bluuebunny/crossref_metadata_2025 huggingface dataset:
Lagrangian moments and mass transport in Stokes waves
Authors: Longuet-Higgins Michael
Published: April 2006

The orbital motions in surface gravity waves are of interest for analysing wave records made by accelerometer buoys. In this paper we derive some exact expressions for the first, second and third cumulants of the vertical orbital displacements in a regular Stokes wave of finite amplitude in terms of previously known integral quantities of the wave: the kinetic and potential energies, the phase speed c and the mass-transport velocity U at the free surface. These results generalize a remarkably simple relation found previously between the Lagrangian-mean surface level and the product Uc.

Expansions are given in powers of the wave steepness parameter ak which show that the third Lagrangian cumulant is very small – of order (ak)6, indicating a high degree of vertical symmetry in the orbit. This contrasts with the situation in random waves, where the third cumulant is of order (ak)4 only. It is shown that the increased skewness in random waves is due mainly to an O(ak)2 shift in the Lagrangian mean level of individual waves. Such shifts in mean level may be too gradual to be fully detected by some accelerometer buoys. In that case the apparent skewness will be reduced.
Coherent baroclinic eddies on a sloping bottom
Authors: Mory M. , Stern M. E. , Griffiths R. W.
Published: April 2006

A coherent and stable baroclinic eddy in a rotating fluid was produced on a sloping bottom by releasing a dome of salt water into the ambient fresh water. A strong cyclonic vortex is produced above the heavy dome. The entire eddy system moves ‘north-westward’ (with the up-slope direction designated ‘north’) as a ‘Taylor column’. The eddy system displays long lifetimes, but it is shown that a theory of isolated systems cannot account for the experimental observations. Instead, it is demonstrated that the vortex flow above the lens is along the lines of constant depth, producing a net pressure force on the lens, which approximately balances the buoyancy force. When Ekman friction is also included, it accounts for the northward motion of the dome.
Oscillations of a gas in a closed tube near half the fundamental frequency
Authors: Althaus R. , Thomann H.
Published: April 2006

The oscillations are driven by the sinusoidal motion of a piston at one end of the tube. Near half the fundamental frequency the first overtone, driven by nonlinear effects, becomes resonant. For small boundary-layer friction the amplitude of this resonant part is comparable with the non-resonant acoustic solution and shocks are formed. Theoretical results are compared with pressure signals measured at the closed end of the tube. The viscous effects are large for air at atmospheric pressure and the nonlinear effects remain small. Experiments with xenon, sulphurhexafluoride (SF6) and Freon RC-318 (C4F8) were therefore conducted and shocks formed as predicted. The comparison of the nonlinear theory by Keller (1975) with the experiments shows very good agreement.
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.
Resonant surface waves and chaotic phenomena
Authors: Gu X. M. , Sethna P. R.
Published: April 2006

Surface waves in a rectangular container subjected to vertical oscillations are studied. Effects of energy dissipation along the lines of Miles (1967) and the effect of surface tension are included. Sufficient conditions, for two modes to dominate the motion, are given. The analysis is along the lines of Miles (1984a) and Holmes (1986). A complete bifurcation analysis is performed, and the modal amplitudes and phases are shown to have chaotic behaviour. This result is obtained under assumptions different from those of Holmes (1986). The conclusions regarding chaotic motions are based on a theorem of šilnikov (1970).
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.
Laminar-film condensation/evaporation on a vertically fluted surface
Authors: Johnson R. E. , Conlisk A. T.
Published: April 2006

Laminar-film flow with condensation or evaporation on a vertical fluted cylinder is examined. A kinematic wave equation describing the evolution of the film profile is obtained and solutions presented. The film profile evolves owing to axial, gravity-driven flow and transverse, surface-tension-driven flow from the crests to the valleys of the fluted cylinder. In the case of condensation the majority of the film reaches a uniform thickness and consequently there is a significant improvement in heat transfer compared with the classical unfluted result where the film thickens in an unbounded fashion. For evaporation a critical value of a parameter which involves the ratio of the Weber number and the gradient of the surface curvature is found below which the film totally drys out and above which the fluid funnels into tapering rivulets and only partially drys out. Typical dry-out lines are presented. For short cylinders the evaporative mass transfer for a fluted cylinder is slightly greater than that predicted for an unfluted case. However, when the cylinder is long the mass transfer is far less for a fluted cylinder owing to the reduction in film area associated with partial film dry out.
The stability of a large gas bubble rising through liquid
Authors: Batchelor G. K.
Published: April 2006

The upper surface of a large gas bubble rising steadily through liquid under gravity is a statically unstable interface, and if the liquid were stationary small sinusoidal disturbances to the interface with wavelength exceeding the critical value Λcdetermined by surface tension would grow exponentially. The existence of the deforming motion of the liquid adjoining the interface of a steadily rising bubble changes the nature of the problem of stability. It is shown that a small sinusoidal disturbance of the part of the interface that is approximately plane and horizontal remains sinusoidal, although with exponentially increasing wavelength. The amplitude of such a disturbance increases, from the instant at which Λ = Λcuntil Λ becomes comparable with the radius of curvature of the interface (R), and the largest amplification occurs for a disturbance whose initial wavelength is approximately equal to Λc. With a plausible guess at the disturbance amplitude and wavelength at which bubble break-up due to nonlinear effects is inevitable, it is possible to obtain an approximate numerical relation between the initial magnitude of the disturbance and the maximum value ofRfor which a bubble remains intact. This relation applies both to a spherical-cap bubble in a large tank and a bubble rising in a vertical tube in which the liquid far ahead of the bubble is stationary. The few published observations of the maximum size of spherical-cap bubbles are not incompatible with the theory, but lack of information about the magnitude of the ambient disturbances in the liquid precludes any close comparison.
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.
Viscous laminar flow in a curved pipe of elliptical cross-section
Authors: Topakoglu H. C. , Ebadian M. A.
Published: April 2006

In this paper, the analysis on secondary flow in curved elliptic pipes of Topakoglu & Ebadian (1985) has been extended up to a point where the rate-of-flow expression is obtained for any value of flatness ratio of the elliptic cross-section. The analysis is based on the double expansion method of Topakoglu (1967). Therefore, no approximation is involved in any step other than the natural limitation of the finite number of calculated terms of the expansions. The obtained results are systematically plotted against the curvature of centreline of the curved pipe for different values of Reynolds number.
Ideal jet flow in two dimensions
Authors: Dias Frédéric , Elcrat Alan R. , Trefethen Lloyd N.
Published: April 2006

A jet is a stream of one fluid entering another at high speed. In the simplest classical model of jet flow, the geometry is two-dimensional, gravity and viscosity are ignored, the moving fluid is a liquid, and the stationary fluid is a gas whose influence is assumed negligible. The description of this idealized flow can be reduced to a problem of complex analysis, but, except for very simple nozzle geometries, that problem cannot be solved analytically. This paper presents an efficient procedure for solving the jet problem numerically in the case of an arbitrary polygonal nozzle.
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.
Direct simulation of a turbulent boundary layer up to Rθ = 1410
Authors: Spalart Philippe R.
Published: April 2006

The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between Rθ = 225 and Rθ = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectral method with up to about 107 grid points. Periodic spanwise and streamwise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.
The run-off condition for coating and rimming flows
Authors: Preziosi Luigi , Joseph Daniel D.
Published: April 2006

A layer of liquid can be supported on the inside or outside of a horizontal rotating cylinder if the viscous forces pulling the liquid around with the cylinder are large enough to overcome the force of gravity. If there are places on the cylinder where the thickness of the layer is larger than a critical value, the excess fluid will run off. For a given maximum thickness the critical condition may be expressed as the minimum speed at which the given layer can be maintained. An approximation of the critical condition using lubrication theory was given by Wallis (1969) and by Deiber & Cerro (1976) for rimming flow and by Moffatt (1977) for coating and rimming flow. Here we address the question of the axial variations of the free surface on the coating layers, and show that they are dominated by the same type of balance between capillarity and centripetal acceleration which determines the shape of rotating drops and bubbles in the absence of gravity. The main results of this paper are the experiments which establish the validity of approximations used to describe the underlying fluid mechanics involved in rimming and coating flows.
Capillary hydrodynamic effects in high magnetic fields
Authors: Berkovsky B. M. , Smirnov N. N.
Published: April 2006

A set of hydrodynamic equations has been applied to processes occurring in non-conductive fluids placed into magnetic fields. The equations are valid for equilibrium magnetization within the framework of a continuous medium. The ranges of physical parameters have been evaluated for which magnetization of a fluid should be taken into account in problems concerning the determination of equilibrium forms, and flows and their stability. The conclusion has been drawn that magnetization of natural fluids in these problems must be taken into consideration for fluids in high (exceeding 1 T) magnetic fields. As examples, the solutions of several typical problems concerning the equilibrium surface of capillary fluids and their stability in external magnetic fields have been considered. Hydrodynamic effects related to magnetization of natural capillary fluids in high magnetic fields are studied with due regard for the above solutions. Hydrodynamic effects in para- and diamagnetic fluids have been studied and the common and distinctive features of these effects discussed.
Three-dimensional Rayleigh-Taylor instability Part 1. Weakly nonlinear theory
Authors: Jacobs J. W. , Catton I.
Published: April 2006

Three-dimensional weakly nonlinear Rayleigh-Taylor instability is analysed. The stability of a confined inviscid liquid and an overlying gas with density much less than that of the liquid is considered. An asymptotic solution for containers of arbitrary cross-sectional geometry, valid up to order ε3 (where ε is the root-mean-squared initial surface slope) is obtained. The solution is evaluated for the rectangular and circular geometries and for various initial modes (square, hexagonal, axisymmetric, etc.). It is found that the hexagonal and axisymmetric instabilities grow faster than any other shapes in their respective geometries. In addition it is found that, sufficiently below the cutoff wavenumber, instabilities that are equally proportioned in the lateral directions grow faster than those with longer, thinner shape. However, near the cutoff wavenumber this trend reverses with instabilities having zero aspect ratio growing faster than those with aspect ratio near 1.
A general method for determining upstream effects in stratified flow of finite depth over long two-dimensional obstacles
Authors: Baines Peter G.
Published: April 2006

A procedure for determining the flow which results from introducing a long two-dimensional obstacle of finite height into a unidirectional, two-dimensional, stable, but otherwise arbitrary stratified shear flow of finite depth is described. The method is based on a generalization of the known results for two-layer flows, described in Baines (1984). The flow is assumed to be hydrostatic with negligible mixing, and the stratified flow is represented by an arbitrary number of discrete layers, so that the model is hydraulic in character. The procedure involves the calculation of the changes to the steady-state flow resulting from successive increases in the height of the topography from zero. For a given initial flow, introduction of an obstacle only alters the flow in its vicinity for obstacle heights hm less than a height hc, where the flow is critical (implying zero wave speed) at the obstacle crest for some particular internal wave mode. Increasing the obstacle height further causes the flow to adjust to maintain a critical condition at the obstacle crest, and this causes disturbances with the structure of the critical mode to be propagated upstream. These may take the form of an upstream hydraulic jump or of a time-dependent rarefaction (implying a disturbance which becomes increasingly spread out with time), or both, depending on the nonlinear dispersive properties of the system. Their passage past a given upstream location results in a permanent change to the local velocity and density profiles. As the obstacle height is further increased these processes will continue until the flow becomes critical just upstream of the obstacle, or a fluid layer becomes blocked. For greater obstacle heights the above phenomena may be repeated with other modes. A numerical procedure which implements these processes has been developed, and examples of applicatons to two- and three-layer systems are given.
Magnetohydrodynamic Flow and Turbulence: a report on the Fifth Beer-Sheva Seminar
Authors: Branover H. , Moffatt H. K. , Mond M. , Pierson E. S. , Sulem P. S. , Yakhot A.
Published: April 2006

This paper is a summary of the Fifth Beer-Sheva Seminar on Magnetohydrodynamic (MHD) Flows and Turbulence, held in Jerusalem during 2–6 March 1987, with 99 participants from 12 countries. Reviews and research papers were presented on general problems of turbulence, MHD turbulence, fundamental MHD, two-phase flows with and without magnetic fields, and on different applications of liquid-metal MHD, especially in power generation nuclear fission and fusion, and in metallurgy.
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.
A jet in crossflow
Authors: Needham D. J. , Riley N. , Smith J. H. B.
Published: April 2006

The flow of a jet of an inviscid, incompressible fluid emerging from a cylindrical pipe, of circular cross-section, into a stream of the same fluid is considered. The component of the external flow normal to the axis of the pipe is taken to be small compared with the speed of the jet. The results throw some light on the mechanisms that are responsible for the observed deflection of jets into the crossflow direction.
Numerical shock propagation in non-uniform media
Authors: Schwendeman D. W.
Published: April 2006

A general numerical scheme is developed to calculate the motion of shock waves in gases with non-uniform properties. The numerical scheme is based on the approximate theory of geometrical shock dynamics. The refracted shockfronts at both planar and curved gas interfaces are calculated. Both regular and irregular refraction patterns are obtained, and in particular, precursor-irregular refraction systems are found using the approximate theory. The numerical results are compared with recent theoretical and experimental investigations. It is shown that the shockfronts determined using geometrical shock dynamics are in good agreement with the actual shock waves.
Simulation of free boundaries in flow systems by lattice-gas models
Authors: Clavin P. , Lallemand P. , Pomeau Y. , Searby G.
Published: April 2006

It has been recently proved that lattice-gas models with Boolean particles can provide a very powerful method to study viscous flows at moderate Reynolds and small Mach numbers (d'Humières, Pomeau & Lallemand 1985; Frisch, Hasslacher & Pomeau 1986; d'Humières & Lallemand 1986). We present here algorithms for an extension of these models to provide a simple and efficient way to simulate a large variety of flow problems with free boundaries. This is done by introducing two different types of particles that can react following a specific kinetic scheme based on autocatalytic reactions. In order to check the powerful character and the reliability of the method we also present preliminary results of two-dimensional computer simulations concerning problems ranging from the competition between molecular diffusion and turbulent mixing in flows presenting a Kelvin-Helmholtz instability to the spontaneous generation of turbulence in premixed flame fronts subject to the Darrieus-Landau instability. The dynamics of an interface developing a Rayleigh-Taylor instability is also considered as well as some typical problems of phase transition such as spinodal decomposition and the nucleation process.
Oscillatory flow and mass transport in a curved tube
Authors: Eckmann David M. , Grotberg James B.
Published: April 2006

Transport of soluble material is analysed for volume-cycled oscillatory flow in a curved tube. The equations of motion are solved using a regular perturbation method for small ratio of tube radius to radius of curvature and order unity amplitude over a range of the Womersley parameter. The transport equation is similarly solved by a regular perturbation scheme where uniform steady end concentrations and no wall flux are assumed. The time-average axial transport of solute is calculated. There is substantial modification of transport compared to the straight-tube case and the results are interpreted with respect to pulmonary gas exchange.
On wavy instabilities of the Taylor-vortex flow between corotating cylinders
Authors: Nagata Masato
Published: April 2006

At least four wavy instabilities are found numerically by analysing the linear stability of Taylor-vortex flow (TVF) in the limit of a small gap between two concentric cylinders which rotate differentially in the same direction. Two of the wavy instabilities, including the one leading to conventional wavy vortex (WVF), have the same axial wavelength as TVF at the onset of instability, while the other two are characterized by subharmonic modes with axial wavelengths twice as long as those of TVF. The two subharmonic instabilities appear to correspond to the wavy-inflow-boundary flow (WIB) and the wavy-outflow-boundary flow (WOB) observed in the experiment of Andereck, Liu & Swinney (1986). The phase velocities, measured in the rotating frame of reference, of all the wavy instabilities are non-zero at the onset except that the phase velocity of WVF vanishes in the region where the average rotation rate Ω of the cylinders is small. By using this simple bifurcation property of WVF for small Ω, time-independent finite-amplitude non-axisymmetric solution branches bifurcating from TVF are followed numerically. The most interesting findings are that some of the solution branches cross the line Ω = 0, producing three-dimensional nonlinear solutions in plane Couette flow.
A simple example from flat-ship theory
Authors: Cole Susan
Published: April 2006

This paper describes the induced pressure distribution, free-surface waves, vortical flow and wave drag of an exact solution of low-aspect-ratio flat-ship theory. An energy balance is derived which relates the spray drag, the energy carried away by the far-field waves and the vortical flow to the total wave drag.
Steady viscous flow past a sphere at high Reynolds numbers
Authors: Fornberg Bengt
Published: April 2006

Numerical solutions are presented for steady incompressible flow past a sphere. At high Reynolds numbers (results are presented up to R = 5000), the wake is found to resemble a Hill's spherical vortex.
On vortex formation from a cylinder. Part 2. Control by splitter-plate interference
Authors: Unal M. F. , Rockwell D.
Published: April 2006

Control of vortex formation from a circular cylinder by a long plate in its wake is examined over the Reynolds number range 140 < Re < 3600. There are two basic flow regimes: a pre-vortex formation regime, in which the plate precludes formation of a large-scale vortex upstream of the tip of the plate; and a post-vortex formation regime in which one or more large-scale vortices are formed upstream of the edge. The unsteady pressure loading at the tip of the plate increases by over an order of magnitude during transition from the pre- to post-vortex formation regime. If the plate is located near the cylinder, it is possible to more than double the vortex formation length, relative to the case of the free wake. Moreover, these observations suggest that: there is a minimum streamwise lengthscale for development of the absolute instability of the near wake and thereby the large-scale vortex; and the vortex formation length may also be influenced by the downstream vorticity dynamics. When the plate is located downstream of the initially formed vortex, effective control is possible when the near-wake fluctuation level and mean base pressure of the corresponding free (non-impinging) wake are sufficiently small. This occurs in the low and moderate subcritical regimes; the substantial control by the wake-plate interaction in this range of Reynolds number implies low strength of the absolute instability of the near wake. However, in the pure von Kármán regime, selfcontrol of the near wake dominates that imposed by the wake-edge interaction, suggesting a strong absolute instability of the near wake.
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〉.
Linearized dynamics of two-dimensional bubbly and cavitating flows over slender surfaces
Authors: D'Agostino Luca , Brennen Christopher E. , Acosta Allan J.
Published: April 2006

The present work investigates the dynamics of two-dimensional, steady bubbly flows over a surface and inside a symmetric channel with sinusoidal profiles. Bubble dynamics effects are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. Energy dissipation due to viscous, thermal and liquid compressibility effects in the dynamics of the bubbles is included, while the relative motion of the two phases and viscous effects at the flow boundaries are neglected. The results are then generalized by means of Fourier synthesis to the case of surfaces with slender profiles of arbitrary shape. The flows display various flow regimes (subsonic, supersonic and super-resonant) with different properties according to the value of the relevant flow parameters. Examples are discussed in order to show the effects of the inclusion of the various energy dissipation mechanisms on the flows subject to harmonic excitation. Finally the results for a flow over a surface with a Gaussian-shaped bump are presented and the most important limitations of the theory are briefly discussed.
The dynamics and structure of double-diffusive layers in sidewall-heating experiments
Authors: Tanny J. , Tsinober A. B.
Published: April 2006

The dynamics and structure of double-diffusive layers were studied experimentally by heating a linear stable solute gradient from a sidewall in a wide tank. The formation and subsequent development of the layers were investigated by various flow-visualization techniques, namely fluorescent dye, fluorescent particles and shadowgraph. Experiments were performed in order to determine the stability diagram of the flow, following in each experiment the phase trajectory of the system in the phase plane of thermal and solute Rayleigh numbers. The experimentally obtained stability diagram appears to be similar to that obtained numerically by Thangam et al. (1981) and by Hart (1971) for a vertical narrow slot and a steady basic flow. It is shown that if the temperature of the sidewall rises slowly to its prescribed value, the thickness of the initial layers, formed at the onset of instability, is a function of the ambient density gradient and fluid properties only. On the other hand, if the wall temperature rises quickly (almost impulsive heating), the thickness of the initial layers is proportional to the imposed temperature difference, provided that the Rayleigh number, based on this difference, is larger than some critical value which is associated with the first merging of the layers. A criterion for the first merging of the initial layers is obtained, and it is suggested that this merging is due to subsequent instability of the system. The subsequent merging process, following the first merging, is not a simple successive doubling of the layer thickness and in each of five nearly identical experiments a different dependence of the average layer thickness on the instantaneous Rayleigh number is obtained. This indicates that the system of layers behaves chaotically after the first merging. The final thickness of the layers depends on the prescribed lateral temperature difference, and the ratio between the final and the initial thickness of the layers is a linear function of the final Rayleigh number. Flow-visualization experiments indicate that the layers consist of vortices with vertical scale of the layer thickness and various horizontal scales.
Statistical characteristics of wall turbulence with a passive scalar
Authors: Nagano Y. , Tagawa M.
Published: April 2006

Various types of moments of velocity and scalar fluctuations of the first to the fourth order have been measured and analysed. First, an orthogonal series expansion for the three-dimensional joint probability density function (p.d.f.) is developed using the cumulants and Hermite polynomials. This p.d.f. is found to provide satisfactory predictions for the statistical characteristics, including triple products, of turbulent momentum and scalar transfer. Next, the conditional sampling and averaging technique is employed to investigate the statistical characteristics of coherent turbulent transfer processes of momentum and scalar. Conditional p.d.f.s are developed for various moments of velocity and scalar up to the third order. It is shown that the present p.d.f.s can predict the detailed role of coherent motions in the dynamics of wall turbulent shear flows and in the relevant process of scalar transport by turbulence. In particular, the importance of coherent motions in the turbulent diffusion process of Reynolds-stress components and scalar fluxes is demonstrated for the first time by the present theory.
Effects of finite depth and current velocity on large amplitude Kelvin-Helmholtz waves
Authors: Bontozoglou V. , Hanratty T. J.
Published: April 2006

Over the past decades a large amount of work has been done on inviscid, steady progressive, gravity waves on a free surface. However, waves which occur in nature are never, in fact, free-surface waves, since they are always beneath a fluid of finite density, if only air. In spite of this, very little work has been done on finite-amplitude interfacial waves. Tsuji & Nagata (1973) carried out a perturbation expansion in wave amplitude to fifth order, for interfacial waves between two stationary fluids. Holyer (1979) extended the calculation using the computer and resorted to Pade approximants to sum the resulting series. Meiron & Saffman (1983) investigated numerically the limiting highest wave and demonstrated the existence of over-hanging gravity waves of permanent form.
Time-periodic convection in porous media: transition mechanism
Authors: Steen Paul H. , Aidun Cyrus K.
Published: April 2006

We resolve the disturbance structures that destabilize steady convection rolls in favour of a time-periodic pattern in two-dimensional containers of fluid-saturated porous material. Analysis of these structures shows that instability occurs as a travelling wave propagating in a closed loop outside the nearly motionless core. The travelling wave consists of five pairs of thermal cells and four pairs of vorticity disturbances in the case of a square container. The wave speed of the thermal disturbances is determined by an average base-state velocity and their structure by a balance between convection and thermal diffusion. Interpretation of the ‘exact’ solution is aided by a one-dimensional convection-loop model which correlates (i) point of transition, (ii) disturbance wavenumber, and (iii) oscillation frequency given the base-state temperature and velocity profiles. The resulting modified Mathieu-Hill equation clarifies the role of the vertical pressure gradient, induced by the impenetrable walls, and the role of the base-state thermal layer.
A study of forces, circulation and vortex patterns around a circular cylinder in oscillating flow
Authors: Obasaju E. D. , Bearman P. W. , Graham J. M. R.
Published: April 2006

Measurements of sectional and total forces and the spanwise correlation of vortex shedding are presented for a circular cylinder in planar oscillatory flow at Keulegan-Carpenter numbers, KC, in the range from about 4 to 55. The viscous parameter β is in the range from around 100 to 1665. Circulation measurements around a circuit close to and enclosing the cylinder, are also presented. A mode-averaging technique was used for both sectional forces and circulation measurements and this gave, for typical modes of vortex shedding, time histories over an average cycle. The transverse force and the circulation tend to fluctuate in sympathy with each other, except around the instant of flow reversal when the force changes sign but the circulation remains high. Values of the strength of shed vortices, estimated from the measured circulation, are found to be comparable with steady-flow results. For KC [lsim ] 30, modes of vortex shedding occur over distinct ranges of KC with spanwise correlation high at the centre of a KC-range for a particular mode of shedding but low at the boundaries. Above KC ≈ 30 the correlation is no longer very sensitive to KC and the correlation length is estimated to be equal to 4.65 cylinder diameters. In the transverse vortex-street regime (8 [lsim ] KC [lsim ] 15) the cylinder was found to experience a steady transverse force, the coefficient of which is estimated to be about 0.5 at KC = 14.