bluuebunny/crossref_metadata_2025 huggingface dataset:
Trajectories of charged tracer particles around a charged sphere in a simple shear flow
Authors: Dukhin A. S. , Ven T. G. M. Van De
Published: April 2006

The trajectories of electrically charged tracer particles travelling around a charged sphere subjected to a simple shear flow have been calculated. This is a limiting case of the relative trajectories of two unequal-sized spheres when the radius ratio a1/a2 approaches zero. Until now these trajectories have been calculated by assuming the additivity of hydrodynamic and electrostatic forces, while neglecting the electroviscous coupling forces. These electroviscous forces are long range and can significantly alter the relative trajectories of spheres. When a1/a2 → 0, it is found that these trajectories depend on two parameters, α and β, which depend on the surface charge density of the tracer particle and the sphere. The relative trajectories of charged particles are qualitatively different from those of neutral particles. There exist six intervals of α-values for which the trajectories of the tracer particle show different features. Several new types of trajectory appear, besides the open and closed trajectories for neutral particles, which we refer to as uni- and bidirectional infinite length trajectories, uni- and bidirectional finite length trajectories, open returning trajectories, and prolate, oblate and circular closed trajectories. This richness of possible trajectories is the result of three electrokinetic phenomena, affecting particle motion: electro-osmotic slip, electrophoretic and diffusiophoretic motion.
Stokes flow through periodic orifices in a channel
Authors: Zeng Y. , Weinbaum S.
Published: April 2006

This paper develops a three-dimensional infinite series solution for the Stokes flow through a parallel walled channel which is obstructed by a thin planar barrier with periodically spaced rectangular orifices of arbitrary aspect ratioB’/d’ and spacingD’. HereB’ is the half-height of the channel andd’ is the half-width of the orifice. The problem is motivated by recent electron microscopic studies of the intercellular channel between vascular endothelial cells which show a thin junction strand barrier with discontinuities or breaks whose spacing and width vary with the tissue. The solution for this flow is constructed as a superposition of Hasimoto's (1958) general solution for the two-dimensional flow through a periodic slit array in an infinite plane wall and a new three-dimensional solution which corrects for the top and bottom boundaries. In contrast to the well-known solutions of Sampson (1891) and Hasimoto (1958) for the flow through zero-thickness orifices of circular or elliptic cross-section or periodic slits in an infinite plane wall, which exhibit characteristic viscous velocity profiles, the present bounded solutions undergo a fascinating change in behaviour as the aspect ratioB’/d’ of the orifice opening is increased. ForB’/d’ [Lt ] 1 and (D’ –-d’)/B’ ofO(1) or greater, which represents a narrow channel, the velocity has a minimum at the orifice centreline, rises sharply near the orifice edges and then experiences a boundary-layer-like correction over a thickness ofO(B’) to satisfy no-slip conditions. ForB’/d’ ofO(1) the profiles are similar to those in a rectangular duct with a maximum on the centreline, whereas forB’/d’ [Gt ] 1, which describes widely separated channel walls, the solution approaches Hasimoto's solution for the periodic infinite-slit array. In the limit (D’ –-d’)/B’ [Lt ] 1, where the width of the intervening barriers is small compared with the channel height, the solutions exhibit the same behaviour as Lee & Fung's (1969) solution for the flow past a single cylinder. The drag on the zero-thickness barriers in this case is nearly the same as for the cylinder for all aspect ratios.
Flows generated by the periodic horizontal oscillations of a sphere in a linearly stratified fluid
Authors: Lin Qiang , Boyer D. L. , Fernando H. J. S.
Published: April 2006

The flow field induced by a sphere oscillating horizontally in a linearly stratified fluid is studied using a series of laboratory experiments. The resulting flows are shown to depend on the Stokes number β, the Keulegan–Carpenter number KC and the internal Froude number Fr. For Fr [clubs ] 0.2, it is shown that the nature of the resulting flow field is approximately independent of Fr and, based on this observation, a flow regime diagram is developed in the (β, KC)-plane. The flow regimes include: (i) fully-attached flow; (ii) attached vortices; (iii) local vortex shedding; and (iv) standing eddy pair. An internal-wave flow regime is also identified but, for such flows, the motion field is a function of Fr as well. Some quantitative measures are given to allow for future comparisons of the present results with analytical and/or numerical models. Wherever possible, the results are compared with the experiments of Tatsuno & Bearman (1990) on right circular cylinders oscillating in homogeneous fluids.
Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface
Authors: Brouillette M. , Sturtevant B.
Published: April 2006

We report on experiments to measure the shock-induced growth of sinusoidal perturbations on thick interfaces separating two gases of different densities. The results show that the growth rates are reduced as the interface thickness is increased. A model that accounts for the growth rate reduction caused by the presence of a finite density gradient on the interface is proposed and good agreement is obtained with the experimental results.
Entropy maximization tendency in topographic turbulence
Authors: Zou Jieping , Holloway Greg
Published: April 2006

Numerical simulations of geostrophic turbulence above topography are used to compare (a) nonlinear generation of system entropy, S, (b) selective damping of enstrophy and (c) development of vorticity–topography correlation. In the damped cases, S initially increases, approaching a quasi-equilibrium (maximum S subject to the instantaneous, though decaying, energy and enstrophy). When strongly scale-selective damping is applied, onset of the vorticity–topography correlation follows the timescales for enstrophy decay. During the period of decay, it is shown that nonlinear interaction continues to generate S, offsetting in part the loss of S to explicit damping.
Curved two-stream turbulent mixing layers: three-dimensional structure and streamwise evolution
Authors: Plesniak Michael W. , Mehta Rabindra D. , Johnston James P.
Published: April 2006

The three-dimensional structure and streamwise evolution of two-stream mixing layers at high Reynolds numbers (Reδ ∼ 2.7 × 104) were studied experimentally to determine the effects of mild streamwise curvature ($\delta/ \overline{R}$ < 3%). Mixing layers with velocity ratios of 0.6 and both laminar and turbulent initial boundary layers, were subjected to stabilizing and destabilizing longitudinal curvature (in the Taylor–Görtler sense). The mixing layer is affected by the angular momentum instability when the low-speed stream is on the outside of the curve, and it is stabilized when the streams are reversed so that the high-speed stream is on the outside. In both stable and unstable mixing layers, originating from laminar boundary layers, well-organized spatially stationary streamwise vorticity was generated, which produced significant spanwise variations in the mean velocity and Reynolds stress distributions. These vortical structures appear to result from the amplification of small incoming disturbances (as in the straight mixing layer), rather than through the Taylor–Görtler instability. Although the mean streamwise vorticity decayed with downstream distance in both cases, the rate of decay for the unstable case was lower. With the initial boundary layers on the splitter plate turbulent, spatially stationary streamwise vorticity was not generated in either the stable or unstable mixing layer. Linear growth was achieved for both initial conditions, but the rate of growth for the unstable case was higher than that of the stable case. Correspondingly, the far-field spanwise-averaged peak Reynolds stresses were significantly higher for the destabilized cases than for the stabilized cases, which exhibited levels comparable to, or slightly lower than, those for the straight case. A part of the Reynolds stress increase in the unstable layer is attributed to ‘extra’ production through terms in the transport equations which are activated by the angular momentum instability. Velocity spectra also indicated significant differences in the turbulence structure of the two cases, both in the near- and far-field regions.
Converging three-dimensional Stokes flow of two fluids in a T-type bifurcation
Authors: Ong Joseph , Enden Giora , Popel Aleksander S.
Published: April 2006

Studies of three-dimensional Stokes flow of two Newtonian fluids that converge in a T-type bifurcation have important applications in polymer coextrusion, blood flow through the venous microcirculation, and other problems of science and technology. This flow problem is simulated numerically by means of the finite element method, and the solution demonstrates that the viscosity ratio between the two fluids critically affects flow behaviour. For the parameters investigated, we find that as the viscosity ratio between the side branch and the main branch increases, the interface between the merging fluids bulges away from the side branch. The viscosity ratio also affects the velocity distribution: at the outlet branch, the largest radial gradients of axial velocity appear in the less-viscous fluid. The distribution of wall shear stress is non-axisymmetric in the outlet branch and may be discontinuous at the interface between the fluids.
Flow due to an oscillating sphere and an expression for unsteady drag on the sphere at finite Reynolds number
Authors: Mei Renwei
Published: April 2006

Unsteady flow due to an oscillating sphere with a velocity U0cosωt’, in which U0 and ω are the amplitude and frequency of the oscillation and t’ is time, is investigated at finite Reynolds number. The methods used are: (i) Fourier mode expansion in the frequency domain; (ii) a time-dependent finite difference technique in the time domain; and (iii) a matched asymptotic expansion for high-frequency oscillation. The flow fields of the steady streaming component, the second and third harmonic components are obtained with the fundamental component. The dependence of the unsteady drag on ω is examined at small and finite Reynolds numbers. For large Stokes number, ε = (ωa2/2v)½ [Gt ] 1, in which a is the radius of the sphere and v is the kinematic viscosity, the numerical result for the unsteady drag agrees well with the high-frequency asymptotic solution; and the Stokes (1851) solution is valid for finite Re at ε [Gt ] 1. For small Strouhal number, St = ωa/U0 [Lt ] 1, the imaginary component of the unsteady drag (Scaled by 6πU0pfva, in which Pf is the fluid density) behaves as Dml ∼ (h0Stlog St–h1St), m = 1,3,5… This is in direct contrast to an earlier result obtained for an unsteady flow over a stationary sphere with a small-amplitude oscillation in the free-stream velocity (hereinafter referred to as the SA case) in which D1∼ –h1St (Mei, Lawrence & Adrian 1991). Computations for flow over a sphere with a free-stream velocity U0(1–α1+α1cosωt’) at Re = U02a/v = 0.2 and St [Lt ] 1 show that h0 for the first mode varies from 0 (at α1 = 0) to around 0.5 (at α1 = 1) and that the SA case is a degenerated case in which the logarithmic dependence of the drag in St is suppressed by the strong mean uniform flow.

The numerical results for the unsteady drag are used to examine an approximate particle dynamic equation proposed for spherical particles with finite Reynolds number. The equation includes a quasi-steady drag, an added-mass force, and a modified history force. The approximate expression for the history force in the time domain compares very well with the numerical results of the SA case for all frequencies; it compares favourably for the PO case for moderate and high frequencies; it underestimates slightly the history force for the PO case at low frequency. For a solid sphere settling in a stagnant liquid with zero initial velocity, the velocity history is computed using the proposed particle dynamic equation. The results compare very well with experimental data of Moorman (1955) over a large range of Reynolds numbers. The present particle dynamic equation at finite Re performs consistently better than that proposed by Odar & Hamilton (1964) both qualitatively and quantitatively for three different types of spatially uniform unsteady flows.
Bounds for threshold amplitudes in subcritical shear flows
Authors: Kreiss Gunilla , Lundbladh Anders , Henningson Dan S.
Published: April 2006

A general theory which can be used to derive bounds on solutions to the Navier-Stokes equations is presented. The behaviour of the resolvent of the linear operator in the unstable half-plane is used to bound the energy growth of the full nonlinear problem. Plane Couette flow is used as an example. The norm of the resolvent in plane Couette flow in the unstable half-plane is proportional to the square of the Reynolds number (R). This is now used to predict the asymptotic behaviour of the threshold amplitude below which all disturbances eventually decay. A lower bound is found to be R−21/4. Examples, obained through direct numerical simulation, give an upper bound on the threshold curve, and predict a threshold of R−1. The discrepancy is discussed in the light of a model problem.
The non-Gaussian statistics of the velocity field in low-resolution large-eddy simulations of homogeneous turbulence
Authors: Briscolini Marco , Santangelo Paolo
Published: April 2006

A low-resolution (643) large-eddy model of forced homogeneous turbulence is numerically simulated using Kraichnan's eddy viscosity. The introduction of a reliable statistical estimate of the ζp exponents allows one to perform a detailed statistical analysis of the velocity field and shows that the probability distribution functions, the structure functions and the power-law exponents ζp agree with previous numerical and experimental results obtained at much higher effective resolution. This result shows how a simple modelling of the energy transfer produces self-similar dynamics extending to the small scales and obtains the right statistical properties of the velocity field.
Advection of a passive scalar by a vortex couple in the small-diffusion limit
Authors: Lingevitch Joseph F. , Bernoff Andrew J.
Published: April 2006

We study the advection of a passive scalar by a vortex couple in the small-diffusion (i.e. large Péclet number, Pe) limit. The presence of weak diffusion enhances mixing within the couple and allows the gradual escape of the scalar from the couple into the surrounding flow. An averaging technique is applied to obtain an averaged diffusion equation for the concentration inside the dipole which agrees with earlier results of Rhines & Young for large times. At the outer edge of the dipole, a diffusive boundary layer of width O(Pe−½) forms; asymptotic matching to the interior of the dipole yields effective boundary conditions for the averaged diffusion equation. The analysis predicts that first the scalar is homogenized along the streamlines on a timescale O(Pe−$\frac{1}{3}$). The scalar then diffuses across the streamlines on the diffusive timescale, O(Pe). Scalar that diffuses into the boundary layer is swept to the rear stagnation point, and a finite proportion is expelled into the exterior flow. Expulsion occurs on the diffusive timescale at a rate governed by the lowest eigenvalue of the averaged diffusion equation for large times. A split-step particle method is developed and used to verify the asymptotic results. Finally, some speculations are made on the viscous decay of the dipole in which the vorticity plays a role analogous to the passive scalar.
Secondary and tertiary excitation of three-dimensional patterns on a falling film
Authors: Chang H.-C. , Cheng M. , Demekhin E. A. , Kopelevich D. I.
Published: April 2006

The primary instability of a falling film selectively amplifies two-dimensional noise down-stream over three-dimensional modes with transverse variation. If the initial three-dimensional noise is weak or if it has short wavelengths such that they are effectively damped by the capillary mechanism of the primary instability, our earlier study (Chang et al. 1993a) showed that the primary instability leads to a weakly nonlinear, nearly sinusoidal γ1 stationary wave which then undergoes a secondary transition to a strongly nonlinear γ2 wave with a solitary wave structure. We show here that the primary transition remains in the presence of significant three-dimensional noise but the secondary transition can be replaced by a selective excitation of oblique triad waves which can even include stable primary disturbances. The resulting secondary checkerboard pattern is associated with a subharmonic mode in the streamwise direction. If the initial transverse noise level is low, a secondary transition to a two-dimensional γ2 solitary wave is followed by a tertiary ‘phase instability’ dominated by transverse wave crest modulations.
The solidification of buoyancy-driven flow in a flexible-walled channel. Part 1. Constant-volume release
Authors: Lister John R.
Published: April 2006

The solidification of hot fluid flowing in a thin buoyancy-driven layer between cold solid boundaries is analysed in a series of two papers. As an approximation to flow in a crack in a weakly elastic solid or to free-surface flow beneath a thin solidified crust, the boundaries are considered to be flexible and to exert negligible resistance to lateral deformation. The resultant equations of continuity and motion reduce to a kinematic-wave equation with a loss term corresponding to the accumulation of solidified material at the boundaries. The Stefan problem for the solidification is coupled back to the flow through the advection of heat by the fluid, which competes with lateral heat loss by conduction to the solid. Heat and mass conservation are used to derive boundary conditions at the propagating nose of the flow. In this paper the two-dimensional flow produced by a line release of a given volume of fluid is investigated. It is shown that at short times the flow solidifies completely only near the point of release where the flow is thinnest, at later times complete solidification also occurs near the nose of the flow where the cooling rates are greatest and, eventually, the flow is completely solidified along its depth. Some transient melting of the boundaries can also occur if the fluid is initially above its solidification temperature. The dimensionless equations are parameterized only in terms of a Stefan number S and a dimensionless solidification temperature Θ. Asymptotic solutions for the flow at short times and near the source are derived by perturbation series and similarity arguments. The general evolution of the flow is calculated numerically, and the scaled time to final solidification, the length and the thickness of the solidified product are determined as functions of S and Θ. The theoretical solutions provide simple models of the release of a pulse of magma into a fissure in the Earth's lithosphere or of lava flow on the flanks of a volcano after a brief eruption. Other geological events are better modelled as flows fed by a continual supply of hot fluid. The solidification of such flows will be investigated in Part 2.
Steady, viscous, free-surface flow on a rotating cylinder
Authors: Hansen Erik B. , Kelmanson Mark A.
Published: April 2006

The commonly observed phenomenon of steady, viscous, free-surface flow on the outer surface of a rotating cylinder is investigated by means of an iterative, integral-equation formulation applied to the Stokes approximation of the Navier-Stokes equations. The method of solution places no restriction on the thickness of the fluid layer residing on the cylinder surface; indeed, results are presented for cases where the layer thickness is of the same order of magnitude as the cylinder radius.

Free-surface profiles and free-surface velocity distributions are presented for a range of flow parameters. Where appropriate, comparisons are made with the results of thinfilm theory; excellent agreement is observed.

For all film thicknesses and surface tensions, results show a high degree of symmetry about a horizontal axis even though the gravity field is vertical. A proof is presented that, for vanishing surface tension, this is a consequence of the Stokes approximation.
Different forms for nonlinear standing waves in deep water
Authors: Bryant Peter J. , Stiassnie Michael
Published: April 2006

Multiple forms for standing waves in deep water periodic in both space and time are obtained analytically as solutions of Zakharov's equation and its modification, and investigated computationally as irrotational two-dimensional solutions of the full nonlinear boundary value problem. The different forms are based on weak nonlinear interactions between the fundamental harmonic and the resonating harmonics of 2, 3,…times the frequency and 4, 9,…respectively times the wavenumber. The new forms of standing waves have amplitudes with local maxima at the resonating harmonics, unlike the classical (Stokes) standing wave which is dominated by the fundamental harmonic. The stability of the new standing waves is investigated for small to moderate wave energies by numerical computation of their evolution, starting from the standing wave solution whose only initial disturbance is the numerical error. The instability of the Stokes standing wave to sideband disturbances is demonstrated first, by showing the evolution into cyclic recurrence that occurs when a set of nine equal Stokes standing waves is perturbed by a standing wave of a length equal to the total length of the nine waves. The cyclic recurrence is similar to that observed in the well-known linear instability and sideband modulation of Stokes progressive waves, and is also similar to that resulting from the evolution of the new standing waves in which the first and ninth harmonics are dominant. The new standing waves are only marginally unstable at small to moderate wave energies, with harmonics which remain near their initial amplitudes and phases for typically 100–1000 wave periods before evolving into slowly modulated oscillations or diverging.
Three-dimensional wave instability near a critical level
Authors: Winters K. B. , D’Asaro E. A.
Published: April 2006

The behaviour of internal gravity wave packets approaching a critical level is investigated through numerical simulation. Initial-value problems are formulated for both small- and large-amplitude wave packets. Wave propagation and the early stages of interaction with the mean shear are two-dimensional and result in the trapping of wave energy near a critical level. The subsequent dynamics of wave instability, however, are fundamentally different for two- and three-dimensional calculations. Three-dimensionality develops by transverse convective instability of the two-dimensional wave. The initialy two-dimensional flow eventually collapses into quasi-horizontal vortical structures. A detailed energy balance is presented. Of the initial wave energy, roughly one third reflects, one third results in mean flow acceleration and the remainder cascades to small scales where it is dissipated. The detailed budget depends on the wave amplitude, the amount of wave reflection being particularly sensitive.
Effects of convex transverse curvature on wall-bounded turbulence. Part 2. The pressure fluctuations
Authors: Neves João C. , Moin Parviz
Published: April 2006

The effects of convex transverse curvature on the wall pressure fluctuations were studied through direct numerical simulations. The flow regime of interest is characterized by large ratio of the shear-layer thickness to the radius of curvature (γ = δ/a) and by small a+, the radius of curvature in wall units. Two direct numerical simulations of a model problem approximating axial flow boundary layers on long cylinders were performed for γ = 5 (a+ ≈ 43) and γ = 11 (a+ ≈ 21). The space-time characteristics of the wall pressure fluctuations of the plane channel flow simulation of Kim, Moin & Moser (1987), which were studied by Choi & Moin (1990) are used to assess the effects of curvature.

As the curvature increases the root-mean-square (r.m.s.) pressure fluctuations decrease and the ratio of the streamwise to spanwise lengthscales of the wall pressure fluctuations increases. Fractional contributions from various layers in the flow to the wall r.m.s. pressure fluctuations are marginally affected by the curvature. Curvature-dependent timescales and lengthscales are identified that collapse the high-frequency range of the wall pressure temporal spectra and the high wave-number range of the wall pressure streamwise spectra of flows with different curvatures. Taylor's hypothesis holds for the wall pressure fluctuations with a lower convection velocity than in the planar case.
Surface quasi-geostrophic dynamics
Authors: Held Isaac M. , Pierrehumbert Raymond T. , Garner Stephen T. , Swanson Kyle L.
Published: April 2006

The dynamics of quasi-geostrophic flow with uniform potential vorticity reduces to the evolution of buoyancy, or potential temperature, on horizontal boundaries. There is a formal resemblance to two-dimensional flow, with surface temperature playing the role of vorticity, but a different relationship between the flow and the advected scalar creates several distinctive features. A series of examples are described which highlight some of these features: the evolution of an elliptical vortex; the start-up vortex shed by flow over a mountain; the instability of temperature filaments; the ‘edge wave’ critical layer; and mixing in an overturning edge wave. Characteristics of the direct cascade of the tracer variance to small scales in homogeneous turbulence, as well as the inverse energy cascade, are also described. In addition to its geophysical relevance, the ubiquitous generation of secondary instabilities and the possibility of finite-time collapse make this system a potentially important, numerically tractable, testbed for turbulence theories.
Two-dimensional flows with zero net momentum: evolution of vortex quadrupoles and oscillating-grid turbulence
Authors: Voropayev S. I. , Afanasyev Y. D. , van Heijst G. J. F.
Published: April 2006

The planar flow arising in an initially quiescent viscous fluid under the action of a localized dipolar-type forcing has been studied analytically and experimentally. The force dipole, with non-dimensional forcing amplitude Re, brings net zero momentum into the fluid and gives rise to the formation of a quadrupolar vortex: a system of two dipolar vortices moving apart. Experimentally, the action of a force dipole was modelled by a vertical cylinder oscillating horizontally in the shallow upper layer of a two-layer fluid. Two cases were studied: single quadrupoles and an array of quadrupoles. It is found that single quadrupoles develop in a self-similar manner: the length L and the translation velocity Ū of the quadrupolar vortex change with time as L ∼ t1/2 and Ū ∼ t-1/2. These quantities are characterized by non-dimensional functions α(Re) and β(Re), respectively, which have been determined theoretically for small Re-values and experimentally for Re-values in the range 160–2200.

To produce an array of quadrupoles an array of oscillating vertical rods was used. Two stages in the flow evolution were studied experimentally: the initial stage, when the interactions between the quadrupoles are weak, and the intermediate stage when the interactions play an essential role and the flow is (two-dimensionally) turbulent. It is found that at both stages the width H of the region with intense vortical motions increases with time as H ∼ t1/2. A theoretical explanation of the experimental results is given.
The viscous flow of charged particles through a charged cylindrical tube
Authors: Venema Paul
Published: April 2006

An analysis is given for the electro-kinetic transport properties in a system consisting of a line of identical spheres placed equidistantly with their centres on the axis of a cylindrical tube containing a viscous fluid. Both the spheres and the wall of the tube are charged and a two-species symmetrical electrolyte with valence Z is present in the system. As a result of the charges on the surface of the spheres and on the surface of the tube electrical double layers will develop. When an electrical field is applied to the system an electrokinetic motion is induced. We will use the thin double layer theory (Dukhin & Derjaguin 1974; O'Brien 1983), valid for sufficiently high electrolyte concentration and where the polarization of the electrical double layer is included. Using a multipole expansion an infinite set of linear equations for the multipoles will be derived from which the electro-kinetic transport coefficients may be determined. These coefficients depend on the system parameters, such as the radius of the tube R, the radius of the sphere a, the separation between the spheres d, the Debije radius κ-1, the zeta-potentials of the spheres ζp and of the wall of the tube ζw and the valency Z of the electrolyte. From these coefficients a relation is found between the pressure drop Δp per unit length and the drag force D on the spheres on one side and with the velocity U of the spheres, the total discharge Q and the applied electrical field E0 on the other side. For some values for the system parameters we have numerically solved the infinite set of linear equations by truncation and calculated the transport coefficients. We have also calculated the streamlines for some situations. The plots of these streamlines show that depending on the conditions on the system vortices may appear.
Effect of polymer additives on Görtler vortices in Taylor—Couette flow
Authors: Lee S. H.-K. , Sengupta S. , Wei T.
Published: April 2006

Taylor—Couette flow is ideal for studying drag-reducing polymer additives because, unlike turbulent boundary layers, the instabilities are better understood. Video records of laser-induced fluorescence experiments with and without polymers will be presented. Polyethylene-oxide (PEO) ‘oceans’ were used in concentrations of 20 and 100 p.p.m. In the Taylor number range, 3 × 104 ≤ Ta ≤ 108, Newtonian flow consisted of Taylor vortices which span the gap between cylinders and much smaller Görtler vortices at the inner cylinder wall. Measurements of core-to-core separation between counter-rotating vortices were made to estimate the Görtler instability wavenumber. These measurements show that PEO addition increases the Görtler wavenumber for a given Taylor number. At the lower Taylor numbers, Görtler vortex formation was suppressed by PEO. This implies that polymers directly affect the evolution of centrifugal instabilities.
On the 3-D inverse potential target pressure problem. Part 2. Numerical aspects and application to duct design
Authors: Dedoussis V. , Chaviaropoulos P. , Papailiou K. D.
Published: April 2006

A potential function/stream function formulation is introduced for the solution of the fully 3-D inverse potential ‘target pressure’ problem. In the companion paper (Part 1) it is seen that the general 3-D inverse problem is ill-posed but accepts as a particular solution elementary streamtubes with orthogonal cross-section. Under this simplification, a novel set of flow equations was derived and discussed. The purpose of the present paper is to present the computational techniques used for the numerical integration of the flow and geometry equations proposed in Part 1. The governing flow equations are discretized with centred finite difference schemes on a staggered grid and solved in their linearized form using the preconditioned GMRES algorithm. The geometry equations which form a set of first-order o.d.e.s are integrated numerically using a second-order-accurate space marching scheme. The resulting computational algorithm is applied to a double turning duct and a 3-D converging-diverging nozzle ‘reproduction’ test case.
Inviscid instability of streamwise corner flow
Authors: Balachandar S. , Malik M. R.
Published: April 2006

Linear stability of the incompressible flow along a streamwise corner is studied by solving the two-dimensional eigenvalue problem governed by partial differential equations. It is found that this fully three-dimensional flow is subject to inviscid instability due to the inflectional nature of the streamwise velocity profile. The higher growth rates for the inviscid instability mode, which is symmetric about the corner bisector, as compared to the viscous Tollmien-Schlichting instability operative away from the corner, is consistent with the experimental findings that the corner flow transitions to turbulence earlier than the two-dimensional Blasius flow away from the corner.
Harbour oscillations generated by shear flow
Authors: Fabrikant A. L.
Published: April 2006

A new mechanism that could be responsible for excitation of long-period oscillations in partially enclosed harbours is discussed. This mechanism is based on the interaction between a shear flow and the harbour-basin natural mode and does not suppose any external exciting forces caused by wind waves, tsunami, etc. The growth rate of harbour oscillations is found in terms of a plane-wave reflection coefficient integrated on the wavenumber spectrum of the oscillating outflow field near the harbour entrance. Analytical considerations for simple shear flows (vortex sheet and jet) show that the growth rate changes its sign depending on the ratio of oscillation frequency to flow speed.
Axial drop motion in rotating fluids
Authors: Bush J. W. M. , Stone H. A. , Bloxham J.
Published: April 2006

A theoretical and experimental investigation of drop motion in rotating fluids is presented. The theory describing the vertical on-axis translation of an axisymmetric rigid body through a rapidly rotating low-viscosity fluid is extended to the case of a buoyant deformable fluid drop of arbitrary viscosity. In the case that inertial and viscous effects are negligible within the bulk external flow, motions are constrained to be two-dimensional in compliance with the Taylor–Proudman theorem, and the rising drop is circumscribed by a Taylor column. Calculations for the drop shape and rise speed decouple, so that theoretical predictions for both are obtained analytically. Drop shapes are set by a balance between centrifugal and interfacial tension forces, and correspond to the family of prolate ellipsoids which would arise in the absence of drop translation. In the case of a drop rising through an unbounded fluid, the Taylor column is dissipated at a distance determined by the outer fluid viscosity, and the rise speed corresponds to that of an identically shaped rigid body. In the case of a drop rising through a sufficiently shallow plane layer of fluid, the Taylor column extends to the boundaries. In such bounded systems, the rise speed depends further on the fluid and drop viscosities, which together prescribe the efficiency of the Ekman transport over the drop and container surfaces.

A set of complementary experiments is also presented, which illustrate the effects of drop viscosity on steady drop motion in bounded rotating systems. The experimental results provide qualitative agreement with the theoretical predictions; in particular, the poloidal circulation observed inside low-viscosity drops is consistent with the presence of a double Ekman layer at the interface, and is opposite to that expected to arise in non-rotating systems. The steady rise speeds observed are larger than those predicted theoretically owing to the persistence of finite inertial effects.
Nonlinear evolution of a pair of oblique instability waves in a supersonic boundary layer
Authors: Leib S. J. , Lee Sang Soo
Published: April 2006

We study the nonlinear evolution of a pair of oblique instability waves in a supersonic boundary layer over a flat plate in the nonlinear non-equilibrium viscous critical layer regime. The instability wave amplitude is governed by the same integro-differential equation as that derived by Goldstein & Choi (1989) in the inviscid limit and by Wu, Lee & Cowley (1993) with viscous effects included, but the coefficient appearing in this equation depends on the mean flow and linear neutral stability solution of the supersonic boundary layer. This coefficient is evaluated numerically for the Mach number range over which the (inviscid) first mode is the dominant instability. Numerical solutions to the amplitude equation using these values of the coefficient are obtained. It is found that, for insulated and cooled wall conditions and angles corresponding to the most rapidly growing waves, the amplitude ends in a singularity at a finite downstream position over the entire Mach number range regardless of the size of the viscous parameter. The explosive growth of the instability waves provides a mechanism by which the boundary layer can break down. A new feature of the compressible problem is the nonlinear generation of a spanwise-dependent mean distortion of the temperature along with that of the velocity found in the incompressible case.
Upstream influence and the form of standing hydraulic jumps in liquid-layer flows on favourable slopes
Authors: Bowles Robert I.
Published: April 2006

Steady planar flow of a liquid layer over an obstacle is studied for favourable slopes. First, half-plane Poiseuille flow is found to be a non-unique solution on a uniformly sloping surface since eigensolutions exist which are initially exponentially small far upstream. These have their origin in a viscous–inviscid interaction between the retarding action of viscosity and the hydrostatic pressure from the free surface. The cross-stream pressure gradient caused by the curvature of the streamlines also comes into play as the slope increases. As the interaction becomes nonlinear, separation of the liquid layer can occur, of a breakaway type if the slope is sufficiently large. The breakaway represents a hydraulic jump in the sense of a localized relatively short-scaled increase in layer thickness, e.g. far upstream of a large obstacle. The solution properties give predictions for the shape and structure of hydraulic jumps on various slopes. Secondly, the possibility of standing waves downstream of the jump is addressed for various slope magnitudes. A limiting case of small gradient, governed by lubrication theory, allows the downstream boundary condition to be included explicitly. Numerical solutions showing the free-surface flow over an obstacle confirm the analytical conclusions. In addition the predictions are compared with the experimental and computational results of Pritchardet al.(1992), yielding good qualitative and quantitative agreement. The effects of surface tension on the jump are also discussed and in particular the free interaction on small slopes is examined for large Bond numbers.
Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow
Authors: Magnaudet Jacques , Rivero Mayela , Fabre Jean
Published: April 2006

This work reports the first part of a series of numerical simulations carried out in order to improve knowledge of the forces acting on a sphere embedded in accelerated flows at finite Reynolds number, Re. Among these forces added mass and history effects are particularly important in order to determine accurately particle and bubble trajectories in real flows. To compute these hydrodynamic forces and more generally to study spatially or temporally accelerated flows around a sphere, the full Navier–Stokes equations expressed in velocity–pressure variables are solved by using a finite-volume approach. Computations are carried out over the range 0.1 ≤ Re ≤ 300 for flows around both a rigid sphere and an inviscid spherical bubble, and a systematic comparison of the flows around these two kinds of bodies is presented.

Steady uniform flow is first considered in order to test the accuracy of the simulations and to serve as a reference case for comparing with accelerated situations. Axisymmetric straining flow which constitutes the simplest spatially accelerated flow in which a sphere can be embedded is then studied. It is shown that owing to the viscous boundary condition on the body as well as to vorticity transport properties, the presence of the strain modifies deeply the distribution of vorticity around the sphere. This modification has spectacular consequences in the case of a rigid sphere because it influences strongly the conditions under which separation occurs as well as the characteristics of the separated region. Another very original feature of the axisymmetric straining flow lies in the vortex-stretching mechanism existing in this situation. In a converging flow this mechanism acts to reduce vorticity in the wake of the sphere. In contrast when the flow is divergent, vorticity produced at the surface of the sphere tends to grow indefinitely as it is transported downstream. It is shown that in the case where such a diverging flow extends to infinity a Kelvin–Helmholtz instability may occur in the wake.

Computations of the hydrodynamic force show that the effects of the strain increase rapidly with the Reynolds number. At high Reynolds numbers the total drag is dramatically modified and the evaluation of the pressure contribution shows that the sphere undergoes an added mass force whose coefficient remains the same as in inviscid flow or in creeping flow, i.e. CM = ½, whatever the Reynolds number. Changes found in vorticity distribution around the rigid sphere also affect the viscous drag, which is markedly increased (resp. decreased) in converging (resp. diverging) flows at high Reynolds numbers.
Large-scale structure and entrainment in the supersonic mixing layer
Authors: Clemens N. T. , Mungal M. G.
Published: April 2006

Experiments were conducted in a two-stream planar mixing layer at convective Mach numbers,Mc, of 0.28, 0.42, 0.50, 0.62 and 0.79. Planar laser Mie scattering (PLMS) from a condensed alcohol fog and planar laser-induced fluorescence (PLIF) of nitric oxide were used for flow visualization in the side, plan and end views. The PLIF signals were also used to characterize the turbulent mixture fraction fluctuations.

Visualizations using PLMS indicate a transition in the turbulent structure from quasi-two-dimensionality at low convective Mach number, to more random three-dimensionality for$M_c\geqslant 0.62$. A transition is also observed in the core and braid regions of the spanwise rollers as the convective Mach number increases from 0.28 to 0.62. A change in the entrainment mechanism with increasing compressibility is also indicated by signal intensity profiles and perspective views of the PLMS and PLIF images. These show that atMc= 0.28 the instantaneous mixture fraction field typically exhibits a gradient in the streamwise direction, but is more uniform in the cross-stream direction. AtMc= 0.62 and 0.79, however, the mixture fraction field is more streamwise uniform and with a gradient in the cross-stream direction. This change in the composition of the structures is indicative of different entrainment motions at the different compressibility conditions. The statistical results are consistent with the qualitative observations and suggest that compressibility acts to reduce the magnitude of the mixture fraction fluctuations, particularly on the high-speed edge of the layer.
A note on bluff body vortex formation
Authors: Griffin Owen M.
Published: April 2006

Green & Gerrard (1993) have presented in a recent paper the results of experiments to measure the distribution of vorticity in the near wake of a circular cylinder at low Reynolds numbers (up to Re = 220). They also compared the various definitions of the vortex formation region length which have been proposed by Gerrard (1966), Griffin (1974), and others for both high and low Reynolds numbers. The purpose of this note is to expand the work of Green & Gerrard, and to further their proposition that the end of the vortex formation region at all Reynolds numbers mark both the initial position of the fully shed vortex and the location at which its strength is a maximum. The agreement discussed here between several definitions for the formation region length will allow further understanding to be gained from investigations of the vortex wakes of stationary bluff bodies, and the wakes of oscillating bodies as well.
Bifurcations and nonlinear dynamics of surface waves in Faraday resonance
Authors: Friedel H. , Laedke E. W. , Spatschek K. H.
Published: April 2006

The nonlinear dynamics of nonlinear modulated cross-waves of resonant frequency ω1 and carrier frequency ω ≈ ω1 is investigated. In a long channel of width b, that contains fluid of depth d and which is subjected to a vertical oscillation of frequency 2ω, the wave can appear in solitary form. As has been shown previously, the solitary wave is only stable in a certain parameter regime; depending on damping and driving amplitudes the wave becomes unstable. The nonlinear development of the instabilities of solitary waves is the central problem of this paper. It is shown how instabilities are saturated following generic routes to chaos in time with spatially coherent structures. Finally, the case of time-modulated driving amplitudes is also considered. In most cases it appears that nonlinear waves of simple spatial structures take part in the nonlinear dynamics, but a few cases of spatial chaos are also reported.
Turbulence evolution and mixing in a two-layer stably stratified
fluid
Authors: Huq Pablo , Britter Rex E.
Published: April 2006

The results of an experimental study of shear-free decaying
grid-generated turbulence on both sides of a sharp interface between two
homogeneous layers of different densities are presented. The evolution of
turbulence and mixing were examined by simultaneously mapping the velocity
(u, w) and density fields (ρ) and the
vertical mass flux $F(=\overline{\rho
w}/\rho\prime w\prime)$ together with flow
visualization in a low-noise water tunnel. Buoyancy was induced by salinity
differences so the value of the Schmidt number
Sc
= 700. Density stratification altered the inertial-buoyancy force balance
(most simply expressed by Nt, the product of the
buoyancy frequency N and turbulent timescale
t) so as to attenuate turbulent velocity
fluctuations, vertical motions and interfacial convolutions, normalized
density fluctuations, vertical flux mass, and mean interfacial thickness.
Vertical velocity fluctuations w′ were found to
increase with distance from the interface, whereas the
u′-distribution can be non-monotonic. The
maximum value of the mass flux, F, was found to
be about 0.5 which was less than the typical value of 0.7 for thermally
stratified wind tunnel experiments for which
Sc
= 0.7. The vertical mass flux can be a combination of down-gradient and
counter-gradient transport with the ratio varying with
Nt (e.g. at Nt ≈
5, the flux is counter-gradient). The flux Richardson number
Rf
was found to increase monotonically to values of approximately
0.05.
Two-dimensional periodic waves in shallow water. Part 2. Asymmetric
waves
Authors: Hammack Joe , Mccallister Daryl , Scheffner Norman , Segur Harvey
Published: April 2006

We demonstrate experimentally the existence of a family of
gravity-induced finiteamplitude water waves that propagate practically
without change of form in shallow water of uniform depth. The surface
patterns of these waves are genuinely two-dimensional, and periodic. The
basic template of a wave is hexagonal, but it need not be symmetric about
the direction of propagation, as required in our previous studies (e.g.
Hammack et al. 1989). Like the symmetric waves in
earlier studies, the asymmetric waves studied here are easy to generate,
they seem to be stable to perturbations, and their amplitudes need not be
small. The Kadomtsev–Petviashvili (KP) equation is known to describe
approximately the evolution of waves in shallow water, and an
eight-parameter family of exact solutions of this equation ought to describe
almost all spatially periodic waves of permanent form. We present an
algorithm to obtain the eight parameters from wave-gauge measurements. The
resulting KP solutions are observed to describe the measured waves with
reasonable accuracy, even outside the putative range of validity of the KP
model.