bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical simulations of the effect of hydrodynamic interactions on diffusivities of integral membrane proteins
Authors: Dodd Travis L. , Hammer Daniel A. , Sangani Ashok S. , Koch Donald L.
Published: April 2006

Proteins in a biological membrane can be idealized as disks suspended in a thin viscous sheet surrounded by a fluid of lower viscosity (Saffman 1976). To determine the effect of hydrodynamic interactions on protein diffusivities in non-dilute suspensions, we numerically solve the Stokes equations of motion for a system of disks in a bounded periodic two-dimensional fluid using a multipole expansion technique. We consider both free suspensions, in which all the proteins are mobile, and fixed beds, in which a fraction of the proteins are fixed. For free suspensions, we determine both translational and rotational short-time self-diffusivities and the gradient diffusivity as a function of the area fraction of the disks. The translational self- and gradient diffusivities computed in this way grow logarithmically with the number of disks owing to Stokes paradox; to obtain finite values, we renormalize our simulation results by treating long-range interactions in terms of a membrane with an enhanced viscosity in contact with a low-viscosity three-dimensional fluid. The diffusivities in fixed beds require no such adjustment because, at non-dilute area fractions of disks, the Brinkman screening of hydrodynamic interactions is more important that the viscous drag due to the surrounding three-dimensional fluid in limiting the range of hydrodynamic interactions. The diffusivities are determined as functions of the area fractions of both mobile and fixed proteins. We compare our results for diffusivities with experimental measurements of long-time protein self-diffusivity after adjusting our short-time diffusivities calculations in an approximate way to account for effects of hindered diffusion due to volume exclusion, and find very good agreement between the two.
Flow regimes and relative permeabilities during steady-state two-phase flow in porous media
Authors: Avraam D. G. , Payatakes A. C.
Published: April 2006

Steady-state two-phase flow in porous media was studied experimentally, using a model pore network of the chamber-and-throat type, etched in glass. The size of the network was sufficient to make end effects negligible. The capillary number, Ca, the flow-rate ratio, r, and the viscosity ratio, k, were changed systematically in a range that is of practical interest, whereas the wettability (moderate), the coalescence factor (high), and the geometrical and topological parameters of the porous medium were kept constant. Optical observations and macroscopic measurements were used to determine the flow regimes, and to calculate the corresponding relative permeabilities and fractional flow values. Four main flow regimes were observed and videorecorded, namely large-ganglion dynamics (LGD), small-ganglion dynamics (SGD), drop-traffic flow (DTF) and connected pathway flow (CPF). A map of the flow regimes is given in figure 3. The experimental demonstration that LGD, SGD and DTF prevail under flow conditions of practical interest, for which the widely held dogma presumes connected pathway flow, necessitates the drastic modification of that assumption. This is bound to have profound implications for the mathematical analysis and computer simulation of the process. The relative permeabilities are shown to correlate strongly with the flow regimes, figure 11. The relative permeability to oil (non-wetting fluid), kro, is minimal in the domain of LGD, and increases strongly as the flow mechanism changes from LGD to SGD to DTF to CPF. The relative permeability to water (wetting fluid), krw, is minimal in the domain of SGD; it increases moderately as the flow mechanism changes from SGD to LGD, whereas it increases strongly as the mechanism changes from SGD to DTF to CPF. Qualitative mechanistic explanations for these experimental results are proposed. The conventional relative permeabilities and the fractional flow of water, fw, are found to be strong functions not only of the water saturation, Sw, but also of Ca and k (with the wettability, the coalescence factor, and all the other parameters kept constant). These results imply that a fundamental reconsideration of fractional flow theory is warranted.
High-resolution simulations of the flow around an impulsively started cylinder using vortex methods
Authors: Koumoutsakos P. , Leonard A.
Published: April 2006

The development of a two-dimensional viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally. An adaptative numerical scheme, based on vortex methods, is used to integrate the vorticity/velocity formulation of the Navier–Stokes equations for a wide range of Reynolds numbers (Re= 40 to 9500). A novel technique is implemented to resolve diffusion effects and enforce the no-slip boundary condition. The Biot–Savart law is employed to compute the velocities, thus eliminating the need for imposing the far-field boundary conditions. An efficient fast summation algorithm was implemented that allows a large number of computational elements, thus producing unprecedented high-resolution simulations. Results are compared to those from other theoretical, experimental and computational works and the relation between the unsteady vorticity field and the forces experienced by the body is discussed.
Two-dimensional secondary instabilities in a strongly stratified shear layer
Authors: Staquet Chantal
Published: April 2006

In a stably stratified shear layer, thin vorticity layers (‘baroclinic layers’) are produced by buoyancy effects and strain in between the Kelvin–Helmholtz vortices. A two-dimensional numerical study is conducted, in order to investigate the stability of these layers. Besides the secondary Kelvin–Helmholtz instability, expected but never observed previously in two-dimensional numerical simulations, a new instability is also found.

The influence of the Reynolds number (Re) upon the dynamics of the baroclinic layers is first studied. The layers reach an equilibrium state, whose features have been described theoretically by Corcos & Sherman (1976). An excellent agreement between those predictions and the results of the numerical simulations is obtained. The baroclinic layers are found to remain stable almost up to the time the equilibrium state is reached, though the local Richardson number can reach values as low as 0.05 at the stagnation point. On the basis of the work of Dritschel et al. (1991), we show that the stability of the layer at this location is controlled by the outer strain field induced by the large-scale Kelvin–Helmholtz vortices. Numerical values of the strain rate as small as 3% of the maximum vorticity of the layer are shown to stabilize the stagnation point region.

When non-pairing flows are considered, we find that only for Re ≤ 2000 does a secondary instability eventually amplify in the layer. (Re is based upon half the initial vorticity thickness and half the velocity difference at the horizontally oriented boundaries.) This secondary instability is not of the Kelvin–Helmholtz type. It develops in the neighbourhood of convectively unstable regions of the primary Kelvin–Helmholtz vortex, apparently once a strong jet has formed there, and moves along the baroclinic layer while amplifying. It next perturbs the layer around the stagnation point and a secondary instability, now of the Kelvin–Helmholtz type, is found to develop there.

We next examine the influence of a pairing upon the flow behaviour. We show that this event promotes the occurrence of a secondary Kelvin–Helmholtz instability, which occurs for Re ≥ 400. Moreover, at high Reynolds number (≥ 2000), secondary Kelvin–Helmholtz instabilities develop successively in the baroclinic layer, at smaller and smaller scales, thereby transferring energy towards dissipative scales through a mechanism eventually leading to turbulence. Because the vorticity of such a two-dimensional stratified flow is no longer conserved following a fluid particle, an analogy with three-dimensional turbulence can be drawn.
Energetics of grid turbulence in a stably stratified fluid
Authors: Liu Hsien-Ta
Published: April 2006

A biplane grid with a mesh spacing of 10.8 cm was towed horizontally in a towing tank to generate turbulence in a non-stratified fluid and in stratified fluids with different constant density gradients. Turbulence velocity components and density fluctuations were measured using an array of cross-film and conductivity probes. Based on the mesh size of the grid, the nominal values of the (internal) Froude numbers were ∞, 80 and 40, and the corresponding Reynolds number was 4.3 × 104. The decay rates of the (turbulence) kinetic, potential and total energies and the dissipation rates of the kinetic and potential energies were calculated from the experimental data. For each of these quantities, the decay may be represented as a function of the downstream distance raised to a given power. The kinetic energy and its dissipation rate are lower for the stratified cases than for the non-stratified case but are almost compensated for by the corresponding potential energy and its dissipation rate. Our results are consistent with those of direct numerical simulations and agree reasonably well with those obtained in stratified wind and water tunnels. However, the results differ from laboratory results obtained using an optical method to measure the turbulent motion of tracer particles in the wake of a vertically towed grid; these latter results show an abrupt reduction in the decay rate of the turbulence kinetic energy after one Brunt–Väisälä period. A similar trend is also observed in results obtained in facilities with fairly high background turbulence or internal waves. This discrepancy is discussed and an explanation is presented. Furthermore, it is demonstrated that strongly stratified thin sheets with density gradients larger than that of the undisturbed fluid may be generated by local but incomplete mixing. The persistence of such thin sheets is proportional to the Schmidt number (≈ 500) in stratified salt water or the Prandtl number (≈ 0.71) in thermally stratified air.
Experiments on supersonic combustion ramjet propulsion in a shock tunnel
Authors: Paull A. , Stalker R. J. , Mee D. J.
Published: April 2006

Measurements have been made of the propulsive effect of supersonic combustion ramjets incorporated into a simple axisymmetric model in a free piston shock tunnel. The nominal Mach number was 6, and the stagnation enthalpy varied from 2.8 to 8.5 MJ kg−1. A mixture of 13% silane and 87% hydrogen was used as fuel, and experiments were conducted at equivalence ratios up to approximately 0.8. The measurements involved the axial force on the model, and were made using a stress wave force balance, which is a recently developed technique for measuring forces in shock tunnels. A net thrust was experienced up to a stagnation enthalpy of 3.7 MJ kg−1, but as the stagnation enthalpy increased, an increasing net drag was recorded. Pilot and static pressure measurements showed that the combustion was supersonic.

The results were found to compare satisfactorily with predictions based on established theoretical models, used with some simplifying approximations. The rapid reduction of net thrust with increasing stagnation enthalpy was seen to arise from increasing precombustion temperature, showing the need to control this variable if thrust performance was to be maintained over a range of stagnation enthalpies. Both the inviscid and viscous drag were seen to be relatively insensitive to stagnation enthalpy, with the combustion chambers making a particularly significant contribution to drag. The maximum fuel specific impulse achieved in the experiments was only 175 s, but the theory indicates that there is considerable scope for improvement on this through aerodynamic design.
Simple shear flows of dilute gas–solid suspensions
Authors: Tsao Heng-Kwong , Koch Donald L.
Published: April 2006

Kinetic theory and numerical simulations are used to explore the dynamics of a dilute gas–solid suspension subject to simple shear flow. The particles experience a Stokes drag force and undergo solid-body interparticle collisions. Two qualitatively different steady-state behaviours are possible: an ignited state, in which the variance of the particle velocity is very large; and a quenched state, in which most of the particles follow the local fluid velocity. Theoretical results for the ignited state are obtained by perturbing from a Maxwell distribution, while predictions for the quenched state result from consideration of the collision of particles that initially move with the fluid. A composite theory, which includes effects of collisions driven by both the mean shear and the velocity fluctuations, predicts the existence of multiple steady states. Dynamic simulations and calculations using the direct-simulation Monte Carlo method confirm the result that, for certain volume fractions and shear rates, either the quenched or ignited state can be achieved depending on the initial velocity variance.

Simulations are also performed for particles experiencing a nonlinear drag force. Both the theory of rapid granular flow, which neglects drag, and our theory for the ignited state with linear drag predict that the particle velocity variance can grow without bound as ϕ → 0, where ϕ is the volume fraction. The nonlinear drag force eliminates the divergence and leads to a particle velocity variance that will always decrease with decreasing volume fraction in the limit ϕ → 0.
A nonlocal theory for stress in bound, Brownian suspensions of slender, rigid fibres
Authors: Schiek Richard L. , Shaqfeh Eric S. G.
Published: April 2006

A nonlocal theory for stress in bound suspensions of rigid, slender fibres is developed and used to predict the rheology of dilute, rigid polymer suspensions when confined to capillaries or fine porous media. Because the theory is nonlocal, we describe transport in a fibre suspension where the velocity and concentration fields change rapidly on the fibre's characteristic length. Such rapid changes occur in a rigidly bound domain because suspended particles are sterically excluded from configurations near the boundaries. A rigorous no-flux condition resulting from the presence of solid boundaries around the suspension is included in our nonlocal stress theory and naturally gives rise to concentration gradients that scale on the length of the particle. Brownian motion of the rigid fibres is included within the nonlocal stress through a Fokker–Planck description of the fibres’ probability density function where gradients of this function are proportional to Brownian forces and torques exerted on the suspended fibres. This governing Fokker–Planck probability density equation couples the fluid flow and the nonlocal stress resulting in a nonlinear set of integral-differential equations for fluid stress, fluid velocity and fibre probability density. Using the method of averaged equations (Hinch 1977) and slender-body theory (Batchelor 1970), the system of equations is solved for a dilute suspension of rigid fibres experiencing flow and strong Brownian motion while confined to a gap of the same order in size as the fibre's intrinsic length. The full solution of this problem, as the fluid in the gap undergoes either simple shear or pressure-driven flow, is solved self-consistently yielding average fluid velocity, shear and normal stress profiles within the gap as well as the probability density function for the fibres’ position and orientation. From these results we calculate concentration profiles, effective viscosities and slip velocities and compare them to experimental data.
The localization length of randomly scattered water waves
Authors: Nachbin André
Published: April 2006

A theory for the reflection-transmission problem of linear water waves in shallow channels with large-amplitude, rapidly varying topographies is given in Nachbin & Papanicolaou (1992b). However, it is very difficult to extract quantitative information from the theory in the large-amplitude regime. In this work, theoretical parameters are evaluated numerically, through the use of a numerical Schwarz–Christoffel transformation and of a Monte Carlo simulation. This enables the theory to be applied to its full extent. As a result we calculate the localization length for any given type of random bottom topography. Additionally, the numerical conformal mapping provides further insight into depth effects arising from potential theory. Statistical results, for numerically generated reflected waves, are in very good agreement with the theory for both piecewise-linear and piecewise-constant topographies of large amplitude.
Drag on a sphere in slow shear flow
Authors: Miyazaki Kunimasa , Bedeaux Dick , Avalos Josep Bonet
Published: April 2006

A general closed form for the mobility tensor of a sphere moving in a fluid in stationary homogeneous flow is derived using the induced force method up to the first order in the square root of the Reynolds number based on the velocity gradient of the unperturbed flow. The closed form for the mobility tensor is valid for the time-dependent case as well as for the stationary case. As a special case, we calculate it explicitly for a simple shear flow. The result for the x, z-component for the stationary case, which gives the lift force, agrees with the value calculated by Saffman.
Deformation of liquid capsules with incompressible interfaces in simple shear flow
Authors: Zhou Hua , Pozrikidis C.
Published: April 2006

The transient deformation of liquid capsules enclosed by incompressible membranes whose mechanical properties are dominated by isotropic tension is studied as a model of red blood cell deformation in simple shear flow. The problem is formulated in terms of an integral equation for the distribution of the tension over the cell membrane which is solved using a point-wise collocation and a spectral-projection method. The computations illustrate the dependence of the deformed steady cell shape, membrane tank-treading frequency, membrane tension, and rheological properties of a dilute suspension, on the undeformed cell shape. The general features of the evolution of two-dimensional cells are found to be similar to those of three-dimensional cells, and the corresponding membrane tank-treading frequency and maximum tension are seen to attain comparable values. The numerical results are compared with previous asymptotic analyses for small deformations and available experimental observations, with satisfactory agreement. An estimate of the maximum shear stress for membrane breakup and red blood cell hemolysis is deduced on the basis of the computed maximum membrane tension at steady state.
Surface-tension-driven Bénard convention at infinite Prandtl number
Authors: Thess A. , Orszag S. A.
Published: April 2006

Surface-tension-driven convection in a planar fluid layer is studied by numerical simulation of the three-dimensional time-dependent governing equations in the limit of infinite Prandtl number. Emphasis is placed on the spatial scale of weakly supercritical flows and on the generation of small-scale structures in strongly supercritical flows. The decrease of the size of weakly supercritical hexagonal convection cells that we find is in agreement with experimental results. In the case of high Marangoni number, discontinuities of the temperature gradient are formed between convection cells, producing a universal spectrum E ∼ k−3 of the two-dimensional surface temperature field. The possibility of experimental verification is discussed on the basis of shadowgraph images calculated from the predicted hydrodynamic fields.
The effect of deformable porous surface layers on the motion of a sphere in a narrow cylindrical tube
Authors: Wang Wen , Parker Kim H.
Published: April 2006

The hydrodynamic influence of deformable porous surface layers on the motion of a rigid sphere falling in a narrow cylindrical tube filled with a stationary Newtonian fluid is studied using lubrication theory. The porous layers on both the surface of the tube and the sphere are modelled as binary mixtures of solid and liquid components. The sphere is placed at an arbitrary position in the tube and is free to rotate. Effects of the clearance between the sphere and the tube, the eccentricity of the position of the sphere and the properties of the surface layers on the velocity and rotation of the sphere are studied. It is found that, when the lengthscale on which the velocity varies within the porous layer is much smaller than the clearance, the effects of the porous layer can be represented by an equivalent slip boundary condition, the slip velocity at the boundary being proportional to the local shear rate. The slip velocities have a strong influence on the motion of the sphere when the clearance is small. For a given clearance and slip parameters, both the falling and rotation velocities of the sphere increase with the sphere eccentricity. The shear stresses on the surfaces of both the tube and the sphere are greatly reduced when slip boundary conditions are applied, as is the pressure gradient in the region between the sphere and the tube wall. This work could have some relevance to the creeping motion of blood cells in the microcirculation where the glycocalyx, a polysaccharide-rich layer, covers the external surfaces of both endothelial and red blood cells.
Long-time behaviour of the drag on a body in impulsive motion
Authors: Lawrence Christopher J. , Mei Renwei
Published: April 2006

We consider the response of the hydrodynamic drag on a body in rectilinear motion to a change in the speed between two steady states, from U1 to U2 [ges ] 0. We consider situations where the body generates no lift, such as occur for bodies with an axis of symmetry aligned with the motion. At large times, the laminar wake consists of two quasi-steady regions – the new wake and the old wake – connected by a transition zone that is convected downstream with the mean speed U2. A global mass balance indicates the existence of a sink flow centred on the transition zone, and this is responsible for the leading-order behaviour of the unsteady force at long times. For the case of U1 [ges ] 0, the force is shown to decay algebraically with the inverse square of time for any finite Reynolds number (Re), and this result is also shown to hold for non-rectilinear motions. A recent analysis for small Reynolds number including terms to O(Re) (Lovalenti & Brady 1993 a) has indicated that the force decays as the inverse square of time for motion started from rest, but decays exponentially for a change between two positive velocities. The former result is found to be correct, but the exponential decay at O(Re) in the latter case is superseded at large times by the inverse-square time decay which is shifted to O(Re2) because the wake flux is nearly constant for small Re. The cases of reversed flow (U1 < 0) and stopped flow (U2 = 0) are treated separately, and it is shown that the transient force is dominated by the effects of the old wake, leading to a slower decay as the simple inverse of time. The force is determined by the far regions of the flow field and so the results are valid for any (symmetric) particle, bubble or drop and (in an average sense) for any Re, provided τ ma {Re, Re−1}, where the time τ is made dimensionless with the convection timescale. The analytical results are compared to detailed numerical calculations for transient flow over spherical particles and bubbles and compelling agreement is observed. These are believed to be the first calculations which adequately resolve the transient far wake behind a bluff body at long times. The asymptotic result for the force is applied to determine that the approach to terminal velocity of a body in free fall is also as the inverse square of time.
Experimental investigation of subharmonic resonance in an axisymmetric jet
Authors: Paschereit C. O. , Wygnanski I. , Fiedler H. E.
Published: April 2006

A resonant subharmonic interaction between two axisymmetric travelling waves was induced in the shear layer of an axisymmetric jet by controlled sinusoidal perturbations with two frequencies separated by one octave. Wherever the two excited waves are non-dispersive and the fundamental is close to its linear neutral point the two waves may interact in a manner that enhances the amplification rate of the subharmonic wave train. The amplified subharmonic will exceed the fundamental's level to become the dominant instability component. The initial phase difference between the subharmonic and the fundamental plays an important role in the amplification of the subharmonic. For specific phase angles between the two excited waves a suppression of the subharmonic may be observed. The influence of other initial parameters such as amplitude ratio, overall forcing level, excitation frequency and flow conditions at the nozzle (i.e. the initial turbulence level and the initial momentum thickness) was also investigated. An increase in the combined forcing level reduces the effect of the initial phase difference on the amplification of the subharmonic. Stronger excitation moves the location at which the two waves are locked in space further upstream while the effect of the initial phase difference decreases. The energy transfer to the subharmonic wave has been analysed by estimating the production terms. The results clearly indicate that most of the energy for the resonant growth of the subharmonic comes directly from the mean flow. The fundamental wave acts as a catalyst, as long as the resonance conditions are satisfied, enhancing the rate of energy transfer from the mean flow to the subharmonic.
Free convection in an electrochemical system with nonlinear reaction kinetics
Authors: Bark Fritz H. , Alavyoon Farid
Published: April 2006

Unsteady electrolysis of a dilute solution of a metal salt made up of two ions in a system with vertical electrodes is considered for large values of the Rayleigh and Schmidt numbers. The mass transfer at the electrodes is assumed to be related to the local charge transfer potential and concentration by a nonlinear Butler–Volmer law. Free convection of the electrolyte appears owing to the variation of the concentration field. After a short initial period, the electrolyte becomes strongly stratified and the motion takes place in boundary layers at the solid boundaries. An approximate model equation for the evolution of the stratification is derived by using perturbation theory. Predictions from the simplified model are found to be in good agreement with numerical solutions of the complete problem. Significant differences compared with earlier studies for linear kinetics, i.e. cases in which the electric current density at the electrodes is constant, are found. Among other things, for large values of the difference ΔV in electric potential between the electrodes, most of the dissolved salt eventually collects near the bottom of the cell. The concentration in the bulk of the electrolyte is, for large values of ΔV, approximately given by a ninth-order polynomial to be compared with a linear behaviour for linear kinetics.
A study of non-parallel and nonlinear effects on the localized receptivity of boundary layers
Authors: Crouch J. D. , Spalart P. R.
Published: April 2006

The acoustic receptivity due to localized surface suction in a two-dimensional boundary layer is studied using a finite-Reynolds-number theory and direct numerical simulation of the Navier-Stokes equations. Detailed comparisons between the two methods are used to determine the bounds for application of the theory. Results show a 4% difference between the methods for receptivity in the neighbourhood of branch I with low suction levels, low acoustic levels, and a moderate frequency; we attribute this difference to non-parallel effects, not included in the theory. The difference is larger for receptivity upstream of branch I, and smaller for receptivity downstream of branch I. As the peak suction level is increased to 1% of the free-stream velocity, the simulations show a nonlinear deviation from the theory. Suction levels as small as 0.1% are shown to have a significant effect on the instability growth between branch I and branch II. Increasing the acoustic amplitude to 1% of the steady free-stream velocity produces no significant nonlinear effect.
Finite-amplitude three-dimensional instability of inviscid laminar boundary layers
Authors: Stern Melvin E.
Published: April 2006

An inviscid laminar boundary layer flow Û(ŷ) with vertical thickness λy, and free stream velocity U is disturbed at time $\tcirc$ = 0 by a normal velocity $\vcirc$ and by a spanwise velocity ŵ([xcirc ],ŷ, $\zcirc$, 0) of finite amplitude αU, with spanwise ($\zcirc$) scale λz, and streamwise ([xcirc ]) scale λx = λz/α; the streamwise velocity û([xcirc ],ŷ,$\zcirc$,$\tcirc$) is initially undisturbed. A long wave λy/λz → 0) expansion of the Euler equations for fixed α and time scale $\tcirc$s = U−1λz/α results in a hyperbolic equation for Lagrangian displacements ŷ. Within the interval $\tcirc$ > $\tcirc$s of asymptotic validity, finite parcel displacements (O(λy)) with finite (O(U)) û fluctuations occur, independent of α no matter how small; the basic flow Û is therefore said to be unstable to streaky (λx [Gt ] λz) spanwise perturbations. The temporal development of the ('spot’) region in the (x,z) plane wherein inflected û profiles appear is computed and qualitatively related to observations of ‘breakdown’ and transition to turbulence in the flow over a flat plate. The maximum $\vcirc$([xcirc ],ŷ,$\zcirc$,$\tcirc$) increases monotonically to infinity as $\tcirc$ → $\tcirc$s.
Non-axisymmetric instability of core–annular flow
Authors: Hu Howard H. , Patankar Neelesh
Published: April 2006

Stability of core-annular flow of water and oil in a vertical circular pipe is studied with respect to non-axisymmetric disturbances. Results show that when the oil core is thin, the flow is most unstable to the asymmetric sinuous mode of disturbance, and the core moves in the form of corkscrew waves as observed in experiments. The asymmetric mode of disturbance is the most dangerous mode for quite a wide range of material and flow parameters. This asymmetric mode persists in vertical pipes with upward and downward flows and in horizontal pipes. The analysis also applies to the instability of freely rising axisymmetric cigarette smoke or a thermal plume. The study predicts a unique wavelength for the asymmetric meandering waves.
The dispersion of chemically active solutes in parallel flow
Authors: Purnama Anton
Published: April 2006

The irreversible loss of chemically active solutes by reactions at the boundary and the reversible adsorption on the flow boundary have been observed experimentally. Removal of solutes at the boundary alone reduces the rate of longitudinal shear dispersion; in contrast, the retention of solutes in the region close to the flow boundary alone increases the rate of longitudinal shear dispersion. Here an extension is given of the method of moments for chemically active solute dispersion to encompass this class of complications. Expressions are derived for the longitudinal shear dispersion coefficient and skewness. The results are applied to the practical example of a chemical flow reactor to quantify the effect of flow boundary retention when there exists reaction at the pipe wall.
Influence of Prandtl number on instability mechanisms and transition in a differentially heated square cavity
Authors: Janssen R. J. A. , Henkes R. A. W. M.
Published: April 2006

The transition from laminar to turbulent of the natural-convection flow inside a square, differentially heated cavity with adiabatic horizontal walls is calculated, using the finite-volume method. The purpose of this study is firstly to determine the dependence of the laminar-turbulent transition on the Prandtl number and secondly to investigate the physical mechanisms responsible for the bifurcations observed. It is found that in the square cavity, for Prandtl numbers between 0.25 and 2.0, the transition occurs through periodic and quasi-periodic flow regimes. One of the bifurcations is related to an instability occurring in a jet-like fluid layer exiting from those corners of the cavity where the vertical boundary layers are turned horizontal. This instability is mainly shear-driven and the visualization of the perturbations shows the occurrence of vorticity concentrations which are very similar to Kelvin–Helmholtz vortices in a plane jet, suggesting that the instability is a Kelvin–Helmholtz-type instability. The other bifurcation for Prandtl numbers between 0.25 and 2.0 occurs in the boundary layers along the vertical walls. It differs however from the related instability in the natural-convection boundary layer along an isolated vertical plate: the instability in the cavity is shear-driven whereas the instability along the vertical plate is mainly buoyancy-driven. For Prandtl numbers between 2.5 and 7.0, it is found that there occurs an immediate transition from the steady to the chaotic flow regime without intermediate regimes. This transition is also caused by instabilities originating and concentrated in the vertical boundary layers.
Multiple equilibria and stable oscillations in thermosolutal convection at small aspect ratio
Authors: Quon Charles , Ghil Michael
Published: April 2006

For thermosolutal convection in an enclosure of arbitrary vertical aspect ratio, mixed boundary conditions – with salt flux and temperature prescribed on a horizontal boundary – can lead to symmetry breaking via pitchfork bifurcation. In the present paper we consider an enclosure of very small height-to-length aspect ratio δ, as encountered in the world's oceans. In this case, if the ratios of the vertical to horizontal components of viscosity, [Pscr ], and of diffusivity, [Lscr ], are of order unity, advective transport cannot set in even at very high Rayleigh numbers. The ratios [Pscr ] and [Lscr ] must be substantially less than unity in order for convection to dominate the heat and solute transport.

We have investigated numerically the effects of monotonic and non-monotonic temperature and salinity boundary conditions in a two-dimensional domain at constant δ = 0.01 and constant [Pscr ] = [Lscr ] = 0.01. This ratio of eddy-mixing coefficients reflects the different scales of motion – vertical and horizontal – in the ocean, rather than a physically realizable laboratory fluid. It is found that when the salt-flux strength, γ, is sufficiently large, the system undergoes a second bifurcation for both types of boundary conditions. It is a Hopf bifurcation, leading from the asymmetric steady states produced by the first one to oscillatory solutions. These periodic solutions are stable and very robust. An approximate Hopf bifurcation diagram has been produced. We conclude that non-monotonic salt-flux conditions are neither necessary nor sufficient to induce the oscillations, while the strength of the salt flux is crucial.
Linear and nonlinear baroclinic instability with rigid sidewalls
Authors: Mundt Michael D. , Brummell Nicholas H. , Hart John E.
Published: April 2006

The behaviour of baroclinic waves growing from instability in a two-layer channel flow with rigid (no-slip) sidewalls is described and contrasted with that for the more traditional free-slip boundary conditions. The linear theory for the onset of small-amplitude disturbances shows that the change in lateral boundary conditions has only a modest effect for typical laboratory parameter values, although the no-slip case is slightly more unstable at very small values of bottom friction. On the other hand, the nonlinear evolution of no-slip modes is completely different. While the free-slip case becomes aperiodic only at large values of the supercriticality (F–Fc)/Fc, the rigid wall case can be subcritically chaotic. Aperiodic, highly nonlinear wave motions are possible for external control values set in the linearly stable region of parameter space. Weakly nonlinear analysis shows that the no-slip case has a negative Landau constant for moderately small values of bottom friction, and it is in this regime that high-resolution numerical simulations exhibit subcritical chaos. At larger values of bottom friction, the rigid-wall simulations undergo a supercritical quasi-periodic transition to chaos at modest, order one, supercriticality, which is substantially smaller than that required for chaos in the free-slip case.
Temporal analysis of capillary jet breakup
Authors: Ashgriz N. , Mashayek F.
Published: April 2006

The temporal instability of a cylindrical capillary jet is analysed numerically for different liquid Reynolds numbers Re, disturbance wavenumbers k, and amplitudes ε0. The breakup mechanism of viscous liquid jets and the formation of satellite drops are described. The results show that the satellite size decreases with decreasing Re, and increasing k and ε0. Marginal Reynolds numbers below which no satellite drops are formed are obtained for a large range of wavenumbers. The growth rates of the disturbances are calculated and compared with those from the linear theory. These results match for low-Re jets, however as Re is increased the results from the linear theory slightly overpredict those from the nonlinear analysis. (At the wavenumber of k = 0.9, the linear theory underpredicts the nonlinear results.) The breakup time is shown to decrease exponentially with increasing the amplitude of the disturbance. The cut-off wavenumber is shown to be strongly dependent on the amplitude of the initial disturbance for amplitudes larger than approximately $\frac13$ of the initial jet radius. The stable oscillations of liquid jets are also investigated. The results indicate that liquid jets with Re ∼ O(1) do not oscillate, and the disturbances are overdamped. However, liquid jets with higher Re oscillate with a period which depends on Re and ε0. The period of the oscillation decreases with increasing Re at small ε0; however, it increases with increasing Re at large ε0. Marginal Reynolds numbers below which the disturbances are overdamped are obtained for a wide range of wavenumbers and ε0 = 0.05.
Turbulent structure in free-surface jet flows
Authors: Walker D. T. , Chen C.-Y. , Willmarth W. W.
Published: April 2006

Results of an experimental study of the interaction of a turbulent jet with a free surface when the jet issues parallel to the free surface are presented. Three different jets, with different exit velocities and jet-exit diameters, all located two jet-exit diameters below the free surface were studied. At this depth the jet flow, in each case, is fully turbulent before significant interaction with the free surface occurs. The effects of the Froude number (Fr) and the Reynolds number (Re) were investigated by varying the jet-exit velocity and jet-exit diameter. Froude-number effects were identified by increasing the Froude number fromFr= 1 to 8 atRe= 12700. Reynolds-number effects were identified by increasing the Reynolds number fromRe= 12700 to 102000 atFr= 1. Qualitative features of the subsurface flow and free-surface disturbances were examined using flow visualization. Measurements of all six Reynolds stresses and the three mean velocity components were obtained in two planes 16 and 32 jet diameters downstream using a three-component laser velocimeter. For all the jets, the interaction of vorticity tangential to the surface with its ‘image’ above the surface contributes to an outward flow near the free surface. This interaction is also shown to be directly related to the observed decrease in the surface-normal velocity fluctuations and the corresponding increase in the tangential velocity fluctuations near the free surface. At high Froude number, the larger surface disturbances diminish the interaction of the tangential vorticity with its image, resulting in a smaller outward flow and less energy transfer from the surface-normal to tangential velocity fluctuations near the surface. Energy is transferred instead to free-surface disturbances (waves) with the result that the turbulence kinetic energy is 20% lower and the Reynolds stresses are reduced. At high Reynolds number, the rate of evolution of the interaction of the jet with the free surface was reduced as shown by comparison of the rate of change with distance downstream of the local Reynolds and Froude numbers. In addition, the decay of tangential vorticity near the surface is slower than for low Reynolds number so that vortex filaments have time to undergo multiple reconnections to the free surface before they eventually decay.
The evolution of the coherent structures in a uniformly distorted plane turbulent wake
Authors: Kopp G. A. , Kawall J. G. , Keffer J. F.
Published: April 2006

A plane turbulent wake generated by a flat plate is subjected to a uniform distortion. It is observed that nearly two-dimensional, quasi-periodic coherent structures dominate the distorted wake. Rapid distortion theory, applied to a kinematic vortex model of the coherent structures in the undistorted far wake, predicts many of the effects revealed by a hot-wire anemometry/pattern-recognition analysis of these structures. Specifically, rapid distortion theory predicts reasonably well the observed changes in the ensemble-averaged velocity patterns and the disproportionate amplification of the large-scale coherent structures relative to the smaller-scale ‘isotropic’ eddies. These results are consistent with the view that self-preservation of the distorted wake is not possible because of the selective amplification of the coherent structures, which control the development of the wake. As well, the entrainment rate in the distorted wake increases at a rate greater than that predicted by the self-preservation theory.
Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers
Authors: Joslin Ronald D.
Published: April 2006

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.
‘Particle stress’ in disperse two-phase potential flow
Authors: Bulthuis H. F. , Prosperetti A. , Sangani A. S.
Published: April 2006

The problem of determining the particle-phase stress in potential flow has been examined recently using two different procedures by Sangani & Didwania (1993a and by Bulthuis (Appendix C of Zhang & Prosperetti 1994). The present study corrects errors in the expression given by Sangani & Didwania, recasts the expression given by Bulthuis in a form suitable for computation, and shows the equivalence of the results obtained by the two methods.
Turbulent mixed-boundary flow in a corner formed by a solid wall and a free surface
Authors: Grega L. M. , Wei T. , Leighton R. I. , Neves J. C.
Published: April 2006

Results from a joint numerical/experimental study of turbulent flow along a corner formed by a vertical wall and a horizontal free surface are presented. The objective of the investigation was to understand transport mechanisms in the corner. Numerical simulations were conducted at NRL to obtain data describing the dynamics of the near corner region. The Reynolds number for the simulations was Reθ ≈ 220. Flow visualization experiments conducted in the Rutgers free surface water tunnel were used to initially identify coherent structures and to determine the effect of these structures on the free surface. Time-resolved streamwise LDA measurements were made for Reθ ≈ 1150. The most significant results were the identification of inner and outer secondary flow regions in the corner. The inner secondary motion is characterized by a weak slowly evolving vortex with negative streamwise vorticity. The outer secondary motion is characterized by an upflow along the wall and outflow away from the wall at the free surface. Additional salient results included observations of surfactant transport away from the surface in cores of vortices connected to the free surface, intermittent energetic transport of fluid to the surface, and attenuation of streak motion by the free surface.
A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves
Authors: Wei Ge , Kirby James T. , Grilli Stephan T. , Subramanya Ravishankar
Published: April 2006

Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlinearity is made, the equations can be applied to simulate strong wave interactions prior to wave breaking. A high-order numerical model based on the equations is developed and applied to the study of two canonical problems: solitary wave shoaling on slopes and undular bore propagation over a horizontal bed. Results of the Boussinesq model with and without strong nonlinearity are compared in detail to those of a boundary element solution of the fully nonlinear potential flow problem developed by Grilli et al. (1989). The fully nonlinear variant of the Boussinesq model is found to predict wave heights, phase speeds and particle kinematics more accurately than the standard approximation.