bluuebunny/crossref_metadata_2025_split huggingface dataset:
Cellular flows of a viscous liquid that partly fills a horizontal rotating cylinder
Authors: Benjamin T. Brooke , Pathak S. K. 
Published: April 2006

This theoretical and experimental investigation inquires into the various steady and unsteady motions that are possible when a highly viscous liquid partly fills a closed circular cylinder rotated about its horizontal axis at constant angular velocity. Fillings leaving an air bubble in the range roughly 10-20% by volume provide the most lively variety of observable phenomena.The full hydrodynamic problem is too complicated to be amenable to quantitative theoretical treatment, except by numerical analysis which is not yet available; but the abstract qualitative theory developed in § 2 appears to capture all the essentials of experimentally found behaviour. An analogous finite-dimensional system, such as would be presented by a close finite-element approximation, is used to illuminate principles governing the order of multiple solutions and their stability. Then the connection between the full problem and the analogue is demonstrated. Finally a simple argument is outlined confirming the observed stability of the motion at small rates of rotation.The experiments are described in § 3 and their results presented in § 4. For various values of the cylinder's aspect ratio, estimated singularities of the time-independent solution set are recorded as several-branched graphs of ωv/gR versus volume fraction filled by liquid (ω is the angular velocity of the container, R its radius and v the kinematic viscosity of the liquid). The experimental observations are discussed in § 5.
Internal gravity waves generated by oscillations of a sphere
Authors: Appleby J. C. , Crighton D. G. 
Published: April 2006

We consider the radiation of internal gravity waves from a spherical body oscillating vertically in a stratified incompressible fluid. A near-field solution (under the Boussinesq approximation) is obtained by separation of variables in an elliptic problem, followed by analytic continuation to the frequencies ω < N of internal wave radiation. Matched expansions are used to relate this solution to a far-field solution in which non-Boussinesq terms are retained. In the outer near field there are parallel conical wavefronts between characteristic cones tangent to the body, but with a wavelength found to be shorter than that for oscillations of a circular cylinder. It is also found that there are caustic pressure singularities above and below the body where the characteristics intersect. Far from the source, non-Boussinesq effects cause a diffraction of energy out of the cones. The far-field wave-fronts are hyperboloidal, with horizontal axes. The case of horizontal oscillations of the sphere is also examined and is shown to give rise to the same basic wave structure.The related problem of a pulsating sphere is then considered, and it is concluded that certain features of the wave pattern, including the caustic singularities near the source, are common to a more general class of oscillating sources.
Long-time molecular diffusion, sedimentation and Taylor dispersion of a fluctuating cluster of interacting Brownian particles
Authors: Brenner H. , Nadim A. , Haber S. 
Published: April 2006

Generalized Taylor dispersion theory, incorporating so-called coupling effects, is used to calculate the transport properties of a single deformable ‘chain’ composed of hydrodynamically interacting rigid Brownian particles bound together by internal potentials and moving through an unbounded quiescent viscous fluid. The individual rigid particles comprising the flexible chain or cluster may each be of arbitrary shape, size and density, and are supposed ‘joined’ together to form the chain by a configuration-dependent internal potentialV. Each particle separately undergoes translational and rotational Brownian motions; together, their relative motions give rise to a conformational or vibrational Brownian motion of the chain (in addition to a translational motion of the chain as a whole). Sufficient time is allowed for all accessible chain configurations to be sampled many times in consequence of this internal Brownian motion. As a result, an internal equilibrium Boltzmann probabilistic distribution of conformations derived fromVeffectively obtains.In contrast with prior analyses of such chain transport phenomena, noad hocpreaveraging hypotheses are invoked to effect the averaging of the input conformation-specific hydrodynamic mobility data. Rather, the calculation is effected rigorously within the usual (quasi-static) context of configuration-specific Stokes-Einstein equations.Explicit numerical calculations serving to illustrate the general scheme are performed only for the simplest case, namely dumb-bells composed of identically sized spheres connected by a slack tether. In this context it is pointed out that prior calculations of flexible-body transport phenomena have failed to explicitly recognize the existence of a Taylor dispersion contribution to the long-time diffusivity of sedimenting deformable bodies. This fluctuation phenomenon is compounded of shape-sedimentation dispersion (arising as a consequence of the intrinsic geometrical anisotropy of the object) and size-sedimentation dispersion (arising from fluctuations in the instantaneous ‘size’ of the object). Whereas shape dispersion exists even for rigid objects, size dispersion is manifested only by flexible bodies. These two Taylor dispersion mechanisms are relevant to interpreting the non-equilibrium sedimentation-diffusion properties of monodisperse polymer molecules in solutions or suspensions.
Generation of upstream advancing solitons by moving disturbances
Authors: Wu T. Yao-Tsu 
Published: April 2006

This study investigates the recently identified phenomenon whereby a forcing disturbance moving steadily with a transcritical velocity in shallow water can generate, periodically, a succession of solitary waves, advancing upstream of the disturbance in procession, while a train of weakly nonlinear and weakly dispersive waves develops downstream of a region of depressed water surface trailing just behind the disturbance. This phenomenon was numerically discovered by Wu & Wu (1982) based on the generalized Boussinesq model for describing two-dimensional long waves generated by moving surface pressure or topography. In a joint theoretical and experimental study, Lee (1985) found a broad agreement between the experiment and two theoretical models, the generalized Boussinesq and the forced Korteweg-de Vries (fKdV) equations, both containing forcing functions. The fKdV model is applied in the present study to explore the basic mechanism underlying the phenomenon.To facilitate the analysis of the stability of solutions of the initial-boundary-value problem of the fKdV equation, a family of forced steady solitary waves is found. Any such solution, if once established, will remain permanent in form in accordance with the uniqueness theorem shown here. One of the simplest of the stationary solutions, which is a one-parameter family and can be scaled into a universal similarity form, is chosen for stability calculations. As a test of the computer code, the initially established stationary solution is found to be numerically permanent in form with fractional uncertainties of less than 2% after the wave has traversed, under forcing, the distance of 600 water depths. The other numerical results show that when the wave is initially so disturbed as to have to rise from the rest state, which is taken as the initial value, the same phenomenon of the generation of upstream-advancing solitons is found to appear, with a definite time period of generation. The result for this similarity family shows that the period of generation, Ts, and the scaled amplitude α of the solitons so generated are related by the formula Ts = const α−3/2. This relation is further found to be in good agreement with the first-principle prediction derived here based on mass, momentum and energy considerations of the fKdV equation.
Natural convection about a heated horizontal cylinder in a porous medium
Authors: Ingham D. B. , Pop I. 
Published: April 2006

The natural convection from a heated circular cylinder in an unbounded region of porous medium is investigated for the full range of Rayleigh numbers. At small Rayleigh numbers a qualitative solution is obtained and at large Rayleigh numbers the second-order boundary-layer solution is found that takes into account the first-order plume solution. In order to find the solution at finite Rayleigh numbers the two governing coupled, nonlinear, elliptic partial differential equations are expressed in finite-difference form using a specialized technique which is second-order accurate everywhere. Further, methods are devised which deal with the plume and infinity boundary conditions. Although numerical results are presented for Rayleigh numbers up to 400 solutions of the finite-difference equations can be obtained for higher values of the Rayleigh numbers but in these cases the mesh size used is too large to adequately deal with the developing boundary-layer on the cylinder and the plume.The numerical results show how the theories at both low and high Rayleigh numbers are approached. The plume solution which develops with increasing Rayleigh number agrees with that predicted by the theory presented using the boundary-layer approximation. No separation of the flow at the top of the cylinder is found and there are no indications that it will appear at higher values of the Rayleigh number. The results presented here give reasonable agreement with the existing experimental results for Rayleigh numbers of order unity. However as the Rayleigh number increases to order 102 there is a large discrepancy between the theoretical and experimental results and this is because at these higher values of the Rayleigh number the Darcy approximation has been violated in the experimental results. This indicates the severe limitations of some of the existing theories which use boundary-layer analyses and the Darcy approximation for flows in a porous medium. The application of Darcy's law requires that the size of the pores be much smaller than the scale of the bulk flow and inertial and thermal lengthscales.
Stable and unstable shear modes of rotating parallel flows in shallow water
Authors: Hayashi Y.-Y. , Young W. R. 
Published: April 2006

This article considers the instabilities of rotating, shallow-water, shear flows on an equatorial β-plane. Because of the free surface, the motion is horizontally divergent and the energy density is cubic in the field variables (i.e. in standard notation the kinetic energy density is ½ h(u2 + v2)). Marinone & Ripa (1984) observed that as a consequence of this the wave energy is no longer positive definite (there is a cross-term Uh′u′). A wave with negative wave energy can grow by transferring energy to the mean flow. Of course total (mean plus wave) energy is conserved in this process. Further, when the basic state has constant potential vorticity, we show that there are no exchanges of energy and momentum between a growing wave and the mean flow. Consequently when the basic state has no potential vorticity gradients an unstable wave has zero wave energy and the mean flow is modified so that its energy is unchanged. This result strikingly shows that energy and momentum exchanges between a growing wave and the mean flow are not generally characteristic of, or essential to, instability.A useful conceptual tool in understanding these counterintuitive results is that of disturbance energy (or pseudoenergy) of a shear mode. This is the amount of energy in the fluid when the mode is excited minus the amount in the unperturbed medium. Equivalently, the disturbance energy is the sum of the wave energy and that in the modified mean flow. The disturbance momentum (or pseudomomentum) is defined analogously.For an unstable mode, which grows without external sources, the disturbance energy must be zero. On the other hand the wave energy may increase to plus infinity, remain zero, or decrease to minus infinity. Thus there is a tripartite classification of instabilities. We suggest that one common feature in all three cases is that the unstable shear mode is roughly a linear combination of resonating shear modes each of which would be stable if the other were somehow suppressed. The two resonating constituents must have opposite-signed disturbance energies in order that the unstable alliance has zero disturbance energy. The instability is a transfer of disturbance energy from the member with negative disturbance energy to the one with positive disturbance energy.
Propulsion of a foil moving in water waves.
Authors: Grue John , Mo Asbjørn , Palm Enok 
Published: April 2006

Propulsion of a foil moving in the water close to a free surface is examined. The foil moves with a forward speed U and is subjected to heaving and pitching motions in calm water, head waves or following waves. The model is two-dimensional and all equations are linearized. The fluid is assumed to be inviscid and the motion irrotational, except for the vortex wake. The fluid layer is infinitely deep.The problem is solved by applying a vortex distribution along the centreline of the foil and the wake. The local vortex strength is found by solving a singular integral equation of the first kind, which appropriately is transformed to a non-singular Fredholm equation of the second kind. The vortex wake, the forward thrust upon the foil and the power supplied to maintain the motion of the foil are investigated. The scattered free surface waves are computed. For moderate values of Uσ/g (U is forward speed of the foil, σ is frequency of oscillation, g is acceleration due to gravity) it is found that the free surface strongly influences the vortex wake and the forces upon the foil. When the foil is moving in incoming waves it is found that a relatively large amount of the wave energy may be extracted for propulsion. As an application of the theory the propulsion of ships by a foil propeller is examined. The theory is compared with experiments.
Breakup of fluid droplets in electric and magnetic fields
Authors: Sherwood J. D. 
Published: April 2006

A drop of fluid, initially held spherical by surface tension, will deform when an electric or magnetic field is applied. The deformation will depend on the electric/magnetic properties (permittivity/permeability and conductivity) of the drop and of the surrounding fluid. The full time-dependent low-Reynolds-number problem for the drop deformation is studied by means of a numerical boundary-integral technique. Fluids with arbitrary electrical properties are considered, but the viscosities of the drop and of the surrounding fluid are assumed to be equal.Two modes of breakup have been observed experimentally: (i) tip-streaming from drops with pointed ends, and (ii) division of the drop into two blobs connected by a thin thread. Pointed ends are predicted by the numerical scheme when the permittivity of the drop is high compared with that of the surrounding fluid. Division into blobs is predicted when the conductivity of the drop is higher than that of the surrounding fluid. Some experiments have been reported in which the drop deformation exhibits hysteresis. This behaviour has not in general been reproduced in the numerical simulations, suggesting that the viscosity ratio of the two fluids can play an important role.
Stochastic estimation of organized turbulent structure: homogeneous shear flow
Authors: Adrian Ronald J. , Moin Parviz 
Published: April 2006

The large-scale organized structures of turbulent flow can be characterized quantitatively by a conditional eddy, given the local kinematic state of the flow as specified by the conditional average of u(x’, t) given the velocity and the deformation tensor at a point x: 〈u(x’, t)|u(x, t), d(x, t)〉. By means of linear mean-square stochastic estimation, 〈u’|u, d〉 is approximated in terms of the two-point spatial correlation tensor, and the conditional eddy is evaluated for arbitrary values of u(x, t) and d(x, t), permitting study of the turbulent field for a wide range of local kinematic states. The linear estimate is applied to homogeneous turbulent shear flow data generated by direct numerical simulation. The joint velocity-deformation probability density function is used to obtain conditions corresponding to those events that contribute most to the Reynolds shear stress. The primary contributions to the second-quadrant and fourth-quadrant Reynolds-stress events in homogeneous shear flow come from flow induced through the ‘legs’ and close to the ‘heads’ of upright and inverted ‘hairpins’, respectively.The equation governing the joint probability density function of fu,d (u, d) is derived. It is shown that this equation contains 〈u’/u, d〉 and that the equations for second-order closure can be derived from it. Closure requires approximation of 〈u’/u, d〉.
A strong-interaction theory for the motion of arbitrary three-dimensional clusters of spherical particles at low Reynolds number
Authors: Hassonjee Qaizar , Ganatos Peter , Pfeffer Robert 
Published: April 2006

This paper contains an ‘exact’ solution for the hydrodynamic interaction of a three-dimensional finite cluster at arbitrarily sized spherical particles at low Reynolds number. The theory developed is the most general solution to the problem of an assemblage of spheres in a three-dimensional unbounded media. The boundary-collocation truncated-series solution technique of Ganatos, Pfeffer & Weinbaum (1978) for treating planar symmetric Stokes flow problems has been extensively modified to treat the non-symmetric multibody problem. The orthogonality properties of the eigenfunctions in the azimuthal direction are used to satisfy the no-slip boundary conditions exactly on entire rings on the surface of each particle rather than just at discrete points.Detailed comparisons with the exact bipolar solutions for two spheres show the present theory to be accurate to five significant figures in predicting the translational and angular velocity components of the particles at all orientations for interparticle gap widths as close as 0.1 particle diameter. Convergence of the results to the exact solution is rapid and systematic even for unequal-sized spheres (a1/a2 = 2). Solutions are presented for several interesting and intriguing configurations involving three or more spherical particles settling freely under gravity in an unbounded fluid or in the presence of other rigidly held particles. Advantage of symmetry about the origin is taken for symmetric configurations to reduce the collocation matrix size by a factor of 64. Solutions for the force and torque on three-dimensional clusters of up to 64 particles have been obtained, demonstrating the multiparticle interaction effects that arise which would not be present if only pair interactions of the particles were considered. The method has the advantage of yielding a rather simple expression for the fluid velocity field which is of significance in the treatment of convective heat and mass transport problems in multiparticle systems.
Interaction of impulsively generated vortex pairs with bodies
Authors: Homa J. , Lucas M. , Rockwell D. 
Published: April 2006

A vortex pair, impulsively generated from a planar nozzle, is shown to have a degree of vorticity concentration in good agreement with inviscid theory, providing well-posed initial conditions for interaction with basic types of bodies (cylinders and plates). The scale of these bodies ranges from the same order as, to over an order of magnitude smaller than, the scale (distance between centres) of the incident vortex pair.The fundamental case of a (primary) vortex pair symmetrically incident upon a very small cylinder shows rapid growth of a secondary vortex pair. These secondary vortices quickly attain a circulation of the same order as that of the corresponding primary vortices within a distance smaller than the lengthscale of the primary vortex pair. At this location, the temporal variation of integrated vorticity of primary and secondary vortices attains a maximum simultaneously. This zero phase shift between arrival of vorticity maxima provides the basis for formation of counter-rotating, primary–secondary vortex pairs, where both the primary and secondary vortices move at the same phase speed.Visualization shows that the mode of secondary vortex formation is highly sensitive to the degree of symmetry of the initial encounter of the incident vortex pair with the body. The symmetrical mode of (in-phase) secondary vortex formation shows very rapid growth of large-scale secondary vortices; their development is relatively independent of the particulars of body shape and scale. On the other hand, the antisymmetrical mode takes two basic forms: large-scale secondary vortex formation, with the phase shift between their formation determined by the lengthscale of the body; and small-scale, antisymmetrical shedding of secondary vortices from the body occurring for a body lengthscale an order of magnitude smaller than that of the incident vortex pair. Correspondingly, there are several types of distortion of the cores and trajectories of the primary (incident) vortices.
Rofecoxib is a potent inhibitor of cytochrome P450 1A2: studies with tizanidine and caffeine in healthy subjects
Authors: Backman Janne T. , Karjalainen Marjo J. , Neuvonen Mikko , Laitila Jouko , Neuvonen Pertti J. 
Published: April 2006

AimsCase reports suggest an interaction between rofecoxib and the CYP1A2 substrate tizanidine. Our objectives were to explore the extent and mechanism of this possible interaction and to determine the CYP1A2 inhibitory potency of rofecoxib.MethodsIn a randomized, double‐blind, two‐phase cross‐over study, nine healthy subjects took 25 mg rofecoxib or placebo daily for 4 days and, on day 4, each ingested 4 mg tizanidine. Plasma concentrations and the urinary excretion of tizanidine, its metabolites (M) and rofecoxib, and pharmacodynamic variables were measured up to 24 h. On day 3, a caffeine test was performed to estimate CYP1A2 activity.ResultsRofecoxib increased the area under the plasma concentration–time curve (AUC0–∞) of tizanidine by 13.6‐fold [95% confidence interval (CI) 8.0, 15.6;P < 0.001), peak plasma concentration (Cmax) by 6.1‐fold (4.8, 7.3;P < 0.001) and elimination half‐life (t1/2) from 1.6 to 3.0 h (P < 0.001). Consequently, rofecoxib markedly increased the blood pressure‐lowering and sedative effects of tizanidine (P < 0.05). Rofecoxib increased several fold the tizanidine/M‐3 and tizanidine/M‐4 ratios in plasma and urine and the tizanidine/M‐5, tizanidine/M‐9 and tizanidine/M‐10 ratios in urine (P < 0.05). In addition, it increased the plasma caffeine/paraxanthine ratio by 2.4‐fold (95% CI 1.4, 3.4;P = 0.008) and this ratio correlated with the tizanidine/metabolite ratios. Finally, the AUC0−25of rofecoxib correlated with the placebo phase caffeine/paraxanthine ratio (r = 0.80,P = 0.01).ConclusionsRofecoxib is a potent inhibitor of CYP1A2 and it greatly increases the plasma concentrations and adverse effects of tizanidine. The findings suggest that rofecoxib itself is also metabolized by CYP1A2, raising concerns about interactions between rofecoxib and other CYP1A2 substrate and inhibitor drugs.