bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mechanics of collisional motion of granular materials. Part 2. Wave propagation through vibrofluidized granular layers
Authors: Goldshtein Alexander , Shapiro Michael , Moldavsky Leonid , Fichman Mati 
Published: April 2006

According to numerous experimental observations and theoretical models vibrated layers composed of large granules behave like a solid plastic body. In contrast, in this study experimental data are presented that reveal that, for constant vibration amplitudes A ≥ 1 cm with the frequency ω increasing from zero, all layers pass through three vibrational states, with the respective behaviours being as of (i) a solid plastic body, (ii) a liquid, (iii) a gas. In the liquid-like vibrational state transverse waves propagating along the layer width were observed. These waves were shown to be gravitational resonance waves, with the corresponding frequencies well correlated by the known formula for incompressible liquids. In the gas-like vibrational state compression (shock) and expansion waves propagating across the layer height, were observed.A theoretical model for time-periodic collisional vibrational regimes was developed on the basis of the Euler-like equations of a granular gas composed of inelastic spheres. The model shows that the vibrational granular state (bed porosity, shock wave speed, granular pressure and kinetic energy) is inter alia governed by the dimensionless parameter V = (Aω)/(hmg)1/2, with g, hm being the gravitational acceleration and the height of the resting layer, respectively. This is in contrast with the previous studies, where the behaviour of vibrated granular layers was interpreted in terms of the dimensionless acceleration Δ = (Aω2)/g. The proposed model was tested by processing the data obtained from photographs of the particle distribution within vibrated layers. Theoretical predictions of the particle average concentration compared favourably with the experimental data.Other phenomena observed in vibrated granular layers include the formation of caverns, circulatory motion of granules and synchronized periodic motion of two adjacent vibrated layers of different widths. The importance of the observed phenomena in relation to various technological processes involving bulk materials (vibromixing, vibroseparation, etc.) is discussed.
The formation of drops through viscous instability
Authors: Cardoso Silvana S. S. , Woods Andrew W. 
Published: April 2006

The stability of an immiscible layer of fluid bounded by two other fluids of different viscosities and migrating through a porous medium is analysed, both theoretically and experimentally. Linear stability analyses for both one-dimensional and radial flows are presented, with particular emphasis upon the behaviour when one of the interfaces is highly stable and the other is unstable. For one-dimensional motion, it is found that owing to the unstable interface, the intermediate layer of fluid eventually breaks up into drops.However, in the case of radial flow, both surface tension and the continuous thinning of the intermediate layer as it moves outward may stabilize the system. We investigate both of these stabilization mechanisms and quantify their effects in the relevant parameter space. When the outer interface is strongly unstable, there is a window of instability for an intermediate range of radial positions of the annulus. In this region, as the basic state evolves to larger radii, the linear stability theory predicts a cascade to higher wavenumbers. If the growth of the instability is sufficient that nonlinear effects become important, the annulus will break up into a number of drops corresponding to the dominant linear mode at the time of rupture.In the laboratory, a Hele-Shaw cell was used to study these processes. New experiments show a cascade to higher-order modes and confirm quantitatively the prediction of drop formation. We also show experimentally that the radially spreading system is stabilized by surface tension at small radii and by the continual thinning of the annulus at large radii.
Rotating free-shear flows. Part 2. Numerical simulations
Authors: Métais Olivier , Flores Carlos , Yanase Shinichiro , Riley James J. , Lesieur Marcel 
Published: April 2006

The three-dimensional dynamics of the coherent vortices in periodic planar mixing layers and in wakes subjected to solid-body rotation of axis parallel to the basic vorticity are investigated through direct (DNS) and large-eddy simulations (LES). Initially, the flow is forced by a weak random perturbation superposed on the basic shear, the perturbation being either quasi-two-dimensional (forced transition) or three-dimensional (natural transition). For an initial Rossby number Ro(i), based on the vorticity at the inflexion point, of small modulus, the effect of rotation is to always make the flow more two-dimensional, whatever the sense of rotation (cyclonic or anticyclonic). This is in agreement with the Taylor–Proudman theorem. In this case, the longitudinal vortices found in forced transition without rotation are suppressed.It is shown that, in a cyclonic mixing layer, rotation inhibits the growth of three-dimensional perturbations, whatever the value of the Rossby number. This inhibition exists also in the anticyclonic case for |Ro(i)| ≤ 1. At moderate anticyclonic rotation rates (Ro(i) < −1), the flow is strongly destabilized. Maximum destabilization is achieved for |Ro(i) ≈ 2.5, in good agreement with the linear-stability analysis performed by Yanase et al. (1993). The layer is then composed of strong longitudinal alternate absolute vortex tubes which are stretched by the flow and slightly inclined with respect to the streamwise direction. The vorticity thus generated is larger than in the nonrotating case. The Kelvin–Helmholtz vortices have been suppressed. The background velocity profile exhibits a long range of nearly constant shear whose vorticity exactly compensates the solid-body rotation vorticity. This is in agreement with the phenomenological theory proposed by Lesieur, Yanase & Métais (1991). As expected, the stretching is more efficient in the LES than in the DNS.A rotating wake has one side cyclonic and the other anticyclonic. For |Ro(i)| ≤ 1, the effect of rotation is to make the wake more two-dimensional. At moderate rotation rates (|Ro(i)| > 1), the cyclonic side is composed of Kármán vortices without longitudinal hairpin vortices. Karman vortices have disappeared from the anticyclonic side, which behaves like the mixing layer, with intense longitudinal absolute hairpin vortices. Thus, a moderate rotation has produced a dramatic symmetry breaking in the wake topology. Maximum destabilization is still observed for |Ro(i)| ≈ 2.5, as in the linear theory.The paper also analyses the effect of rotation on the energy transfers between the mean flow and the two-dimensional and three-dimensional components of the field.
Observations and scaling of travelling bubble cavitation
Authors: De Chizelle Y. Kuhn , Ceccio S. L. , Brennen C. E. 
Published: April 2006

Recent observations of growing and collapsing bubbles in flows over axisymmetric headforms have revealed the complexity of the ‘micro-fluid-mechanics’ associated with these bubbles (van der Meulen & van Renesse 1989; Briancon-Marjollet et al. 1990; Ceccio & Brennen 1991). Among the complex features observed were the bubble-to-bubble and bubble-to-boundary-layer interactions which leads to the shearing of the underside of the bubble and alters the collapsing process. All of these previous tests, though, were performed on small headform sizes. The focus of this research is to analyse the scaling effects of these phenomena due to variations in model size, Reynolds number and cavitation number. For this purpose, cavitating flows over Schiebe headforms of different sizes (5.08, 25.4 and 50.8 cm in diameter) were studied in the David Taylor Large Cavitation Channel (LCC). The bubble dynamics captured using high-speed film and electrode sensors are presented along with the noise signals generated during the collapse of the cavities.In the light of the complexity of the dynamics of the travelling bubbles and the important bubble/bubble interactions, it is clear that the spherical Rayleigh-Plesset analysis cannot reproduce many of the phenomena observed. For this purpose an unsteady numerical code was developed which uses travelling sources to model the interactions between the bubble (or bubbles) and the pressure gradients in the irrotational flow outside the boundary layer on the headform. The paper compares the results of this numerical code with the present experimental results and demonstrates good qualitative agreement between the two.
The interaction of a moving fluid/fluid interface with a flat plate
Authors: Billingham J. , King A. C. 
Published: April 2006

A well-known technique for metering a multiphase flow is to use small probes that utilize some measurement principle to detect the presence of different phases surrounding their tips. In almost all cases of relevance to the oil industry, the flow around such local probes is inviscid and driven by surface tension, with negligible gravitational effects. In order to study the features of the flow around a local probe when it meets a droplet, we analyse a model problem: the interaction of an infinite, initially straight, interface between two inviscid fluids, advected in an initially uniform flow towards a semi-infinite thin flat plate oriented at 90° to the interface. This has enabled us to gain some insight into the factors that control the motion of a contact line over a solid surface, for a range of physical parameter values.The potential flows in the two fluids are coupled nonlinearly at the interface, where surface tension is balanced by a pressure difference. In addition, a dynamic contact angle boundary condition is imposed at the three-phase contact line, which moves along the plate. In order to determine how the interface deforms in such a flow, we consider the small- and large-time asymptotic limits of the solution. The small-time and linearized large-time problems are solved analytically, using Mellin transforms, whilst the general large-time problem is solved numerically, using a boundary integral method.The form of the dynamic contact angle as a function of contact line velocity is the most important factor in determining how an interface deforms as it meets and moves over the plate. Depending on this, the three-phase contact line may, at one extreme, hang up on the leading edge of the plate or, at the other extreme, move rapidly along the surface of the plate. At large times, the solution asymptotes to an interface configuration where the contact line moves at the far-field velocity.
Inception of channelization and drainage basin formation: upstream-driven theory
Authors: Izumi Norihiro , Parker Gary 
Published: April 2006

The ubiquitous presence of river drainage basins in the terrestrial environment suggests that distributed overland flow generated by rainfall tends to spontaneously organize itself into dendritic systems of discrete channels. Several recent numerical models describe the evolution of complete drainage basins from the initial condition of rainfall on a flat, tilted plateau, the surface of which has been provided with random elevation perturbations. These analyses model overland flow via the assumption of a perfect balance between gravitational and frictional terms, i.e. in terms of normal flow.Linear stability analysis applied to the normal flow model has been shown, however, to fail to select a wavelength corresponding to a finite distance of separation between incipient basins. This suggests that the normal flow model may not be a sufficient basis for studying drainage basin development, especially at the finest scales of morphologic significance.Here the concept of a threshold condition for bed erosion is combined with an analysis of the full equations of shallow overland flow in order to study wavelength selection. Classical linear stability analysis is shown to be inadequate to analyse the problem at the level of inception. An alternative linear analysis of bed perturbations based on the threshold condition is developed, and shown to lead to the selection of finite wavelength of the correct order of magnitude.The analysis here is driven from the upstream direction in that bed erosion is first caused only when sufficient flow has gathered from upstream due to rainfall. A downstream-driven theory of incipient channelization that is not necessarily dependent upon rainfall is presented in Izumi (1993), and is presently in preparation for publication.
Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics. Part 1. Pseudomomentum-based theory
Authors: Kushner Paul J. , Shepherd Theodore G. 
Published: April 2006

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics.In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms.The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent.This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii).In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.
Critical microjets in collapsing cavities
Authors: Longuet-Higgins Michael S. , Oguz Hasan 
Published: April 2006

Inward microjets are commonly observed in collapsing cavities, but here we show that jets with exceptionally high velocities and accelerations occur in certain critical flows dividing jet formation from bubble pinch-off. An example of the phenomenon occurs in the family of flows which evolve from a certain class of initial conditions: the initial flow field is that due to a moving point sink within the cavity.A numerical study of the critical flow shows that in the neighbourhood of microjet formation the flow is self-similar. The local accelerations, velocities and distances scale as tβ-2, tβ-1 and tβ respectively, where β = 0.575. The velocity potential is approximately a spherical harmonic of degree ¼.
Quasi-periodic cylinder wakes and the Ginzburg–Landau model
Authors: Albarède Pierre , Provansal Michel 
Published: April 2006

The time-periodic phenomena occurring at low Reynolds numbers (Re [lsim ] 180) in the wake of a circular cylinder (finite-length section) are well modelled by a Ginzburg–Landau (GL) equation with zero boundary conditions (Albarède & Monkewitz 1992). According to the GL model, the wake is mainly governed by a rescaled length, based on the aspect ratio and the Reynolds number. However, the determination of coefficients is not complete: we correct a former evaluation of the nonlinear Landau coefficient, we show difficulties in obtaining a consistent set of coefficients for different Reynolds numbers or end configurations, and we propose the use of an ‘influential’ length. New two-point velocimetry results are presented: phase measurements show that a subtle property is shared by the three-dimensional wake and the GL model.Two time-quasi-periodic phenomena – the second mode observed for smaller aspect ratios, and the dislocated chevron observed for larger aspect ratios – are presented and precisely related to the GL model. Only the linear characteristics of the second mode are readily explained; its existence depends on the end conditions. Moreover, through a quasi-static variation of the length, the second mode evolves continuously to end cells (and vice versa). Observations of the dislocated chevron are recalled. A very similar instability is found on the chevron solution of the GL equation, when the model parameters (c1, c2) move towards the phase diffusion unstable region. The early stages of this instability are qualitatively similar to the observed patterns.
Modelling and analysis of meniscus roll coating
Authors: Gaskell P. H. , Savage M. D. , Summers J. L. , Thompson H. M. 
Published: April 2006

Three mathematical models are developed for meniscus roll coating in which there is steady flow of a Newtonian fluid in the narrow gap, or nip, between two contrarotating rolls in the absence of body forces.The zero flux model predicts a constant pressure gradient within the central core and two eddies, each with an inner structure, in qualitative agreement with observation. The small flux model takes account of a small inlet flux and employs the lubrication approximation to represent fluid velocity as a combination of Couette and Poiseuille flows. Results show that the meniscus coating regime is characterized by small flow rates (λ [Lt ] 1) and a sub-ambient pressure field generated by capillary action at the upstream meniscus. Such flows are found to exist for small modified capillary number, Ca(R/H0)1/2 [lsim ] 0.15, where Ca and R/H0 represent capillary number and the radius to semi-gap ratio, respectively.A third model incorporates the full effects of curved menisci and nonlinear free surface boundary conditions. The presence of a dynamic contact line, adjacent to the web on the upper roll, requires the imposition of an apparent contact angle and slip length. Numerical solutions for the velocity and pressure fields over the entire domain are obtained using the finite element method. Results are in accord with experimental observations that the flow domain consists of two large eddies and fluid transfer jets or ‘snakes’. Furthermore, the numerical results show that the sub-structure of each large eddy consists of a separatrix with one saddle point, two sub-eddies with centres, and an outer recirculation.Finally finite element solutions in tandem with lubrication analysis establish the existence of three critical flow rates corresponding to a transformation of the pressure field, the emergence of a ‘secondary snake’ (another fluid transfer jet) and the disappearance of a primary snake.
Convection in3He–superfluid-4He mixtures. Part 1. A Boussinesq analogue
Authors: Metcalfe Guy , Behringer R. P. 
Published: April 2006

Dilute mixtures of3He in superfluid4He have Prandtl numbers easily tunable between those of liquid metals and water: 0.04 <Pr< 2. Moreover, owing to the tight coupling of the temperature and concentration fields, superfluid mixture convection is closely analogous to classical Rayleigh–Bénard convection, i.e. superfluid mixtures convect as if they were classical, single-component fluids, well described by the Boussinesq equations. This work has two goals. The first is to put the theory of superfluid mixture convection on a firmer basis. We accomplish this by combining experiment and analysis to measure superfluid effects on the onset of convection. In the process, we demonstrate quantitative control over superfluid effects and, in particular, that deviations from classical convective behaviour can be made small or at worst no larger than finite aspect ratio effects. The size of superfluid effects at convective onset can be less than a few percent for temperatures 1 <T< 2 K. Comparison of the measured properties of superfluid mixture roll instabilities above the onset of convection (e.g. skewed varicose, oscillatory, and particularly near the codimension-2 point) to the properties predicted by Boussinesq calculations further verifies that superfluid mixtures convect as classical fluids.With superfluid effects understood and under control, the second goal, presented in Part 2, is to exploit the uniquePrrange of superfluid mixtures and the variable aspect ratio (Γ) capabilities of our experiment to survey convective instabilities in the broad, and heretofore largely unexplored, parameter space 0.12 <Pr< 1.4 and 2 < Γ < 95. The aim is to identify and characterize time-dependence and chaos, and to discover new dynamical behaviour in strongly nonlinear convective flows.