bluuebunny/crossref_metadata_2025 huggingface dataset:
Amplitude equations for wave packets in slightly inhomogeneous unstable flows
Authors: Balsa T. F.
Published: April 2006

We derive several versions of the (complex) amplitude equation of an inviscid wave packet travelling on a slightly inhomogeneous (and possibly unsteady and viscous) unstable base flow. This is done with complete generality, without any reference to the dimensions of physical and propagation spaces, by using the usual high-frequency ansatz. The final results are extremely simple: volume integrals of a complex wave action density are conserved subject to an appropriate flux and a source term. The latter is expressible in a remarkably concise way in terms of the gradient of the base flow acceleration and vanishes when the base flow is inviscid. The simplicity of our results hinges on a transformation of the dependent variables and on a suitable decomposition of these in cross- and propagation spaces. Our results are also discussed with the help of three different Lagrangian densities and their associated kinematic wave theories which are based on a basic identity due to Hayes.
Secondary flows and vortex formation around a circular cylinder in constant-shear flow
Authors: Woo H. G. C. , Cermak J. E. , Peterka J. A.
Published: April 2006

A pair of curved gauzes with non-uniform porosity was used to generate a strong constant-shear flow with low turbulence intensity. The complex features of this flow around a circular cylinder with its axis normal to the vorticity and mean velocity vectors were studied. Methods such as the use of end plates, inclusion of gaps at the junctions of the cylinder with the end plates, and fluid withdrawal were applied to minimize end effects. Exploratory studies were made to investigate shear effects on the vortex-wake formation region with Reynolds numbers between 800 and 1.4 × 104. Effects of the steepness factor on vortex formation were explained by regarding secondary flow in the base region of the cylinder as negative base bleeding which behaves as a wake interference element.
The superharmonic instability of Stokes waves in deep water
Authors: Jillians W. J.
Published: April 2006

The method of Tanaka (1983) is used to solve the eigenvalue problem determining the form of the first superharmonic instability of periodic Stokes waves. Comparisons are made with other approaches to this problem and a discussion of the advantages of Tanaka's method is given. The accurately resolved eigenfunction solution is then taken as the initial state for commencing the computational time-stepping method of Dold & Peregrine (1985), by which we investigate the full nonlinear development of the growing and decaying modes of this instability. It is observed that all unstable modes develop to breaking in the periodic regime and this result is compared and contrasted with the solitary wave case.
On the stability of Kelvin waves
Authors: Melville W. K. , Tomasson G. G. , Renouard D. P.
Published: April 2006

We consider the evolution of weakly nonlinear dispersive long waves in a rotating channel. The governing equations are derived and approximate solutions obtained for the initial data corresponding to a Kelvin wave. In consequence of the small nonlinear speed correction it is shown that weakly nonlinear Kelvin waves are unstable to a direct nonlinear resonance with the linear Poincaré modes of the channel. Numerical solutions of the governing equations are computed and found to give good agreement with the approximate analytical solutions. It is shown that the curvature of the wavefront and the decay of the leading wave amplitude along the channel are attributable to the Poincaré waves generated by the resonance. These results appear to give a qualitative explanation of the experimental results of Maxworthy (1983), and Renouard, Chabert d'Hières & Zhang (1987).
Flow in random porous media: mathematical formulation, variational principles, and rigorous bounds
Authors: Rubinstein Jacob , Torquato S.
Published: April 2006

The problem of the slow viscous flow of a fluid through a random porous medium is considered. The macroscopic Darcy's law, which defines the fluid permeabilityk, is first derived in an ensemble-average formulation using the method of homogenization. The fluid permeability is given explicitly in terms of a random boundary-value problem. General variational principles, different to ones suggested earlier, are then formulated in order to obtain rigorous upper and lower bounds onk. These variational principles are applied by evaluating them for four different types of admissible fields. Each bound is generally given in terms of various kinds of correlation functions which statistically characterize the microstructure of the medium. The upper and lower bounds are computed for flow interior and exterior to distributions of spheres.
Rotating stratified flow past a steep-sided obstacle: incipient separation
Authors: Foster M. R.
Published: April 2006

Many of the most interesting phenomena observed to occur in the flow of rotating and stratified fluids past obstacles, for example eddy shedding and wake unsteadiness, are due to separation of the boundary layer on the obstacle or its Taylor column. If the Rossby number of the flow lies between E½ and E (E is the Ekman number) and the Burger number is small, the structure of a viscous shear layer of width E⅙ on the circumscribing cylinder of an axisymmetric obstacle controls the inviscid flow. The surface boundary layer is not an Ekman layer, but a Prandtl layer, even at small Rossby numbers. As the slope of the obstacle at its base increases, the nature of the inviscid motion is altered substantially, in the rotation-dominated regime. We show that, for sufficiently large slopes, the flow develops a small region of non-uniqueness external to the column, simultaneously with the separation of the narrow band of fluid flowing round the base of the object.
On the lengthscales of laminar shock/boundary-layer interaction
Authors: Katzer Edgar
Published: April 2006

The interaction of an oblique shock with a laminar boundary layer on an adiabatic flat plate is analysed by solving the Navier-Stokes equations numerically. Mach numbers range from 1.4 to 3.4 and Reynolds numbers range from 105 to 6 × 105. The numerical results agree well with experiments. The pressure distribution at the edge of the boundary layer is proposed as a sensitive indicator of the numerical resolution. Local and global properties of the interaction region are discussed. In the vicinity of the separation point, local scaling laws of the free interaction are confirmed. For the length of the separation bubble a new similarity law reveals a linear influence of the shock strength. A comparison with the triple-deck theory shows that, for finite Reynolds numbers, the triple deck tends to overestimate the lengthscale substantially and that this discrepancy increases with increasing Mach number. The triple-deck model of displacing the main part of the boundary layer is substantiated by the numerical results. An asymmetrical structure within the separation bubble causes a characteristic distribution of the wall shear stress.
Numerical simulations of multiple flow transitions in axisymmetric annulus convection
Authors: Quéré P. Le , Pécheux J.
Published: April 2006

We examine numerically the behaviour of the solutions of the axisymmetric Boussinesq equations in a tall, differentially heated, air-filled annulus. The numerical algorithm integrates the time-dependent equations in primitive variables and combines a pseudospectral Chebyshev spatial expansion with a second-order time-stepping scheme. The instability of the conduction regime is found to be unsteady cross-rolls. By assuming Hopf bifurcation, we can accurately determine the critical Rayleigh number. As the Rayleigh number increases, the solution is monoperiodic at first. Then it undergoes a period-doubling bifurcation. When the Rayleigh number is further increased, the solution reverts to a monocellular steady state through suberitical bifurcations with hysteresis. At even higher Rayleigh number, boundary-layer instability sets in, in the form of travelling waves. This instability has the characteristics of a supercritical Hopf bifurcation. We examine the space-time structure of the two types of unsteady solutions. We have presented the basic periods of the steady oscillations as functions of the Rayleigh number in the vicinity of the Hopf bifurcation points, and have also computed the Nusselt numbers for the various flow regimes.
On the flow between a porous rotating disk and a plane
Authors: Goldshtik M. A. , Javorsky N. I.
Published: April 2006

Axisymmetric flow of viscous incompressible fluid between a rotating porous disk and an impermeable fixed plane is investigated. It is shown that with injection and suction through a porous disk rotating with sufficiently large angular velocity there are many isolated steady self-similar solutions. In the case of suction through a fixed porous disk at a certain Reynolds number there exists bifurcation of the stable rotational regime of flow, implying a spontaneous break of the flow symmetry and an arbitrary rise of the fluid rotation within the framework of self-similarity. This unusual effect is discussed in detail, and the results of a relevant experiment are presented. Another unusual result is the existence of multicellular regimes consistent with suction, when the lift force acting on a rapidly rotating porous disk is anomalously large; in this case some of these regimes are stable relative to self-similar perturbations.

With sufficiently strong suction and rotation the stationary solution with large lift becomes unstable and the regime of self-oscillations arises. Diagrams of the possible stationary flow regimes have been constructed, and the stable ones have been identified. At the limit of vanishing viscosity we find, in the case of the suction, non-classical boundary layers on the solid surfaces characterized by a finite jump of the normal component of the velocity and unlimited tangential components. In this limit, in the interior flow region the singular non-viscous solution with an infinite velocity of rotation arises, while all limited non-singular admissible non-viscous solutions are not stable.
Nonlinear evolution of oblique waves on compressible shear layers
Authors: Goldstein M. E. , Leib S. J.
Published: April 2006

We consider the effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams. The analysis shows that mean temperature non-uniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integro-differential equation which bears some resemblance, to the Landau equation in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. We show that inviscid solutions always end in a singularity at a finite downstream distance but that viscosity can eliminate this singularity for certain parameter ranges.
Momentum disturbances and wave trains
Authors: Dixon A.
Published: April 2006

The effects of a reduction in momentum flux on the downstream flow characteristics of a steady, two-dimensional flow are investigated. In particular, quantities such as the changes in mean depth, mean fluid velocity, mean kinetic and potential energies and the length of the induced downstream wave are examined. This is done with the use of a fourth-order perturbation expansion in wave slope. The results are compared with the conflicting results that had been obtained previously by different authors. Agreement is found with the second-order theory of Benjamin (1970), but the work of Doctors & Dagan (1980) is found to be in error and is corrected.
Spectra and energy transfer in stably stratified turbulence
Authors: Itsweire E. C. , Helland K. N.
Published: April 2006

The influence of stabilizing buoyancy forces on the spectral characteristics and spectral energy transfer of grid-generated turbulence was studied in a ten-layer closed-loop stratified water channel. The results are compared to the limiting ideal cases of the three-dimensional turbulence and two-dimensional turbulence theories. The velocity power spectra evolve from a classical isotropic shape to a shape of almost k−2 after the suppression of the net vertical mixing. This final spectral shape is rather different from the k−3 to k−4 predicted by the theory of two-dimensional turbulence and could result from the interaction between small-scale internal waves and quasi-two-dimensional turbulent structures as well as some Doppler shift of advected waves. Several lengthscales are derived from the cospectra of the vertical velocity and density fluctuations and compared with the buoyancy, overturning and viscous lengthscales measured in previous studies, e.g. Stillinger, Helland & Van Atta (1983) and Itsweire, Helland & Van Atta (1986). The smallest turbulent scale, defined when the buoyancy flux goes to zero, can be related to the peak of the cospectra of the buoyancy flux. This new relationship can be used to provide a measure of the smallest turbulent scale in cases where the buoyancy flux never goes to zero, i.e. a growing turbulent stratified shear flow. Finally, the one-dimensional energy transfer term computed from the bispectra shows evidence of a reverse energy cascade from the small scales to the large scales far from the grid where buoyancy forces dominate inertial forces. The observed reverse energy transfer could be produced by the development of quasi-two-dimensional eddies as the original three-dimensional turbulence collapses.
Convection in a rotating cavity: modelling ocean circulation
Authors: Condie Scott A. , Griffiths Ross W.
Published: April 2006

Large-scale oceanic flows, ranging from large estuaries to basin-scale abyssal circulation, can be driven by imposed lateral density gradients and are significantly influenced by the Earth's rotation. Some essential features of such flows have been incorporated into a laboratory model by differentially heating and cooling the vertical endwalls of a shallow rectangular cavity, rotating about a vertical axis through its centre. In this paper, the flow observed after this system had been allowed to develop to a steady mean state is described. Measurements were made of the velocity and temperature fields, as well as the variability in temperature field associated with eddy motions. The temperature data were also used to calculate the potential vorticity distribution within the cavity. These results indicate that the heated and cooled end-walls acted not only as continuous sources of buoyancy, but also of anomalous potential vorticity. It is shown that the potential vorticity served as an indicator and tracer of the laboratory flow. The structure and location of boundary currents were largely determined by nonlinear potential vorticity dynamics which resulted in a mean circulation consisting of two basin-scale counter-rotating gyres. This flow differed markedly from the initial boundary currents set up by Kelvin waves.
Lagrangian approach to the mean-field electrodynamics for turbulent fluids with arbitrary conductivities
Authors: Kichatinov L. L.
Published: April 2006

A modification is made to the traditional Lagrangian approach to the derivation of the mean EMF of turbulent fluids which allows for finite conductivities. Consideration is confined to the case of homogeneous, isotropic but generally mirrornon-invariant and compressible turbulence. The eddy magnetic diffusivity and the coefficient α of the alpha-effect are expressed in terms of statistical moments of displacements of adjacent particles which undergo convective transport and microscopic diffusion in a turbulent flow. These expressions, being valid for arbitrary conductivities, reproduce known results in the cases of both very large and very small magnetic Reynolds numbers. Difficulties and advantages of the use of the results obtained for evaluations of the mean EMF are discussed.
Wave patterns in plane Poiseuille flow created by concentrated disturbances
Authors: Li Fei , Widnall Sheila E.
Published: April 2006

A model is constructed for perturbations created in the surrounding laminar flow by a turbulent spot in plane Poiseuille flow. The turbulent spot is represented as a distribution of increased Reynolds stress, which travels steadily through the surrounding laminar flow. The Navier-Stokes equations are linearized and are solved by using Fourier transforms in the plane parallel to the channel walls and a finite-difference method in the direction perpendicular to the walls. The travelling Reynolds stress distribution acts as a forcing term in the equations.

Numerical results show that a packet of oblique waves are generated around the disturbance when the force is antisymmetric with respect to the channel centreline, whereas no identifiable wave crests are found when the forcing is symmetric. Furthermore, wavelengths of the typical waves composing the packet are insensitive to the size of the region of Reynolds stress. The dependencies of the flow field on Reynolds number and spot speed are investigated. In the case of symmetric forcing, the flow is forced around the disturbance, causing distortions to the basic velocity profiles. These results are in qualitative agreement with experimental observations.
Large-scale structure in the far field of byoyant jets
Authors: Papantoniou Dimitris , List E. John
Published: April 2006

The flow structure and entrainment mechanisms in the far field of a round vertical buoyant jet have been studied experimentally by use of an optical technique based on laser-induced fluorescence (LIF). A large number of essentially instantaneous tracer concentration profiles were recorded for each experimental run by combining LIF with linear photodiode array imaging and high-speed digital data acquisition. Analysis of the resulting high-resolution flow images indicates that the far-field region is dominated by the periodic passage of structures spanning the entire radial flow extent. Ambient fluid is entrained by vortical motions and is transported to regions deep into the flow interior. Correlation analysis discloses that the passage frequency of the structures scales with the local mean velocity and flow width. Conditional averaging of the data indicates that the downstream frontal region of the structure is well mixed and at higher concentration level than the back and side regions where ambient fluid is intermittently present. This results in an axial concentration gradient within the structure, analogous to the ramp-like pattern previously observed in heated air jets. In comparison to the momentum-driven flow the ambient fluid presence in the flow interior is greatly increased when body forces are the driving mechanism. This appears to result from the influence of buoyancy forces in the production of turbulent vortices at the integral scale. An important feature of both the momentum-driven and buoyancy-driven flows investigated is the strongly intermittent character of the concentration field. This raises the issue of the appropriateness of gradient-diffusion theories for the description of such flows.
Long-time evolution and regions of existence of parametrically excited nonlinear cross-waves in a tank
Authors: Shemer Lev , Kit Eliezer
Published: April 2006

Results of an experimental and numerical study of parametrically excited nonlinear cross-waves in the vicinity of the cut-off frequency, are reported. Experiments are performed at three cross-wave modes and in the whole range of existence of cross-waves. Numerical studies are based on the solution of the nonlinear Schrödinger equation with a boundary condition at the wavemaker which corresponds to parametric excitation. The validity of the scaling procedure adopted in the model is verified experimentally. Dissipation is incorporated in the model equation and in the wavemaker boundary condition. The influence of the wave breaking on the range of existence of cross-waves is discussed and the relation between the maximum possible steepness of cross-waves and the limits of their existence is obtained.
Chaotic advection by laminar flow in a twisted pipe
Authors: Jones Scott W. , Thomas Oran M. , Aref Hassan
Published: April 2006

The appearance of chaotic particle trajectories in steady, laminar, incompressible flow through a twisted pipe of circular cross-section is demonstrated using standard dynamical systems diagnostics and a model flow based on Dean's perturbation solutions. A study is performed to determine the parameters that control fluid stirring in this mixing device that has no moving parts. Insight into the chaotic dynamics are provided by a simple one-dimensional map of the pipe boundary onto itself. The results of numerical experiments illustrating the stretching of material lines, stirring of blobs of material, and the three-dimensional trajectories of fluid particles are presented. Finally, enhanced longitudinal particle dispersal due to the coupling between chaos in the transverse direction and the non-uniform longitudinal transport of particles is shown.
Geometric properties of deep-water breaking waves
Authors: Bonmarin P.
Published: April 2006

The time-space evolution of a steep water wave reaching the breaking stage is observed by means of a visualization technique. In particular, the asymmetry of the wave profile in the near-breaking region is displayed. Measurements at breaking onset on a sample of breaking waves show a relation between the rate of asymmetry growth and the breaker type. The shape evolution of a plunging crest after breaking has started, and the related splash-up phenomenon and its part in the air-entrainment process are also observed.
Two-dimensional periodic waves in shallow water
Authors: Hammack Joe , Scheffner Norman , Segur Harvey
Published: April 2006

Experimental data are presented that demonstrate the existence of a family of gravitational water waves that propagate practically without change of form on the surface of shallow water of uniform depth. The surface patterns of these waves are genuinely two-dimensional and fully periodic, i.e. they are periodic in two spatial directions and in time. The amplitudes of these waves need not be small; their form persists even up to breaking. The waves are easy to generate experimentally, and they are observed to propagate in a stable manner, even when perturbed significantly. The measured waves are described with reasonable accuracy by a family of exact solutions of the Kadomtsev-Petviashvili equation (KP solutions of genus 2) over the entire parameter range of the experiments, including waves well outside the putative range of validity of the KP equation. These genus-2 solutions of the KP equation may be viewed as two-dimensional generalizations of cnoidal waves.
Hydrodynamic theory of glancing impact
Authors: Frankel I. , Weihs D.
Published: April 2006

Penetration of high-speed targets, such as missiles or satellites, involves a glancing impact resulting from the velocities of the target and the projectile not necessarily being parallel to one another. Glancing is different from oblique impact in that here the target is in lateral motion relative to the projectile (at speeds that may be comparable).

The effect of the transverse motion of the target on the penetration performance is analysed by means of a hydrodynamic model. As is usually done, both the projectile and target materials are taken to behave as ideal fluids, owing to the large stresses obtained upon impact. A complete description of the flow field is obtained for the planar case, making use of a transformation to the hodograph plane. Owing to the lack of symmetry, the solution is obtained indirectly from the known solution for asymmetrically impinging jets, obtaining a determinate solution by a limit process where the jet representing the target fluid becomes infinitely wide.

The variations of the rate of penetration and the streamline pattern with the respective ratios of target to projectile speeds and densities are studied. It is found that the relative lateral motion of the target causes a decrease in the rate of penetration (in comparison to normal impact). The analysis is utilized to obtain an estimate for the total depth of penetration (relative to the projectile width). Comparison with experimental data of yawed impact available in the open literature shows good agreement with the theoretical predictions when the latter are modified to account for the deceleration of a finite-length projectile.
One-dimensional vibratory instability of planar flames propagating in tubes
Authors: Clavin Paul , Pelcé Pierre , He Longting
Published: April 2006

A complete analysis of the one-dimensional vibratory instability of planar flames of premixed gases propagating in tubes is provided. The driving mechanism results from unsteady coupling between flame structure and acoustic waves through temperature fluctuations. In certain conditions, the strength of such an instability will be proved to be sufficiently strong to produce large-amplitude fluctuations as soon as the flame has travelled a distance of the order of the acoustic wavelength. Stability limits and total amplification of an initial perturbation are computed in the framework of the simple flame mode of a one-step exothermic reaction governed by an Arrhenius law with an activation energy much larger than the thermal energy. Diffusive and thermal effects within the flame are included with a Lewis number different from unity. Damping mechanisms associated with viscous and thermal dissipation at the walls, as well as with loss of acoustic energy by sound radiation from the open end of the tube, are retained. In ordinary conditions, for a reactive mixture with an effective Lewis number close to unity, the predicted instability is weak. In the framework of the simplified flame model used here, islands of strong instabilities are predicted to occur at low Mach numbers for Lewis numbers larger than unity.
Resonantly excited regular and chaotic motions in a rectangular wave tank
Authors: Tsai Wu-Ting , Yue Dick K. P. , Yip Kenneth M. K.
Published: April 2006

We consider the resonant excitation of surface waves inside a rectangular wave tank of arbitrary water depth with a flap-type wavemaker on one side. Depending on the length and width of the tank relative to the sinusoidal forcing frequency of the wave paddle, three classes of resonant mechanisms can be identified. The first two are the well-known synchronous, resonantly forced longitudinal standing waves, and the subharmonic, parametrically excited transverse (cross) waves. These have been studied by a number of investigators, notably in deep water. We rederive the governing equations and show good comparisons with the experimental data of Lin & Howard (1960). The third class is new and involves the simultaneous resonance of the synchronous longitudinal and subharmonic cross-waves and their internal interactions. In this case, temporal chaotic motions are found for a broad range of parameter values and initial conditions. These are studied by local bifurcation and stability analyses, direct numerical simulations, estimations of the Lyapunov exponents and power spectra, and examination of Poincaré surfaces. To obtain a global criterion for widespread chaos, the method of resonance overlap (Chirikov 1979) is adopted and found to be remarkably effective.
On the instabilities of supersonic mixing layers: a high-Mach-number asymptotic theory
Authors: Balsa Thomas F. , Goldstein M. E.
Published: April 2006

The stability of a family of tanh mixing layers is studied at large Mach numbers using perturbation methods. It is found that the eigenfunction develops a multilayered structure, and the eigenvalue is obtained by solving a simplified version of the Rayleigh equation (with homogeneous boundary conditions) in one of these layers which lies in either of the external streams. Our analysis leads to a simple hypersonic similarity law which explains how spatial and temporal phase speeds and growth rates scale with Mach number and temperature ratio. Comparisons are made with numerical results, and it is found that this similarity law provides a good qualitative guide for the behaviour of the instability at high Mach numbers.

In addition to this asymptotic theory, some fully numerical results are also presented (with no limitation on the Mach number) in order to explain the origin of the hypersonic modes (through mode splitting) and to discuss the role of oblique modes over a very wide range of Mach number and temperature ratio.
Centrifugal instability of an oscillatory flow over periodic ripples
Authors: Hara Tetsu , Mei Chiang C.
Published: April 2006

An oscillating flow over a sandy beach can initiate and enhance the formation of bed ripples, with crests perpendicular to the direction of the ambient oscillation. Under certain circumstances, bridges may develop to span adjacent ripple crests, resulting in a brick pattern. It has been suggested that the onset of this transition is due to a three-dimensional centrifugal instability of an otherwise two-dimensional flow over periodic long-crested ripples. Here we analyse theoretically such an instability by assuming that the ripples are rigid and smooth. Two complementary cases are studied. We first consider a weak ambient oscillation over ripples of finite slope in Case (i). The three-dimensional disturbance is found to be localized in a small region either along the crests or along the troughs. In Case (ii) we analyse finite oscillations over ripples of mild slope. The region influenced by the instability is now comparable with a ripple wavelength and the unstable disturbance along adjacent ripples may interact with each other. Four types of harmonic and subharmonic instabilities are found. The associated steady streaming close to the ripple surface shows various tendencies of possible sand accumulations, some of which appear to be qualitatively relevant to the initiation of brick-patterned ripples.
The blockage of gravity and capillary waves by longer waves and currents
Authors: Shyu Jinn-Hwa , Phillips O. M.
Published: April 2006

Surface waves superimposed upon a larger-scale flow are blocked at the points where the group velocities balance the convection by the larger-scale flow. Two types of blockage, capillary and gravity, are investigated by using a new multiple-scale technique, in which the short waves are treated linearly and the underlying larger-scale flows are assumed steady but can have a considerably curved surface and uniform vorticity. The technique first provides a uniformly valid second-order ordinary differential equation, from which a consistent uniform asymptotic solution can readily be obtained by using a treatment suggested by the result of Smith (1975) who described the phenomenon of gravity blockage in an unsteady current with finite depth.

The corresponding WKBJ solution is also derived as a consistent asymptotic expansion of the uniform solution, which is valid at points away from the blockage point. This solution is obviously represented by a linear combination of the incident and reflected waves, and their amplitudes take explicit forms so that it can be shown that even with a significantly varied effective gravity g’ and constant vorticity, wave action will remain conserved for each wave. Furthermore, from the relative amplitudes of the incident and reflected waves, we clearly demonstrate that the action fluxes carried by the two waves towards and away from the blockage point are equal within the present approximation.

The blockage of gravity–capillary waves can occur at the forward slopes of a finite-amplitude dominant wave as suggested by Phillips (1981). The results show that the blocked waves will be reflected as extremely short capillaries and then dissipated rapidly by viscosity. Therefore, for a fixed dominant wave, all wavelets shorter than a limiting wavelength will be suppressed by this process. The minimum wavelengths coexisting with the long waves of various wavelengths and slopes are estimated.
Buoyancy-driven fluid fracture: similarity solutions for the horizontal and vertical propagation of fluid-filled cracks
Authors: Lister John R.
Published: April 2006

Buoyancy-driven flows resulting from the introduction of fluid of one density into a crack embedded in an elastic solid of different density are analysed. Scaling arguments are used to determine the regimes in which different combinations of the buoyancy force, elastic stress, viscous pressure drop and material toughness provide the dominant pressure balance in the flow. The nonlinear equations governing the shape and rate of spread of the propagating crack are formulated for the cases of vertical propagation of buoyant fluid released into a solid of greater density and of lateral propagation of fluid released at an interface between an upper layer of lesser density and a lower layer of greater density. Similarity solutions of these equations are derived under the assumption that the volume of fluid is given by Qtα, where Q and α are constants. Both laminar and turbulent flows are considered.

Fluid fracture is an important mechanism for the transport of molten rock from the region of production in the Earth's mantle to surface eruptions or near-surface emplacement. The theoretical solutions provide simple models which describe the relation between the elastic and fluid-mechanical phenomena involved in the vertical transport of melt through the Earth's lithosphere and in the lateral intrusion of melt at a neutral-buoyancy level close to the Earth's surface.
A note on liquid vortex sloshing and Kelvin's equilibria
Authors: Vatistas Georgios H.
Published: April 2006

Observations of liquid vortex sloshing and Kelvin's equilibrium states were made inside a cylindrical container using a spinning disk near its base. Both steady and periodic free-surface sloshing phenomena were found to take place. During periodic sloshing, the air core sustained shape transformations, assuming an elliptical cross-section at the end, and then collapsed forming a pair of vortices. Kelvin's equilibrium states emerged at lower liquid levels. These were stable within an interval of rotational speeds. The bandwidth of stationary states decreased as the wavenumber (N) increased. For N greater than six, the states appeared critically stable. Between equilibria, unstable transitional regions were found to exist. As the liquid level was decreased, the core shape spectrum shifted towards smaller frequencies.
Competing and coexisting dynamical states of travelling-wave convection in an annulus
Authors: Bensimon D. , Kolodner Paul , Surko C. M. , Williams Hugh , Croquette V.
Published: April 2006

We describe experiments on convection in binary fluid mixtures in a large-aspect-ratio annular container. In this geometry, the convective rolls align radially and travel azimuthally, providing a model of travelling waves in an extended one-dimensional nonlinear dynamical system. Several different stable non-equilibrium states can be produced in this experiment, and the competition between them leads to a wide variety of steady and time-dependent behaviour. The observed spatiotemporal behaviour may shed light on recent theories of the nature of stable nonlinear travelling-wave convection, the pinning of travelling waves, and the creation of spatiotemporal defects.
The mechanism for the long-wave instability in thin liquid films
Authors: Smith Marc K.
Published: April 2006

A physical mechanism for the long-wave instability of thin liquid films is presented. We show that the many diverse systems that exhibit this instability can be classified into two large groups. Each group is studied using the model of a thin liquid film with a deformable top surface flowing down a rigid inclined plane. In the first group, the top surface has an imposed stress, while in the other, an imposed velocity. The proposed mechanism shows how the details of the energy transfer from the basic state to the disturbance are handled differently in each of these cases, and how a common growth mechanism produces the unstable motion of the disturbance.
Dynamical behaviour of natural convection in a single-phase loop
Authors: Ehrhard Peter , Müller Ulrich
Published: April 2006

A one-dimensional model is derived for natural convection in a closed loop. The physical model can be reduced to a set of nonlinear ordinary differential equations of the Lorenz type. The model is based on a realistic heat transfer law and also accounts for a non-symmetric arrangement of heat sources and sinks. A nonlinear analysis of these equations is performed as well as experiments to validate the model predictions.

Both the experimental and the analytical data show that natural convection in a loop is characterized by strong nonlinear effects. Distinct subcritical regions are observed in addition to a variety of stable steady flow regimes. Thus, in certain ranges of the forcing parameter the flow stability depends significantly on the presence of finite perturbation amplitudes. An absolutely unstable range also exists which is characterized by a chaotic time behaviour of the flow quantities. It is also shown that the steady solutions are subject to an imperfect forward bifurcation if heating of the loop is performed non-symmetrically. In such a case one flow direction is preferred at the onset of convection and, moreover, the corresponding steady solution is more stable than a second, isolated, steady solution. The second solution has the opposite flow direction and is stable only in a relatively small, isolated interval. The preferred steady solution becomes unstable against time-periodic perturbations at a higher value of the forcing parameter. A backward- or a forward-directed bifurcation of the periodic solutions is found depending on the non-symmetry parameter of the system.
On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface
Authors: Yiantsios Stergios G. , Davis Robert H.
Published: April 2006

The deformation of a viscous drop, driven by buoyancy towards a solid surface or a deformable interface, is analysed in the asymptotic limit of small Bond number, for which the deformation becomes important only when the drop is close to the solid surface or interface. Lubrication theory is used to describe the flow in the thin gap between the drop and the solid surface or interface, and boundary-integral theory is used in the fluid phases on either side of the gap. The evolution of the drop shape is traced from a relatively undeformed state until a dimple is formed and a long-time quasi-steady-state pattern is established. A wide range of drop to suspending phase viscosity ratios is examined. It is shown that a dimple is always formed, independently of the viscosity ratio, and that the long-time thinning rates take simple forms as inverse fractional powers of time.
A stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence, and its application to the problem of concentration variance
Authors: Thomson D. J.
Published: April 2006

A new stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence is proposed. The model is three-dimensional and its formulation takes account of recent improvements in the understanding of one-particle models. In particular the model is designed so that if the particle pairs are initially well mixed in the fluid, they will remain so. In contrast to previous models, the new model leads to a prediction for the particle separation probability density function which is in qualitative agreement with inertial subrange theory. The values of concentration variance from the model show encouraging agreement with experimental data. The model results suggest that, at large times, the intensity of concentration fluctuations (i.e. standard deviation of concentration divided by mean concentration) tends to zero in stationary conditions and to a constant in decaying turbulence.
Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors
Authors: Lister John R.
Published: April 2006

When buoyant fluid is released into the base of a crack in an elastic medjura the crack will propagate upwards, driven by the buoyancy of the fluid. Viscous fluid flow in such a fissure is described by the equations of lubrication theory with the pressure given by the sum of the hydrostatic pressure of the fluid and the elastic pressures exerted by the walls of the crack. The elastic pressure and the width of the crack are further coupled by an integro-differential equation derived from the theory of infinitesimal dislocations in an elastic medium. The steady buoyancy-driven propagation of a two-dimensional fluid-filled crack through an elastic medium is analysed and the governing equations for the pressure distribution and the shape of the crack are solved numerically using a collocation technique. The fluid pressure in the tip of an opening crack is shown to be very low. Accordingly, a region of relatively inviscid vapour or exsolved volatiles in the crack tip is predicted and allowed for in the formulation of the problem. The solutions show that the asymptotic width of the crack, its rate of ascent and the general features of the flow are determined primarily by the fluid mechanics; the strength of the medium and the vapour pressure in the crack tip affect only the local structure near the advancing tip of the crack. When applied to the transport of molten rock through the Earth's lithosphere by magma-fracture, this conclusion is of fundamental importance and challenges the geophysicist's usual emphasis on the controlling influence of fracture mechanics rather than that of fluid mechanics.
Frequency of sublayer bursting in a curved bend
Authors: Anwer Mohammed , So Ronald M. C.
Published: April 2006

The characteristics of sublayer bursting in turbulent pipe flow through a 180° curved bend at a pipe Reynolds number of 50000 were investigated. In particular, the effects of bend curvature on the bursting frequency were studied in detail. A flush-mounted shear stress gauge was used to measure the wall shear stress and the VITA technique was applied to isolate the bursting events in the wall shear signals. The results show that the bursting frequency starts to drop rather dramatically at the inlet region of the inner bend (closest to the centre of curvature of the bend). Contrary to expectation, the bursting frequency remains fairly constant along the outer bend, but increases sharply as the flow comes out of the bend. Possible explanations for this behaviour are proposed based on the important external effects present in a pipe bend; that is, those due to centrifugal force, streamline curvature and the superimposed secondary flow. Even though wall pressure measurements show that the flow recovers to a fully developed straight pipe condition at a short distance downstream of the bend exit, the circumferential wall shear stress distribution, the spectral content of the wall shear signal and the associated bursting frequency suggest that the near-wall flow takes a much longer distance to return to an unperturbed straight-pipe condition.
Curvature- and rotation-induced instabilities in channel flow
Authors: Matsson O. John E. , Alfredsson P. Henrik
Published: April 2006

In a curved channel streamwise vortices, often called Dean vortices, may develop above a critical Reynolds number owing to centrifugal effects. Similar vortices can occur in a rotating plane channel due to Coriolis effects if the axis of rotation is normal to the mean flow velocity and parallel to the walls. In this paper the flow in a curved rotating channel is considered. It is shown from linear stability theory that there is a region for which centrifugal effects and Coriolis effects almost cancel each other, which increases the critical Reynolds number substantially. The flow visualization experiments carried out show that a complete cancellation of Dean vortices can be obtained for low Reynolds number. The rotation rate for which this occurs is in close agreement with predictions from linear stability theory. For curved channel flow a secondary instability of travelling wave type is found at a Reynolds number about three times higher than the critical one for the primary instability. It is shown that rotation can completely cancel the secondary instability.
Oscillating flows over periodic ripples
Authors: Hara Tetsu , Mei Chiang C.
Published: April 2006

Oscillating flows over periodic ripples are of practical as well as scientific interest because of their relevance to beach processes. When either the ripples are sufficiently steep or the amplitude of ambient oscillations large, streamlines of a viscous flow are no longer parallel to the ripple surface. Circulation cells are formed which can help redistribute suspended sediments. Here we study theoretically these cells for a low-viscosity fluid such as pure water over rigid ripples. In particular we have calculated cells whose dimensions are as large as the ripple wavelength and therefore represent viscous effects far above the usual Stokes boundary layer. An idea of Stuart which was originated for stationary mean circulations around a cylinder is extended here. For large ambient amplitude, large oscillating vortices drifting with the ambient flow are found by seeking the stationary cells in a moving coordinate system.
Vortex street impinging upon an elliptical leading edge
Authors: Gursul Ismet , Rockwell Donald
Published: April 2006

The interaction of a Kármán vortex street with an elliptical edge is investigated experimentally. Basic types of interaction, as a function of scale and transverse displacement of the incident vortex street, are revealed using flow visualization. Unsteady pressure fields induced by these interactions are measured by a phase-averaging technique and correlated with the visualized flow patterns for basic classes of interactions.

For a generic vortex–edge interaction, measurements of the phase-averaged velocity field allow construction of streamlines and vorticity contours showing the details of the interaction, including distortion of the vortical structures near the edge. The pressure field is calculated from the measured velocity field and interpreted in relation to the vortical structures.

Simulation of flow visualization using the measured velocity field demonstrates possible misinterpretations related to the underlying vorticity field.
An experimental study of a turbulent vortex ring
Authors: Glezer Ari , Coles Donald
Published: April 2006

A turbulent vortex ring having a relatively thin core is formed in water by a momentary jet discharge from an orifice in a submerged plate. The necessary impulse is provided by a pressurized reservoir and is controlled by a fast programmable solenoid valve. The main aim of the research is to verify the similarity properties of the mean flow, as defined by ensemble averaging, and to find the distribution of mean vorticity, turbulent energy, and other quantities in the appropriate non-steady similarity coordinates. The velocity field of the vortex is measured for numerous realizations with the aid of a two-channel tracking laser-Doppler velocimeter. The problem of dispersion in the trajectories of the individual rings is overcome by development of a signature-recognition technique in two variables. It is found that the turbulence intensity is largest near the vortex core and that at least the radial component is not negligible in the near wake. The slow growth of the ring structure is controlled by a slight excess of entrainment over de-entrainment. An important inference is that the growth process and the process of turbulence production probably involve secondary vortices wrapped around the core in azimuthal planes.