bluuebunny/crossref_metadata_2025 huggingface dataset:
Flow and stability of helium II between concentric cylinders
Authors: Donnelly Russell J. , Lamar Michelle M.
Published: April 2006

We discuss our present knowledge of the flow and stability of helium II between concentric cylinders. The flow problem for helium II leads us to consider the formation of quantized vortices in the uniform rotation of helium II in an open bucket as well as quantized circulation states and vortices in a rotating annulus. We then consider how to treat the first appearance of vortices in the presence of shear, which allows us to characterize the basic flow which must be examined for stability. The results suggest an explanation for heretofore unexplained experiments. Future directions for research on the stability of helium II are suggested.
The mechanisms underlying flow-induced instabilities of cylinder arrays in crossflow
Authors: Paiudoussis M. P. , Price S. J.
Published: April 2006

This paper aims to shed some light on the physical mechanisms involved in flowinduced instabilities of arrays of cylinders in crossflow. In the framework of quasi-steady fluid-dynamic theory, two distinct mechanisms are discussed. The first is similar but not identical to that associated with classical galloping; i.e. it is a negative fluid-dynamic damping mechanism and may obtain even if a single cylinder in the array is free to oscillate with only one degree of freedom. Unlike classical galloping, it is intimately related to the time delay experienced in the wake structure, and hence the fluid forces, adjusting to displacements of the cylinder. The second mechanism is similar to wake flutter; i.e. it is controlled by non-conservative fluid-dynamic stiffness effects and generally requires relative motion between adjacent cylinders in the array, although there is no reason why it should not occur for a single flexible cylinder with two degrees of freedom. The two mechanisms generally coexist, but each is predominant over different ranges of system parameters.
Settling behaviour of heavy and buoyant particles from a suspension in an inclined channel
Authors: Law David Hin-Sum , Mactaggart Robert S. , Nandakumar K. , Masliyah Jacob H.
Published: April 2006

Settling characteristics of bidisperse suspensions containing light and heavy particles in inclined channels have been studied both experimentally and theoretically. The suspension is relatively dilute with a total volume fraction of no more than 0.16. In this dilute range the flow-visualization experiments indicate the formation of distinct zones with clear interfaces between them. There is no evidence of lateral segregation of particles. The convection currents formed near an inclined boundary are transferred to different zones depending on the relative concentration of the two species. Based on the flow-visualization experiments, the well known Ponder-Nakamura-Kuroda (PNK) model has been adopted to predict the settling characteristics of bidisperse suspensions.
An investigation of shock/boundary-layer interactions on curved surfaces at transonic speeds
Authors: Liu X. , Squire L. C.
Published: April 2006

A detailed experimental investigation has been made of shock/boundary-layer interactions on curved surfaces at transonic speeds. The shock waves were generated above circular-arc models with different radii mounted on the floor of the wind-tunnel test section. The ratio of the boundary-layer thickness (U/Ue = 0.99) in front of the shock to the radius of the surface curvature ranged from 0 (i.e. a flat surface) to 0.068. The Mach number just in front of the shock varied from 1.00 to 1.82 and the Reynolds number based on the model chord length was about 1.6 million. Interacting-flow studies include flows with shock-induced separation, flows with trailing-edge separation and flows with no separation. From all these studies it was found that separation was most extensive at the critical peak Mach number at which the separation changes from trailing-edge separation to shock-induced separation.
Separation and reattachment near the leading edge of a thin oscillating airfoil
Authors: Cebeci Tuncer , Khattab A. A. , Schimke S. M.
Published: April 2006

The evolution of unsteady boundary layers in the vicinity of the leading edge of a thin oscillating airfoil has been examined with a novel numerical method which is able to deal with the movement of the stagnation point and with regions of reverse and separated flow. Solutions to the unsteady boundary-layer equations, with a prescribed pressure distribution which causes flow reversal and separation, demonstrate the importance of numerical steps in distance and time and that a requirement similar to the stability criterion of Courant, Friedrichs and Lewy must be satisfied to avoid numerical errors. At the lower reduced frequencies of the investigation, solutions could not be obtained with this procedure and it was necessary to introduce interaction between the viscous and inviscid flows. The solutions obtained with the interactive method were increasingly different from those without interaction as the reduced frequency was decreased towards zero and, for some combinations of Reynolds number and frequency, exhibited behaviour consistent with the instability of separation bubbles.
Developing fluid flow in a curved duct of square cross-section and its fully developed dual solutions
Authors: Soh W. Y.
Published: April 2006

Developing fluid flow in a curved duct of square cross-section is studied numerically by a factored ADI finite-difference method on a staggered grid. A central-difference scheme with primitive variables is used inside the computational domain to reduce numerical diffusion. Two Reynolds numbers, 574 and 790, based upon a bulk velocity and hydraulic diameter are chosen for curvature ratios of 1/6.45 and 1/2.3, respectively. It is found that the secondary flow is far more complicated than expected, with the appearance of at least two pairs of vortices. Main-flow separation is also observed for the higher curvature ratio. Furthermore, it is observed that the flow develops into two quite different states downstream, depending upon the inlet conditions.

Solution of the fully developed Navier-Stokes equations is shown to be not unique beyond a certain critical Reynolds number. Developing flow seems to evolve into the fully developed state along a particular branch, into which the fully developed solution bifurcates.
Surface waves of large amplitude beneath an elastic sheet. Part 2. Galerkin solution
Authors: Forbes Lawrence K.
Published: April 2006

This study continues the work of Forbes (1986) on periodic waves beneath an elastic sheet floating on the surface of an infinitely deep fluid. The solution is sought as a Fourier series with coefficients that are computed numerically. Waves of extremely large amplitude are found to exist, and results are presented for waves belonging to several different nonlinear solution branches, characterized by different numbers of inflexion points in the wave profiles. The existence of multiple solutions, conjectured in the previous paper (Forbes 1986), is confirmed here by direct numerical computation.
A model for the onset of penetrative convection
Authors: Matthews P. C.
Published: April 2006

The stability of an S-shaped, cubic temperature profile, maintained by internal heating, is considered as a model for circumstances in which an unstably stratified layer of fluid is bounded by two stable layers. Critical Rayleigh numbers are computed for the cases of an infinitely deep layer, and for a layer of finite depth with symmetrically placed free or rigid boundaries. It is found that the introduction of boundaries can reduce the stability of the system. A weakly nonlinear analysis shows that the bifurcation is supercritical and that rolls are preferred to squares for all values of the Prandtl number. This result prompts a re-examination of the model of penetrative convection in water above ice, in which the bifurcation is subcritical, in order to understand the difference between the two models.
Vorticity generation by shock propagation through bubbles in a gas
Authors: Picone J. M. , Boris J. P.
Published: April 2006

We present a new theoretical model of ‘late-time’ phenomena related to the interaction of a planar shock with a local, discrete inhomogeneity in an ambient gas. The term ‘late-time’ applies to the evolution of the inhomogeneity and the flow field after interaction with the incident shock has ceased. Observations of a shock propagating through a bubble or a spherical flame have exhibited or implied the formation of vortex structures and have showed continual distortion of the bubble or flame. Our theory shows that this is due to the generation of long-lived vorticity at the edge of the discrete inhomogeneity. The vorticity interacts with itself through the medium of the fluid, and, depending on the geometry of the discrete inhomogeneity, can roll up into vortex filaments or vortex rings. To verify and amplify this theoretical description, we use numerical solutions of the fluid equations for conservation of mass, momentum, and energy to study the interaction of a weak shock with a cylindrical or spherical bubble. The simulated bubble has either a higher or lower density than the ambient gas. In this way, the calculations provide insights into the effects of both geometry and distortion of the local sound speed. The Mach number of the shock is 1.2, the ambient gas is air, and the pressure is 1 atmosphere. Because of the simple geometry of each bubble, the vorticity generated at the boundary rolls up into a vortex filament pair (cylindrical bubble) or a vortex ring (spherical bubble). The structural features and timescales of the phenomena observed in the calculations agree closely with recent experiments of Haas & Sturtevant, in which helium and Freon bubbles were used to provide the local departures from ambient density. The discussion of results includes a survey of alternative numerical methods, sources of uncertainty in velocities of interfaces or structures, as derived from the laboratory and numerical experiments, and the relationship of our analysis to other theories.
Numerical models and experiments on immiscible displacements in porous media
Authors: Lenormand Roland , Touboul Eric , Zarcone Cesar
Published: April 2006

Immiscible displacements in porous media with both capillary and viscous effects can be characterized by two dimensionless numbers, the capillary number C, which is the ratio of viscous forces to capillary forces, and the ratio M of the two viscosities. For certain values of these numbers, either viscous or capillary forces dominate and displacement takes one of the basic forms: (a) viscous fingering, (b) capillary fingering or (c) stable displacement. We present a study in the simple case of injection of a non-wetting fluid into a two-dimensional porous medium made of interconnected capillaries. The first part of this paper presents the results of network simulators (100 × 100 and 25 × 25 pores) based on the physical rules of the displacement at the pore scale. The second part describes a series of experiments performed in transparent etched networks. Both the computer simulations and the experiments cover a range of several decades in C and M. They clearly show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged. The domains of validity of the three different basic mechanisms are mapped onto the plane with axes C and M, and this mapping represents the ‘phase-diagram’ for drainage. In the final section we present three statistical models (percolation, diffusion-limited aggregation (DLA) and anti-DLA) which can be used for describing the three ‘basic’ domains of the phase-diagram.
The onset of convection and turbulence in rectangular layers of normal liquid 4He
Authors: Motsay R. W. , Anderson K. E. , Behringer R. P.
Published: April 2006

We have carried out high-precision measurements of the heat transport in intermediate-size rectangular layers of convecting normal liquid 4He with Prandtl numbers of 0.52 and 0.70. The containers used for these experiments had horizontal dimensions, in units of the height d, of 13.4 × 5.95 (cell I) and 18.2 × 8.12 (cell II). The slopes N1 of the Nusselt curves were 0.56 and 0.70 respectively for cell I and cell II. These values are significantly lower than predictions for N1 for horizontally unbound layers, but comparable with results obtained in cylindrical containers of liquid helium with roughly the same number of convection rolls. For the two containers, the onset of the first instability after the onset of convection occurred at Rayleigh numbers R1 that were in reasonable quantitative agreement with the predictions of Busse and Clever for the skewed-varicose instability. For both containers, the transition at R1 was characterized by long transients ranging from ∼ 102 to ∼ 103 vertical-thermal-diffusion times. A decrease in the Nusselt number was also observed. As the Rayleigh number was increased above R1, a new steady state evolved and then additional transitions were observed. These transitions occurred at Rayleigh numbers labelled R2, R3,…, with a total of five transitions seen in cell I and a total of three transitions seen for cell II. The transition for each cell at R2 can be related quantitatively to the skewed-varicose instability, and the transition at R3 is associated with an oscillatory instability. For cell II, the time-dependence beginning at R3 persisted to the highest Rayleigh number studied, R = 11.7Rc. However, for container I, two more regimes of time-independent flow were observed; the last of these was at an unexpectedly high Rayleigh number of 6.7Rc. This work extends to lower Prandtl number recent studies made on moderate-size rectangular layers of convecting water and alcohol.
Particle size segregation in inclined chute flow of dry cohesionless granular solids
Authors: Savage S. B. , Lun C. K. K.
Published: April 2006

If granular materials comprising particles of identical material but different sizes are sheared in the presence of a gravitational field, the particles are segregated according to size. The small particles fall to the bottom and the larger ones drift to the top of the sheared layer. In an attempt to isolate and study some of the essential segregation mechanisms, the paper considers a simplified problem involving the steady two-dimensional flow of a binary mixture of small and large spherical particles flowing down a roughened inclined chute. The flow is assumed to take place in layers that are in motion relative to one another as a result of the mean shear. For relatively slow flows, it is proposed that there are two main mechanisms responsible for the transfer of particles between layers. The first mechanism, termed the ‘random fluctuating sieve’, is a gravity-induced, size-dependent, void-filling mechanism. The probability of capture of a particle in one layer by a randomly generated void space in the underlying layer is calculated as a function of the relative motion of the two layers. The second, termed the ‘squeeze expulsion’ mechanism, is due to imbalances in contact forces on an individual particle which squeeze it out of its own layer into an adjacent one. It is assumed that this mechanism is not size preferential and that there is no inherent preferential direction for the layer transfer. This second physical mechanism in particular was proposed on the basis of observations of video recordings that were played back at slow speed. Since the magnitude of its contribution is determined by the satisfaction of overall mass conservation, the exact physical nature of the mechanism is of less importance. By combining these two proposed mechanisms the net percolation velocity of each species is obtained. The mass conservation equation for fines is solved by the method of characteristics to obtain the development of concentration profiles with downstream distance. Although the theory involves a number of empirical constants, their magnitude can be estimated with a fair degree of accuracy. A solution for the limiting case of dilute concentration of fine particles and a more general solution for arbitrary concentrations are presented. The analyses are compared with experiments which measured the development of concentration profiles during the flow of a binary mixture of coarse and fine particles down a roughened inclined chute. Reasonable agreement is found between the measured and predicted concentration profiles and the distance required for the complete separation of fine from coarse particles.
Linear stability of a non-symmetric, inviscid, Kármán street of small uniform vortices
Authors: Jiménez Javier
Published: April 2006

The classical point-vortex model for a Kármán vortex street is linearly stable only for a single, isolated, marginally stable, case. This property has been shown numerically to hold for streets formed by symmetric rows of uniform vortices of equal area. That result is extended here to the case in which the areas of the vortices in the two rows are not necessarily equal. The method used is an analytic perturbation valid when the vortex areas are small, and applied using an automatic symbolic manipulator.
Large structure in the far wakes of two-dimensional bluff bodies
Authors: Cimbala John M. , Nagib Hassan M. , Roshko Anatol
Published: April 2006

Smoke-wire flow visualization and hot-wire anemometry have been used to study near and far wakes of two-dimensional bluff bodies. For the case of a circular cylinder at 70 < Re < 2000, a very rapid (exponential) decay of velocity fluctuations at the Kármán-vortex-street frequency is observed. Beyond this region of decay, larger-scale (lower wavenumber) structure can be seen. In the far wake (beyond one hundred diameters) a broad band of frequencies is selectively amplified and then damped, the centre of the band shifting to lower frequencies as downstream distance is increased.

The far-wake structure does not depend directly on the scale or frequency of Kármán vortices shed from the cylinder; i.e. it does not result from amalgamation of shed vortices. The growth of this structure is due to hydrodynamic instability of the developing mean wake profile. Under certain conditions amalgamation can take place, but is purely incidental, and is not the driving mechanism responsible for the growth of larger-scale structure. Similar large structure is observed downstream of porous flat plates (Re ≈ 6000), which do not initially shed Kármán-type vortices into the wake.

Measured prominent frequencies in the far cylinder wake are in good agreement with those estimated by two-dimensional locally parallel inviscid linear stability theory, when streamwise growth of wake width is taken into account. Finally, three-dimensionality in the far wake of a circular cylinder is briefly discussed and a mechanism for its development is suggested based on a secondary parametric instability of the subharmonic type.
Steady-state coating flows inside a rotating horizontal cylinder
Authors: Johnson R. E.
Published: April 2006

Thin coating flows inside a rotating circular cylinder are investigated when the axis of rotation is perpendicular to the direction of gravity. Attention is restricted to flows of power-law fluids having negligible inertia. Four distinct steady-state liquid-film profiles are found to be possible. Two of the cases correspond to a continuous coating, i.e. films that cover the entire inner surface of the cylinder. The other two cases involve partial films covering a limited portion of the cylinder surface. Of the two continuous films, one is the expected configuration involving a coating that gradually changes in thickness as one moves around the cylinder, the film being thicker on the ascending portion of the cylinder and thinner on the descending portion. The second continuous-film configuration has regions on the rising side of cylinder where a rapid change in depth is possible. This case also has the potential to have recirculating zones where a portion of the fluid is trapped in either one or two eddies at fixed locations on the rising side of the cylinder. Of the two partial films, one corresponds to a weakly deformed puddle at the bottom of the cylinder and is the appropriate solution at small rotation rates. The second partial film is a film which coats a portion of the ascending side of the cylinder, the extent of which depends on the film volume.
A study of the collapse of arrays of cavities
Authors: Dear J. P. , Field J. E.
Published: April 2006

This paper describes a method for examining the collapse of arrays of cavities using high-speed photography and the results show a variety of different collapse mechanisms. A two-dimensional impact geometry is used to enable processes occurring inside the cavities such as jet motion, as well as the movement of the liquid around the cavities, to be observed. The cavity arrangements are produced by first casting water/gelatine sheets and then forming circular holes, or other desired shapes, in the gelatine layer. The gelatine layer is placed between two thick glass blocks and the array of cavities is then collapsed by a shock wave, visualized using schlieren photography and produced from an impacting projectile. A major advantage of the technique is that cavity size, shape, spacing and number can be accurately controlled. Furthermore, the shape of the shock wave and also its orientation relative to the cavities can be varied. The results are compared with proposed interaction mechanisms for the collapse of pairs of cavities, rows of cavities and clusters of cavities. Shocks of kbar (0.1 GPa) strength produced jets ofc.400 m s−1velocity in millimetre-sized cavities. In closely-spaced cavities multiple jets were observed. With cavity clusters, the collapse proceeded step by step with pressure waves from one collapsed row then collapsing the next row of cavities. With some geometries this leads to pressure amplification. Jet production by the shock collapse of cavities is suggested as a major mechanism for cavitation damage.
Do large structures control their own growth in a mixing layer? An assessment
Authors: Kaul Upender K.
Published: April 2006

This study makes a specific comparison between two different two-dimensional free shear layers: the T-layer which develops in time from an initial tangential velocity discontinuity separating the two half-spaces; and the S-layer which develops downstream of the origin where two uniform streams of unequal velocity are brought into tangential contact. The method of comparison is to assume that the vorticity of the S-layer is given parabolically by a Galilean mapping of that of the T-layer; to satisfy the appropriate boundary conditions in the S-layer and to compute the velocity induced at any point in the S-layer by its vorticity field; and to compare this velocity to that which can be derived from the velocity of the T-layer at corresponding points by a Galilean transformation of the velocity itself. The purpose of this calculation is to assess approximately how far the flow in the S-layer is from parabolic and, in particular, to what extent the perturbations induced upstream by large concentrations of vorticity found downstream are instrumental in hastening or retarding the subharmonic instability that leads to the formation of these large structures. The calculations suggest that this elliptic influence, or the feedback, in a mixing layer is relatively small, at least for small velocity ratios.
Shocks and singularities in the pressure field of a supersonically rotating propeller
Authors: Chapman C. J.
Published: April 2006

When linear acoustic theory is applied to the thickness noise problem of a supersonic propeller, it can give rise to a surface on which the pressure is discontinuous or singular. A method is described for obtaining the equation of this surface (when it exists), and the pressure field nearby; jumps, logarithms and inverse square roots occur, and their coefficients may be calculated exactly. The special case of a blade with a straight radial edge gives a cusped cone, whose sheets, each with a different type of discontinuity or singularity in pressure, are separated by lines of cusps; the coefficients in formulae for the pressure near the surface tend to infinity as a cusp line is approached, in proportion to the inverse quarter power of distance from the line. These results determine regions of space where nonlinear effects are important, and they suggest a strong analogy with sonic boom.
Similarity solutions for two-dimensional steady laminar gravity currents
Authors: Brighton P. W. M.
Published: April 2006

Similarity solutions have been found for steady two-dimensional laminar flow in which dense fluid is emitted upwards from a horizontal plane into a laminar shear flow or into a uniform flow. The solutions also apply to a light fluid released at an upper horizontal surface. The Navier-Stokes equations and the diffusion-advection equation are simplified by making the Boussinesq approximation and the boundary-layer approximation, which here also implies that pressure is hydrostatic.

For an oncoming linear shear flow representing flow near a solid surface, a similarity solution is obtained with depth proportional to $x^{\frac{1}{3}}$ where x is the horizontal coordinate. Horizontal velocity and concentration of dense fluid both increase as $x^{\frac{1}{3}}$, so that the solution represents fluid propagating upstream along the surface, and diffusing vertically to be swept downstream again. Numerical solutions for vertical profiles of velocity and concentration are presented for a Schmidt or Prandtl number σ between 0.71 and infinity. Two alternative sets of boundary conditions are possible. In one set, the pressure above the boundary layer is unchanged but the velocity profile is displaced upwards. In the second, this displacement is forced to be zero with the result that a pressure gradient is generated in the outer flow. These two boundary conditions are known to apply to disturbances in a laminar boundary-layer on horizontal lengthscales respectively greater or smaller than the triple-deck scale.

With a uniform velocity upstream and a stress-free boundary, representing flow at a free surface, similarity solutions exist only for a plume growing downstream from the source of a buoyancy flux B, with depth increasing as x½ and concentration decreasing as x−½. When gravity has negligible effects, so that B = 0, the solution is a Gaussian plume. With finite B, there is an adverse gradient of hydrostatic pressure and the plume is decelerated so that it is deeper than in neutral flow. Numerical solutions for σ = 0.71 reveal that there is a maximum buoyancy flux Bcrit above which no similarity solution exists. This occurs with a non-zero value of the surface velocity. For B < Bcrit it is found that there are in fact two possible solutions. One has surface velocity greater than at the critical flux and tends to the passive Gaussian plume as B → 0. In the other, surface velocity decreases from Bcrit, reaching zero at a non-zero value of B. Similar behaviour is found in an asymptotic solution for very large σ.
The dynamics of coherent structures in the wall region of a turbulent boundary layer
Authors: Aubry Nadine , Holmes Philip , Lumley John L. , Stone Emily
Published: April 2006

We have modelled the wall region of a turbulent boundary layer by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem (Lumley 1967, 1981). We truncate the representation to obtain low-dimensional sets of ordinary differential equations, from the Navier–Stokes equations, via Galerkin projection. The experimentally determined eigenfunctions of Herzog (1986) are used; these are in the form of streamwise rolls. Our model equations represent the dynamical behaviour of these rolls. We show that these equations exhibit intermittency, which we analyse using the methods of dynamical systems theory, as well as a chaotic regime. We argue that this behaviour captures major aspects of the ejection and bursting events associated with streamwise vortex pairs which have been observed in experimental work (Klineet al.1967). We show that although this bursting behaviour is produced autonomously in the wall region, and the structure and duration of the bursts is determined there, the pressure signal from the outer part of the boundary layer triggers the bursts, and determines their average frequency. The analysis and conclusions drawn in this paper appear to be among the first to provide a reasonably coherent link between low-dimensional chaotic dynamics and a realistic turbulent open flow system.
The mixing layer and its coherence examined from the point of view of two-dimensional turbulence
Authors: Lesieur Marcel , Staquet Chantal , Roy Pascal Le , Comte Pierre
Published: April 2006

A two-dimensional numerical large-eddy simulation of a temporal mixing layer submitted to a white-noise perturbation is performed. It is shown that the first pairing of vortices having the same sign is responsible for the formation of a continuous spatial longitudinal energy spectrum of slope between k−4 and k−3. After two successive pairings this spectral range extends to more than 1 decade. The vorticity thickness, averaged over several calculations differing by the initial white-noise realization, is shown to grow linearly, and eventually saturates. This saturation is associated with the finite size of the computational domain.

We then examine the predictability of the mixing layer, considering the growth of decorrelation between pairs of flows differing slightly at the first roll-up. The inverse cascade of error through the kinetic energy spectrum is displayed. The error rate is shown to grow exponentially, and saturates together with the levelling-off of the vorticity thickness growth. Extrapolation of these results leads to the conclusion that, in an infinite domain, the two fields would become completely decorrelated. It turns out that the two-dimensional mixing layer is an example of flow that is unpredictable and possesses a broadband kinetic energy spectrum, though composed mainly of spatially coherent structures.

It is finally shown how this two-dimensional predictability analysis can be associated with the growth of a particular spanwise perturbation developing on a Kelvin-Helmholtz billow: this is done in the framework of a one-mode spectral truncation in the spanwise direction. Within this analogy, the loss of two-dimensional predictability would correspond to a return to three-dimensionality and a loss of coherence. We indicate also how a new coherent structure could then be recreated, using an eddy-viscosity assumption and the linear instability of the mean inflexional shear.
A note on vortex shedding from axisymmetric bluff bodies
Authors: Monkewitz Peter A.
Published: April 2006

The linear parallel and incompressible stability of a family of axisymmetric wake profiles is studied in the range of Reynolds numbers where helical vortex shedding from bluff bodies of revolution is observed. The family of mean flow profiles allows for the variation of the wake depth as well as for a variable ratio of wake width to mixing-layer thickness. It is found that, even without reverse flow, the first helical mode is absolutely unstable in the near wake for Reynolds numbers, based on wake diameter and free-stream velocity, in excess of 3.3 × 103. A survey of the region of local absolute instability as a function of profile parameters and Reynolds number suggests that the large-scale helical vortex shedding, which is observed between Reynolds numbers of 6000 and 3 × 105for spheres, may be ‘driven’ by a self-excited oscillation in the near wake.
Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows
Authors: Shepherd Theodore G.
Published: April 2006

A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnol'd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions.
Semigeostrophic theory as a Dirac-bracket projection
Authors: Salmon Rick
Published: April 2006

This paper presents a general method for deriving approximate dynamical equations that satisfy a prescribed constraint typically chosen to filter out unwanted high frequency motions. The approximate equations take a simple general form in arbitrary phase-space coordinates. The family of semigeostrophic equations for rotating flow derived by Salmon (1983, 1985) fits this general form when the chosen constraint is geostrophic balance. More precisely, the semigeostrophic equations are equivalent to a Dirac-bracket projection of the exact Hamiltonian ønto the phase-space manifold corresponding to geostrophically balanced states. The more widely used quasi-geostrophic equations do not fit the general form and are instead equivalent to a metric projection of the exact dynamics on to the same geostrophic manifold. The metric, which corresponds to the Hamiltonian of the linearized dynamics, is an artificial component of the theory, and its presence explains why the quasi-geostrophic equations are valid only near a state isopycnals.
On direct methods in water-wave theory
Authors: Shields Jonathan J. , Webster William C.
Published: April 2006

Model equations for three-dimensional, inviscid flow between two arbitrary, time-varying material surfaces are derived using a ‘direct’ or variational approach due to Kantorovich. This approach results in a hierarchy of approximate theories, each of a higher level of spatial approximation and complexity. It can be shown that the equations are equivalent in substance to ‘the theory of directed fluid sheets’ of Green & Naghdi (1974, 1976).

The theory can be used to study the propagation of long waves in water of finite depth and, as such, competes with theories derived using the classical Rayleigh–Boussinesq perturbation methods. In order to demonstrate that there is an advantage to the present approach, we compare predictions for steady, two-dimensional waves over a horizontal bottom. Numerical solutions indicate that the direct theory converges more rapidly than the perturbation theories. Also, the equations of the higher-order direct theories contain singularities related to waves of limiting height, and indeed such waves can be predicted with relative accuracy. Finally, the range of applicability of the direct theory is far greater: waves as short as three times the water depth can be modelled. This is essentially a deep-water condition, well beyond the range of convergence of the Rayleigh–Boussinesq approach.
On the instability of geostrophic vortices
Authors: Flierl Glenn R.
Published: April 2006

The instabilities of barotropic and baroclinic, quasi-geostrophic, f-plane, circular vortices are found using a linearized contour dynamics model. We model the vortex using a circular region of horizontally uniform potential vorticity surrounded by an annulus of uniform, but different, potential vorticity. We concentrate mostly upon isolated vortices with no circulation in the basic state outside the outer radius b. In addition to linear analyses, we also consider weakly nonlinear waves. The amplitude equation has a cubic nonlinearity and, depending upon the sign of the coefficient of the cubic term, may give nonlinear stabilization or nonlinear enhancement of the growth. Barotropic isolated eddies are unstable when the outer annulus is narrow enough; on the other hand, if the scale of the whole vortex is sufficiently small compared to the radius of deformation of a baroclinic mode, the break up may be preferentially to a depth-varying disturbance corresponding to a twisting and tilting of the vortex. As the vortex becomes more baroclinic, we find that large-scale vortices show an elliptical mode baroclinic instability as well which is relatively insensitive to the scale of the outer annulus. When the baroclinic currents in the basic state dominate, the twisting mode disappears, and we see only the instabilities associated with either strong enough shear in the annular region or sufficiently large vortices compared with the deformation radius. The finite amplitude results show that the baroclinic instability mode for large enough vortices is nonlinearly stabilized while in most cases, the other two kinds of instability are nonlinearly destabilized.
Critical layers in accelerating two-layer flows
Authors: Altman Donald B.
Published: April 2006

A series of laboratory experiments on accelerating two-layer shear flows over topography is described. The mean flow reverses at the interface of the layers, forcing a critical layer to occur there. It is found that for a sufficiently thin interface, a slowly growing recirculating region, the ‘acceleration rotor’, develops on the interfacial wave at mean-flow Richardson numbers of O(0.5). This, in turn, can induce a secondary dynamical shear instability on the trailing edge of the wave. A single-mode, linear, two-layer numerical model reproduces many features of the acceleration rotor if mean-flow acceleration and bottom forcing are included. Velocity measurements are obtained from photographs using image processing software developed for the automated reading of particle-streak photographs. Typical results are shown.
The compressible turbulent shear layer: an experimental study
Authors: Papamoschou Dimitri , Roshko Anatol
Published: April 2006

The growth rate and turbulent structure of the compressible, plane shear layer are investigated experimentally in a novel facility. In this facility, it is possible to flow similar or dissimilar gases of different densities and to select different Mach numbers for each stream. Ten combinations of gases and Mach numbers are studied in which the free-stream Mach numbers range from 0.2 to 4. Schlieren photography of 20-ns exposure time reveals very low spreading rates and large-scale structures. The growth of the turbulent region is defined by means of Pitot-pressure profiles measured at several streamwise locations. A compressibility-effect parameter is defined that correlates and unifies the experimental results. It is the Mach number in a coordinate system convecting with the velocity of the dominant waves and structures of the shear layer, called here the convective Mach number. It happens to have nearly the same value for each stream. In the current experiments, it ranges from 0 to 1.9. The correlations of the growth rate with convective Mach number fall approximately onto one curve when the growth rate is normalized by its incompressible value at the same velocity and density ratios. The normalized growth rate, which is unity for incompressible flow, decreases rapidly with increasing convective Mach number, reaching an asymptotic vaue of about 0.2 for supersonic convective Mach numbers.
Fragments of Boethius: the reconstruction of the Cotton manuscript of the Alfredian text
Authors: Irvine Susan
Published: April 2006

‘These fragments I have shored against my ruins’: T. S. Eliot's metaphor in The Waste Land evokes the evanescent frailty of human existence and worldly endeavour with a poignancy that the Anglo-Saxons would surely have appreciated. Such a concept lies at the heart of Boethius's De consolatione Philosophiae, and perhaps prompted King Alfred to include this work amongst those which he considered most necessary for all men to know. Written in the early sixth century, Boethius's work was translated from Latin into Old English at the end of the ninth century, possibly by Alfred himself. It survives in two versions, one in prose (probably composed first) and the other in prose and verse, containing versifications of Boethius's Latin metres which had originally been rendered as Old English prose. It is the latter of these versions which will be the focus of my discussion here. Damaged beyond repair by fire and water, the set of fragments which contains this copy will be seen to epitomize the ideas imparted by the work in ways that Alfred could never have envisaged.
Virgin spouses as model Christians: the legend of Julian and Basilissa in Ælfric's Lives of Saints
Authors: Upchurch Robert K.
Published: April 2006

Of the three legends of virgin spouses in Ælfric's Lives of Saints, Julian and Basilissa would have been the least familiar to an Anglo-Saxon audience. Yet it is the most useful among the stories of chaste marriage and martyrdom for demonstrating how Ælfric uses them to emphasize the importance of constancy in the Christian faith. Altering verbally and structurally his Latin source, he rewrites Julian and Basilissa to model the asceticism and orthodoxy he feels are lacking among his flock. As odd a choice as the legend may seem, his selection suits his aim of rekindling the faith of the English laity with the Lives and is consistent with the larger goals of his programme of pastoral care.
Stray-field-induced modification of coherent spin dynamics
Authors: Meier L. , Salis G. , Ellenberger C. , Ensslin K. , Gini E.
Published: April 2006

Electron spins in an InGaAs semiconductor quantum well are used as a magnetometer of magnetic stray fields from patterned Fe stripes. Using time-resolved Faraday rotation, the coherent precession of quantum-well spins in the inhomogeneous field below the Fe stripes is measured for varying magnetic fields. Comparing with reference stripes made of Au, we find an enhancement of the spin precession frequency proportional to the Fe magnetization, in line with a decrease of the spin decay time, which is attributed to the inhomogeneous magnetic stray field in the quantum-well layer.
Resonant tunneling magnetoresistance in antiferromagnetically coupled Fe-based structures with multilayered Si/Ge spacers
Authors: Gareev R. R. , Weides M. , Schreiber R. , Poppe U.
Published: April 2006

We report on the experimental evidence of the tunneling magnetoresistance (TMR) effect near 3% and its inversion in strongly antiferromagnetically coupled Fe(001)∕([Si(0.2nm)∕Ge(0.2nm)]*5)∕Fe epitaxial structures with diffused interfaces. We explain the inversion of TMR with biasing voltage by resonant tunneling across impurity states with weak spin split ΔE∼10meV and spin-dependent filtering in the spacer layer. The resonant tunneling is manifested in spin-dependent resonances close to zero biasing voltages related to antiferromagnetic coupling across impurity states.
What's in a Name? A Multiracial Investigation of the Role of Occupational Stereotypes in Selection Decisions
Authors: King Eden B. , Mendoza Saaid A. , Madera Juan M. , Hebl Mikki R. , Knight Jennifer L.
Published: April 2006

Bertrand & Mullainathan (2002) found evidence that race‐typed names can have a significant influence on the evaluation of résumés. The current study expanded on their research by manipulating both the race (Asian American, Black, Hispanic, White) and quality of the résumé (high, low), and by considering occupational stereotypes as an explanatory mechanism. White male participants (N=155) read a fictitious résumé, evaluated the applicant, and judged his suitability for jobs. The results revealed that Asian American individuals were evaluated highly for high‐status jobs, regardless of their résumé quality. White and Hispanic applicants both benefited from a high‐quality résumé, but Black applicants were evaluated negatively, even with strong credentials. Results of mediation analyses demonstrated that occupational stereotypes accounted for the relationship between race and evaluations of applicants.
Trust in People Among Hispanic Americans
Authors: Weaver Charles N.
Published: April 2006

There is a dearth of reliable information about the attitudes of the largest minority, Hispanic Americans. The attitudes that were reliably examined were practically identical to the larger population of non‐Hispanic Whites, at least for those who speak English very well. This study of English‐speaking Hispanic Americans (n=971) and non‐Hispanic White respondents (n=16,202) to 18 recent nationwide public‐opinion surveys produced an anomalous result. On a generalized attitude toward human nature widely used to reflect trust in people, misanthropy, and social capital, Hispanic Americans of both sexes were significantly less likely to say they believe people can be trusted, try to be fair, and try to be helpful. These significant differences existed across many control variables. Doubt was cast on the possibility that the differences were explained by economic status, feelings of being discriminated against, or acculturation.
Liver iron content assessment by routine and simple magnetic resonance imaging procedure in highly transfused patients
Authors: Rose Christian , Vandevenne Philippe , Bourgeois Emmanuelle , Cambier Nathalie , Ernst Olivier
Published: April 2006

Abstract:  Background: Liver iron content (LIC) assessment by magnetic resonance imaging (MRI) is validated but not standardized. In a single center, we tried to assess the accuracy of a specific, simple MRI procedure adapted to high LIC from a well‐established simple and routine procedure known to quantify LIC. Methods: In 27 cases of monthly transfused patients, we compared biochemical values of LIC assessed on liver biopsy specimens and results obtained by two signal intensity ratio of gradient echo imaging (R2*) MRI protocols. The first was Gandon's routine procedure previously validated in liver disease and the second, our own method, was an addition of a gradient echo sequence specifically adapted to high LIC encountered in hematology practice. Results: Twenty‐seven liver biopsies were performed in 18 adult patients (myelodysplastic syndrome = 5, β‐thalassemia = 13). LIC by biopsy ranged from 1.4 to 54 mg/g liver dry weight (mg/g dw) (median 9.4 mg/g dw). Correlation between LIC by biopsy and by MRI with Gandon's procedure was good (R = 0.80) in patients with LIC falling within the range reported by Gandon. By contrast, a weak correlation was demonstrated (R = 0.52) in patients with high LIC (above 11.2 mg/g dw). With our sequences, the correlation was good both in the entire group of patients (R = 0.83) and in patients with LIC above 11.2 mg/g dw (R = 0.85). Conclusion: Our results suggest that the addition of a specific shorter‐gradient echo sequence to a very simple, fast technique produces an accurate estimation of LIC in post‐transfusional iron overload.