonian capillary ridge with the precursor film model was first examined by Troian et al. [Europhys. Lett. 10, 25 (1989)]. Using energy analysis, we show that in this case the stability of the advancing capillary ridge is governed by rearrangement of fluid in the flow direction, whereby thicker regions develop that advance more rapidly under the influence of a body force. In addition, we solve the Newtonian linear stability problem for the slip model and obtain results very similar to those from the precursor film model. Interestingly, stability results for the two models compare quantitatively when the precursor film thickness b is numerically equal to the slip parameter α. With the slip model, it is possible to examine the effect of contact angle on the stability of the advancing front, which, for small contact angles, was found to be independent of the contact angle. The stability of an Oldroyd‐B fluid was examined via perturbation theory in Weissenberg number. It is found that elastic effects tend to stabilize the capillary ridge for the precursor film model, and this effect is more pronounced as the precursor film thickness is reduced. The perturbation result was examined in detail, indicating that viscoelastic stabilization arises primarily due to changes of momentum transfer in the flow direction, while elasticity has little effect on the response of the fluid to flow in the spanwise direction.

Coarse‐grained description of thermo‐capillary flow

Abstract: A mesoscopic or coarse‐grained approach is presented to study thermo‐capillary induced flows. An order parameter representation of a two‐phase binary fluid is used in which the interfacial region separating the phases naturally occupies a transition zone of small width. The order parameter satisfies the Cahn–Hilliard equation with advective transport. A modified Navier–Stokes equation that incorporates an explicit coupling to the order parameter field governs fluid flow. It reduces, in the limit of an infinitely thin interface, to the Navier–Stokes equation within the bulk phases and to two interfacial forces: a normal capillary force proportional to the surface tension and the mean curvature of the surface, and a tangential force proportional to the tangential derivative of the surface tension. The method is illustrated in two cases: thermo‐capillary migration of drops and phase separation via spinodal decomposition, both in an externally imposed temperature gradient.

Particle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flows

Abstract: The motion of dense particles in a turbulent gas flow has been studied by means of numerical simulations. The single‐phase turbulent pipe flow was modelled using Direct Numerical Simulation and Large Eddy Simulation. At tube Reynolds numbers of 5300, 18300 and 42000 particles with dimensionless relaxation times ranging from 5 to 104 were released. Assuming the system to be dilute, the characteristics of particle dispersion, deposition and concentration distribution were studied under various conditions of gravity and lift. This study shows that for small particles the deposition process is governed by the properties of the near‐wall layer where the wall‐normal turbulence intensity is low, while for large inertial particles turbulent dispersion determines the chances for particles to hit the tube wall. The motion of the latter particles appears to scale properly with the Lagrangian integral time scale of the turbulence. Furthermore we demonstrated the segregation of particles towards the wall, as a result of particle‐turbulence interaction.

Marangoni effects on drop deformation in an extensional flow: The role of surfactant physical chemistry. I. Insoluble surfactants

Abstract: The shape of a drop centered in an axisymmetric extensional flow is determined by the viscous stresses that deform the drop and surface tension γ′ that resists the deformation. The ratio of these stresses is given by the capillary number, Ca. When Ca is small enough, the drop attains a steady shape. However, above a threshold value, Cacr, the drop elongates continuously, and no steady shape is attained. When surfactants are present on the drop interface, the surface tension is determined by the surface concentration profile, which varies throughout the deformation process. Initially, the surface tension is given by γeq′, in equilibrium with the uniform surface concentration Γeq′. When the flow is initiated, surfactant is swept toward the drop tips, reducing the surface tension there, and altering the interfacial stress balance tangentially through Marangoni stresses and normally through the Laplace pressure. In this paper, the effects of an insoluble surfactant on drop deformation are studied. In previous work, either a surface equation of state for the surface tension γ′ that is linear in the surface concentration Γ′ was used, an approximation that is valid only for dilute Γ′, or Γ′ sufficiently dilute for the linear approximation to be valid were studied. In this paper, a nonlinear surface equation of state that accounts for surface saturation and nonideal interactions among the surfactant molecules is adopted. The linear framework results are recovered for Γ′ that are sufficiently dilute. As Γ′ is increased, the effects of saturation and surfactant interactions are probed at constant initial Γeq′ and at constant initial γeq′. Finally, the case of strong intersurfactant cohesion is treated with a first‐order surface phase transformation model. At moderate surface concentrations, these nonlinear phenomena strongly alter the steady drop deformations and Cacr relative to the uniform surface tension and linear equation of state results.

Head-on collision of drops: A numerical investigation

Abstract: The head-on collision of equal sized drops is studied by full numerical simulations. The Navier-Stokes equations are solved for fluid motion both inside and outside the drops using a front tracking/finite difference technique. The drops are accelerated toward each other by a body force that is turned off before the drops collide. When the drops collide, the fluid between them is pushed outward leaving a thin later bounded by the drop surface. This layer gets progressively thinner as the drops continue to deform and in several of the calculations this double layer is artificially removed once it is thin enough, thus modeling rupture. If no rupture takes place, the drops always rebound, but if the film is ruptured the drops may coalesce permanently or coalesce temporarily and then split again.

The effect of surfactant on the rise of a spherical bubble at high Reynolds and Peclet numbers

Abstract: Experiments and numerical simulations of rising spherical bubbles in quiescent surfactant solutions are presented. The rise velocities versus the concentration in the bulk are measured using three surfactants, Triton X100, Brij30 and SDS for different bubble sizes, between 0.4 and 1 mm equivalent radius. We also present a brief description of the finite‐difference numerical method developed to solve the full Navier‐Stokes equations around the contaminated bubble for Reynolds numbers ranging from 50 to 200. The distributions of the tangential velocity, the vorticity, the pressure and the surfactant concentration on the bubble surface are calculated. In the case of high Peclet numbers surfactant molecules, which adsorb on the surface are convected and collected at the rear part of the bubble forming a stagnant cap where the no‐slip condition holds. The concentration on the bubble interface is obtained for surfactants having a desorption rate much slower than the convective rate. The sudden increase of the shear stress and pressure at the leading edge of the cap contributes mainly to decrease the rise velocity. This rapid slowdown of the bubble occurs when nearly half of the bubble surface is covered by the surfactant layer, and this is due to the particularly high values obtained for the shear stress and the pressure at the leading edge of this cap‐angle. Measured and calculated rise velocities for bubbles of 0.4 mm equivalent radius show good agreement when the sorption kinetics controls the surfactant exchange between the bulk and the surface. Calculated critical concentrations needed to cover completely the bubble agree with the measurements even for larger bubbles.

Turbulence in homogeneous shear flows

Abstract: Homogeneous shear flows with an imposed mean velocity U=Syx are studied in a period box of size Lx×Ly×Lz, in the statistically stationary turbulent state. In contrast with unbounded shear flows, the finite size of the system constrains the large‐scale dynamics. The Reynolds number, defined by Re≡SL2y/ν varies in the range 2600⩽Re⩽11300. The total kinetic energy and enstrophy in the volume of numerical integration have large peaks, resulting in fluctuations of kinetic energy of order 30%–50%. The mechanism leading to these fluctuations is very reminiscent of the ‘‘streaks’’ responsible for the violent bursts observed in turbulent boundary layers. The large scale anisotropy of the flow, characterized by the two‐point correlation tensor 〈uiuj〉 depends on the aspect ratio of the system. The probability distribution functions (PDF) of the components of the velocity are found to be close to Gaussian. The physics of the Reynolds stress tensor, uv, is very similar to what is found experimentally in wall bounded ...

Dynamics of coherent structures and transition to turbulence in free square jets

Abstract: We report results of time‐dependent numerical simulation of spatially developing free square jets initialized with a thin square vortex‐sheet with slightly rounded corner‐regions The studies focus on the near field of jets with Mach number 03–06 and moderately high Reynolds numbers A monotonically‐integrated large‐eddy‐simulation approach is used, based on the solution of the unfiltered inviscid equations and appropriate inflow/outflow open boundary conditions The simulations show that the initial development of the square jet is characterized by the dynamics of vortex rings and braid vortices Farther downstream, strong vortex interactions lead to the breakdown of the vortices, and to a more disorganized flow regime characterized by smaller scale elongated vortices and spectral content consistent with that of the Kolmogorov (K41) inertial subrange Entrainment rates significantly larger than those for round jets are directly related to the enhanced fluid and momentum transport between jet and surroundings determined by the vortex dynamics underlying the axis‐rotation of the jet cross‐section The first axis‐rotation of the jet cross‐section can be directly correlated with self‐induced vortex‐ring deformation However, subsequent jet axis‐rotations are the result of strong interactions between ring and braid vortices, rather than being correlated with successive self‐induced vortex‐ring deformations, as previously conjectured based on laboratory observations The interaction between braid and ring vortices has the effect of inhibiting the periodic self‐induced axis‐rotations observed in the case of isolated square vortex rings

Autogeneration of near-wall vortical structures in channel flow

Abstract: The evolution of a symmetric pair of quasistreamwise vortical structures extracted from the two‐point correlation tensor of turbulent channel flow data by a linear stochastic estimation procedure is studied through direct numerical simulation. It is observed that an Ω‐shaped hairpin vortex is formed quickly from this initial structure. Sufficiently strong hairpin vortices are observed to generate a hierarchy of secondary hairpin vortices, and the mechanism of their creation closely resembles the formation of the primary hairpin vortex. New streamwise vortices are also generated, and this process provides a means for a few vortical disturbances of adequate strength to reproduce themselves and eventually populate the near‐wall layer.

On the surfactant mass balance at a deforming fluid interface

Abstract: The amount of surfactants ~surface active agents! adsorbed onto a fluid interface affects its surface tension. Thus the distribution of surfactants must be determined to find the jump in the normal and tangential stresses across the interface. Scriven ~see also Aris, Slattery, and Edwards et al.! uses differential geometry to derive the correct surface balance equation for an arbitrary surface coordinate system. Also invoking differential geometry, Waxman develops a correct form in ~‘‘fixed’’! surface coordinates that advance only normal to the surface. To arrive at this balance without appealing to differential geometry, Stone presents a simple physical derivation which leads to a form of the mass balance which is easy to solve numerically. Unfortunately, Stone’s derivation leaves the nature of the unsteady time derivative ambiguous. Here we follow the spirit set in Stone to derive geometrically the surface balance in a way that keeps the nature of the time derivative explicit. We verify that in Stone’s form the time derivative must hold the fixed coordinates constant, as the numerical implementation of this form of the mass balance actually do. We also derive a new form valid in an arbitrary surface coordinate system. Consider a fixed point A on a fluid surface with local normal n as in Fig. 1. We locate any two perpendicular planes which intersect along n. The intersection of each of these planes with the surface near the point A define curves whose unit tangents are t1 and t2 . By construction ]t1/]s152~1/R1!n and ]t2/]s252~1/R2!n, where ds1 and ds2 are differential arcs and R1~.0! and R2~.0! are the radii of curvature of the curves. Geometrically, these differential arcs are ds15R1df1 and ds25R2df2 , where df1 and df2 are the differential angles in the figure, and ]t1/]f152n and ]t2/]f252n. Thus in this locally orthogonal system, the components of the surface metric tensor aab are: Aa115R1 , a1250, and Aa225R2 and the diagonal elements simply act as scale factors. These arcs define a patch of area dA5Aa11Aa22df1df25Aadf1df2 where a is the determinant of the metric tensor. The diagonal components of the curvature tensor bab are defined by @]ta /]fa#–n 5 baa /Aaaa ~no sum on a!; so b1152R1 and b2252R2 . The curvatures are negative because as drawn in Fig. 1 both arcs are concave down with respect to the normal. If U is the instantaneous material velocity vector at the fixed point, its components along $n,t1 ,t2% are U5Us(1)t11Us(2)t21Wn, where W is the normal component and Us(1) and Us(2) are the physical components tangent to the surface. The fixed point advances along the normal ~n! as shown in the Fig. 1 a distance WDt so that the patch perimeters have lengths (R11WDt)df1 and (R21WDt)df2 at the time t1Dt; thus the change in area of the patch is WDt(R11R2)df1df2 and the per unit area per unit time rate of change is

Vertical water entry of disks at low Froude numbers

Abstract: As basilisk lizards (Basiliscus basiliscus) and shore birds run along the water surface they support their body weight by slapping and stroking into the water with their feet. The foot motions exploit the hydrodynamic forces of low‐speed water entry. To determine the forces that are produced during water entry at low speeds, we measured directly the impact and drag forces for disks dropped into water at low Froude numbers (u2/gr=1–80). Also, we measured the period during which the air cavity behind the disk remains open to atmospheric air. We found that the force impulse produced during the impact phase is due to the acceleration of the virtual mass of fluid associated with a disk at the water surface. A dimensionless virtual mass M, defined as M=mvirtual/(4/3)πρr3, has a value near 1/π for disks. After impact, as penetration depth of the disk increases, the drag force can rise by as much as 76% even though the downward velocity is steady. However, a dimensionless force which includes the contribution fro...

Experimental study of incompressible Richtmyer–Meshkov instability

Abstract: The Richtmyer–Meshkov instability of a two‐liquid system is investigated experimentally. These experiments utilize a novel technique that circumvents many of the experimental difficulties that have previously limited the study of Richtmyer–Meshkov instability. The instability is generated by vertically accelerating a tank containing two stratified liquids by bouncing it off of a fixed coil spring. A controlled two‐dimensional sinusoidal initial shape is given to the interface by oscillating the container in the horizontal direction to produce standing waves. The motion of the interface is recorded during the experiments using standard video photography. Instability growth rates are measured and compared with existing linear theory. Disagreement between measured growth rates and the theory are accredited to the finite bounce length. When the linear stability theory is modified to account for an acceleration pulse of finite duration, much better agreement is attained. Late time growth curves of many different experiments seem to collapse to a single curve when correlated with the circulation deposited by the impulsive acceleration. A theory based on modeling the late time evolution of the instability using a row of vortices is developed. The growth curve given by this model has similar shape to those measured, but underestimates the late‐time growth rate.

NMR imaging of velocity profiles and velocity distributions in bead packs

Abstract: Spatially resolved velocity profiles and spatially nonresolved velocity distributions of steady flow in a tube and bead packs were measured. Two different NMR experiments were used to measure velocity distributions. In one, the velocity histogram was calculated from spatially resolved velocity phase encoded images acquired in a 6 mm bead pack. In the other, a Fourier flow method was used to measure the velocity distribution directly in a 0.25 mm bead pack. Axial velocity profiles in the pore space of the 6 mm bead pack at Reynolds numbers of 14.9, 29.9, and 44.8 proved to be roughly parabolic, with maxima near the pore centers. Both NMR methods yielded the same dimensionless velocity distributions that contain negative as well as positive velocity components. The velocity distribution function derived from a bundle‐of‐tubes‐model accounts for the positive part of the velocity distribution.

On secondary vortices in the cylinder wake

Abstract: The wake of a circular cylinder is investigated for Reynolds numbers between 160 and 500 by means of particle image velocimetry (PIV). For the first time cross‐stream velocity fields are determined for two classes of secondary vortices (A‐mode and B‐mode). The circulation of the A‐mode secondary vortices in this plane is approximately twice the circulation of the B‐mode secondary vortices. The spanwise wavelength of the secondary vortices is four to five cylinder diameters for the A‐mode and one diameter for the B‐mode. The spatio‐temporal development of the wake is analyzed by acquiring a time sequence of PIV images covering several Karman periods. On the basis of the vorticity field, the A‐ and B‐modes can be identified as topologically different vortex structures. Two vortex models are developed to explain the differences between these modes.

The role of chaotic orbits in the determination of power spectra of passive scalars

Abstract: This paper relates properties of the power spectrum of a passive scalar convected by a chaotic fluid flow to the distribution of finite time Lyapunov exponents. The properties considered include the early time evolution of the power spectrum, the late time exponential decay of the scalar variance, and the wave number dependence of the power spectrum in the presence of a source of scalar variance. Theoretical predictions are tested by comparing full numerical solutions of the relevant partial differential equation to solutions of a model system which includes diffusion and involves integrations along the fluid orbits only. The model system is shown to give results in close agreement with the numerical solutions of the full problem. This suggests the possible general utility of the model equations for a broad range of problems involving passive scalar convection.

Secondary instability in the wake of a circular cylinder

Abstract: Secondary instability of flow past a circular cylinder is examined using highly accurate numerical methods. The critical Reynolds number for this instability is found to be Rec=188.5. The secondary instability leads to three‐dimensionality with a spanwise wavelength at onset of 4 cylinder diameters. Three‐dimensional simulations show that this bifurcation is weakly subcritical.

Subgrid‐scale energy transfer and near‐wall turbulence structure

Abstract: Conditional averages of the velocity field, subgrid‐scale (SGS) stresses and SGS dissipation are calculated using the velocity fields obtained from the DNS of plane channel flow. The detection criteria isolate the coherent turbulent structures that contribute most strongly to the energy transfer between the large, resolved scales and the subgrid, unresolved, ones. Separate averages are computed for forward and backward scatter. The interscale energy transfer is found to be strongly correlated with the presence of the turbulent structures typical of wall‐bounded flows: quasi‐streamwise and hairpin vortices, sweeps and ejections. In the buffer layer, strong SGS dissipation is observed near lifted shear layers; the forward scatter is associated with ejections, the backscatter with sweeps. Both backward and forward scatter occur in close proximity to longitudinal vortices that form a very shallow angle to the wall. Further away from the solid boundary, in the logarithmic region and beyond, both forward and backward energy transfer are associated prevalently with ejections. Eddy viscosity models do not predict the three‐dimensional structure of these events adequately, while scale‐similar models reproduce the correlation between the large‐scale coherent structures and the SGS events more accurately.

Pinching threads, singularities and the number 0.0304...

Abstract: The dynamics of capillary pinching of a fluid thread are described by similarity solutions of the Navier–Stokes equations. Eggers [Phys. Rev. Lett. 71, 3458 (1993)] recently proposed a single universal similarity solution for a viscous thread pinching with an inertial–viscous–capillary balance in an inviscid environment. In this paper it is shown that there is actually a countably infinite family of such similarity solutions which are each an asymptotic solution to the Navier–Stokes equations. The solutions all have axial scale t′1/2 and radial scale t′, where t′ is the time to pinching. The solution obtained by Eggers appears to be special in that it is selected by the dynamics for most initial conditions by virtue of being less susceptible to finite‐amplitude instabilities. The analogous problem of a thread pinching in the absence of inertia is also investigated and it is shown that there is a countably infinite family of similarity solutions with axial scale t′β and radial scale t′, where each solution...