bluuebunny/crossref_metadata_2025 huggingface dataset:
Non-isothermal flow of a liquid film on a horizontal cylinder
Authors: Reisfeld B. , Bankoff S. G.
Published: April 2006

We consider the flow of a viscous liquid film on the surface of a cylinder that is heated or cooled. Lubrication theory is used to study a thin film under the influence of gravity, capillary, thermocapillary, and intermolecular forces. We derive evolution equations for the interface shapes as a function of the azimuthal angle about the cylinder that govern the behaviour of the film subject to the above coupled forces. We use both analytical and numerical techniques to elucidate the dynamics and steady states of the thin layer over a wide range of thermal conditions and material properties. Finally, we extend our derivation to the case of three-dimensional dynamics and explore the stability of the film to small axial disturbances.
Structure of a particle-laden round jet
Authors: Longmire Ellen K. , Eaton John K.
Published: April 2006

The interaction of solid particles with the temporal features of a turbulent flow has direct relevance to problems in particle and spray combustion and the processing of particulate solids. The object of the present study was to examine the behaviour of particles in a jet dominated by vortex ring structures. An axisymmetric air jet laden with 55 μm glass particles was forced axially with an acoustic speaker to organize the vortex ring structures rolling up in the free shear layer downstream of the nozzle exit. Visualization studies of forced and unforced flow with Reynolds number of the order of 20000 were completed using a pulsed copper vapour laser. Instantaneous photographs and videotapes of strobed forced flow show that particles become clustered in the saddle regions downstream of the vortex rings and are propelled away from the jet axis by the outwardly moving flow in these regions. Phase-averaged spatial distribution of particle number density computed from digitized photographs and phase-averaged particle velocity measurements yield further evidence that local particle dispersion and concentration are governed by convection due to large-scale turbulence structures. The large-scale structures and convection mechanisms were shown to persist for particle-to-air mass loading ratios up to 0.65.
Subharmonic growth by parametric resonance
Authors: Hajj M. R. , Miksad R. W. , Powers E. J.
Published: April 2006

An experimental investigation is conducted in order to quantify the nonlinear and parametric resonance mechanisms that are associated with the subharmonic growth in the transition to turbulence in plane mixing layers. Higher-order digital statistical analysis techniques are used to investigate the nonlinear and parametric mechanisms responsible for the energy transfer to the subharmonic. The results show that the dominant interaction is a parametric resonance mechanism between the fundamental and the subharmonic modes which leads to a pronounced growth of the subharmonic. Measurements also indicate that the fundamental, besides interacting with the subharmonic, is also engaged in redistributing its energy to the other Fourier components of the flow via nonlinear three-wave interactions. Local wavenumber measurements verify that frequency—wavenumber resonance matching conditions exist between the fundamental and subharmonic in the region where the subharmonic gains its energy by parametric resonance. The results are in general agreement with theoretical models by Kelly (1967), and Monkewitz (1988) on subharmonic growth.
The kinematics of stretching and alignment of material elements in general flow fields
Authors: Dresselhaus Eliot , Tabor M.
Published: April 2006

A rigorous, kinematic description of the stretching and alignment of infinitesimal material elements in general flow fields is presented. An evolution equation is derived, in the Lagrangian frame, for the alignment angles between a material element and the principal axes of strain. The equation identifies the precise roles played by the local angular velocity and the rotation of the strain axes in the alignment process and provides the framework in which to investigate the extent to which the straining field is ‘persistent’. This general kinematical picture is specialized to study line and vortex stretching in fluid flows and analytically predicts the numerically observed alignment of the vorticity vector with the intermediate strain axis. The alignment equations are solved exactly for a number of special flow fields and investigated numerically for the ABC and STF flows. The kinematic formalism and numerical phenomenology suggests the use of new criteria to analyse the material element stretching properties of large-scale numerical simulations.
The oblique ascent of a viscous vortex pair toward a free surface
Authors: Lugt Hans J. , Ohring Samuel
Published: April 2006

The problem of a vortex pair, rising obliquely at an angle of 45° toward a deformable free surface in a viscous, incompressible fluid, is solved with the aid of the Navier—Stokes equations. The full nonlinear boundary conditions at the free surface are applied. The oblique interaction of the vortex pair with the free surface results in a number of novel features that have not been observed for the special case of a vertical rise, reported earlier. These features include the directional change of trajectories near the free surface and the occurrence of waves driven by the vortex pair. Moreover, surface tension can completely change the flow characteristics such as the direction of the trajectories and the generation of secondary vortices. Numerical solutions are presented for selected Reynolds, Froude, and Weber numbers.
Prediction of film inversion in two-phase flow in coiled tubes
Authors: Hewitt G. F. , Jayanti S.
Published: April 2006

Depending on the flow conditions, the liquid film in annular two-phase flow in coiled tubes may be pushed towards the outer or the inner side by the centrifugal force. It is important to understand the mechanism of this ‘film inversion’ in order to develop a predictive model for the film thickness distribution. In this paper, this phenomenon is studied analytically, and a new criterion, based on the secondary flow in the thin liquid film, is proposed to predict its occurrence. The criterion shows good agreement with available experimental data. It is suggested that the analytical model can readily be extended to predict the distribution of the film thickness and film flow rate in coiled tubes.
Spiralling columnar convection in rapidly rotating spherical fluid shells
Authors: Zhang K.
Published: April 2006

It is shown that the fundamental features of both thermal instabilities and the corresponding nonlinear convection in rapidly rotating spherical systems (in the range of the Taylor number 109 < T < 1012) are determined by the fluid properties characterized by the size of the Prandtl number. Coefficients of the asymptotic power law for the onset of convection at large Taylor number are estimated in the range of the Prandtl number 0.1 ≤ Pr ≤ 100. For fluids of moderately small Prandtl number, a new type of convective instability in the form of prograde spiralling drifting columnar rolls is discovered. The linear columnar rolls extend spirally from near latitude 60° to the equatorial region, and each spans azimuthally approximately five wavelengths with the inclination angle between a spirally elongated roll and the radial direction exceeding 45°. As a consequence, the radial lengthscale of the linear roll becomes comparable with the azimuthal lengthscale. A particularly significant finding is the connection between the new instability and the predominantly axisymmetric convection. Though non-axisymmetric motions are preferred at the onset of convection, the nonlinear convection (at the Rayleigh number of the order of (R—Rc)/Rc = O(0.1)) bifurcating supercritically from the spiralling mode is primarily dominated by the component of the axisymmetric zonal flow, which contains nearly 90% of the total kinetic energy. For fluids of moderately large Prandtl numbers, thermal instabilities at the onset of convection are concentrated in a cylindrical annulus coaxial with the axis of rotation; the position of the convection cylinder is strongly dependent on the size of the Prandtl number. The associated nonlinear convection consists of predominantly non-axisymmetric columnar rolls together with a superimposed weak mean flow that contains less than 10% of the total kinetic energy at (R—Rc)/Rc = O(0.1). A double-layer structure of the temperature field (with respect to the basic state) forms as a result of strong nonlinear interactions between the nonlinear flow and the temperature field. It is also demonstrated that the aspect ratio of the spherical shell does not substantially influence the fundamental properties of convection.
Three-dimensional dynamics and transition to turbulence in the wake of bluff objects
Authors: Karniadakis George Em , Triantafyllou George S.
Published: April 2006

The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast’ transition, from a laminar two-dimensional state at Reynolds number 200 to a turbulent state at Reynolds number 400. The process has been documented in several experimental investigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the Navier—Stokes equations at representative Reynolds numbers, up to 500. A high-order time-accurate, mixed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vortex street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vortex filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vortex filaments.

Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance of intermittent phenomena. It is concluded that the wake undergoes transition to turbulence following the period-doubling route.
Near-wall response in turbulent shear flows subjected to imposed unsteadiness
Authors: Mankbadi Reda R. , Liu Joseph T. C.
Published: April 2006

Rapid-distortion theory is adapted to introduce a truly unsteady closure into a simple phenomenological turbulence model in order to describe the unsteady response of a turbulent wall layer exposed to a temporarily oscillating pressure gradient. The closure model is built by taking the ratio of turbulent shear stress to turbulent kinetic energy to be a function of the effective strain. The latter accounts for the history of the flow. The computed unsteady velocity fluctuations and modulated turbulent stresses compare favourably in the ‘non-quasi-steady’ frequency range, where quasi-steady assumptions would fail. This suggests that the concept of rapid distortion is especially appropriate for unsteady flows. This paper forms the basis for acoustical studies of the problem to be reported elsewhere.
Interfacial waves in core-annular flow
Authors: Miesen R. , Beijnon G. , Duijvestijn P. E. M. , Oliemans R. V. A. , Verheggen T.
Published: April 2006

In this paper we present experiments and an analysis of interfacial waves in core—annular flow; these waves are important for the flow to be stable. The observed wave velocity is about equal to the speed of the fluids near the interface, and the wavelength is 1–10 times the thickness of the annulus. These results are predicted by our analysis, which is valid provided the Reynolds number of the fluid in the annulus, and the ratio of the viscosities of the fluids in the core and the annulus, are large. The theory gives the growth rate of a wave as a function of this ratio, the Reynolds number, the surface tension and the wavenumber. For parameter values of interest, the growth rate is positive for a range wavenumbers which we compare with the experiments. Qualitative agreement between theory and experiment is excellent; quantitative comparison reveals discrepancies for which a possible explanation is the neglect of nonlinear terms.
Toward the large-eddy simulation of compressible turbulent flows
Authors: Erlebacher G. , Hussaini M. Y. , Speziale C. G. , Zang T. A.
Published: April 2006

New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a963grid using Fourier collocation methods. Extensive comparisons between the direct and modelled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence – conducted on a coarse323grid – is shown to yield results that are in excellent agreement with the fine-grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly.
Axisymmetric electrophoresis of multiple colloidal spheres
Authors: Chen Shing B. , Keh Huan J.
Published: April 2006

A study of the electrophoretic motion of a chain of colloidal spheres along the line through their centres is presented. The spheres may differ in radius and in zeta potential and they are allowed to be unequally spaced. Also, the spheres can be either freely suspended in the fluid or linked by infinitesimally thin rods with arbitrary lengths. The fluid can contain an arbitrary combination of general electrolytes. Although the thin-double-layer assumption is employed, the polarization effect of the mobile ions in the diffuse layer is taken into account. A slip velocity of fluid and normal fluxes of ions at the outer edge of the double layer can be derived and used as the boundary conditions for the fluid domain outside the thin double layer. Using a collocation technique along with these boundary conditions, a set of electrokinetic equations governing this problem is solved in the quasi-steady state and the particle interaction effects are computed for various cases. The most important discovery is that a group of particles with the same zeta potential will interact with one another, unlike the no-interaction results obtained in previous investigations assuming that the double layer is infinitesimally thin. For most situations, the particle interaction among the spheres is a complicated function of the properties of the spheres and ions. Also, it no longer varies monotonically with the extent of separation for some cases. The phenomena cannot be predicted systematically by a simple general rule.
On a class of unsteady three-dimensional Navier—Stokes solutions relevant to rotating disc flows: threshold amplitudes and finite-time singularities
Authors: Hall Philip , Balakumar P. , Papageorgiu D.
Published: April 2006

A class of ‘exact’ steady and unsteady solutions of the Navier—Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating in the (x, y)-plane with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x, — y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large Kármán's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation-point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Kármán's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite-time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial-value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.
Steady-state nonlinear internal gravity-wave critical layers satisfying an upper radiation condition
Authors: Lamb Kevin G. , Pierrehumbert Raymond T.
Published: April 2006

We consider the behaviour of an internal gravity wave encountering a critical level in a stratified fluid, assuming the critical-level flow to be dominated by nonlinear effects. The background flow is a shear layer, and the stratification is sufficiently strong to support wave propagation everywhere. Incident and reflected waves are permitted below the critical level, and a radiation condition is imposed far above it. For this geometry we construct, by a combination of asymptotic and numerical means, steady, nonlinear solutions, and discuss the associated transmission coefficients, reflection coefficients, phase shifts, and resonance positions when the system is forced from below.

The inviscid solutions we exhibit have continuous density and velocity everywhere, and so do not require the introduction of internal viscous boundary layers. Further, the streamlines bounding the recirculating cat's-eye regions have corners, just as in the unstratified case. For weak stratification, the transmitted wave is nearly as strong as the incident wave, and there is accompanying strong over-reflection. As the stratification increases, the critical level becomes a nearly perfect reflector. The amount of transmission depends on wave amplitude, and the sensitivity increases with increasing stratification.

There are regions of parameter space for which steady solutions could not be found. The critical-layer structure appears to break down by unbounded thickening when the stratification becomes too strong, suggesting that in these cases some neglected physical process must intervene to limit growth of the recirculating region.
Motion of a rigid particle in Stokes flow: a new second-kind boundary-integral equation formulation
Authors: Liron Nadav , Barta Efrath
Published: April 2006

A new singular boundary-integral equation of the second kind is presented for the stresses on a rigid particle in motion in Stokes flow. The integral equation is particularly suitable for the mobility problem – when the forces and moments on the particle are given. A generalized Faxén law is also presented. The power of the method is demonstrated by easily reproducing known results as well as new ones, both analytically and numerically, in infinite medium as well as in confined regions.
Bénard convection in binary mixtures with Soret effects and solidification
Authors: Zimmermann G. , Müller U. , Davis S. H.
Published: April 2006

Bénard convection of a two-component liquid is considered. The liquid displays Soret effects and the boundary temperatures are fixed to span the solidification temperature of the mixture. Near the lower, heated plate the material is liquid and near the upper cooled plate there is a layer of pure solid solvent; all the solute is rejected during freezing. Linear stability theory is used to determine the effects on the critical conditions for Soret convection in the presence of the solidified layer and the interface between solid and liquid.

Experiments on mixtures of ethyl alcohol and water are performed using interferometry, photography and thermocouple measurements. The measured onset of instability to travelling waves at negative Soret coefficient compares well with those predicted by our linear theory. In the absence of ice the waves develop at finite amplitude to a fixed-amplitude state. However, when ice is present, these waves fail to persist but evolve to a state of steady finite-amplitude (overturning) convection. These differences are attributed to the presence of the ice and the nonlinear density profile of the basic state, both of which act as sources of non-Boussinesq effects.
Scaling of adverse-pressure-gradient turbulent boundary layers
Authors: Durbin P. A. , Belcher S. E.
Published: April 2006

An asymptotic analysis is developed for turbulent boundary layers in strong adverse pressure gradients. It is found that the boundary layer divides into three distinguishable regions: these are the wall layer, the wake layer and a transition layer. This structure has two key differences from the zero-pressure-gradient boundary layer: the wall layer is not exponentially thinner than the wake; and the wake has a large velocity deficit, and cannot be linearized. The mean velocity profile has a y½ behaviour in the overlap layer between the wall and transition regions.

The analysis is done in the context of eddy viscosity closure modelling. It is found that k-ε-type models are suitable to the wall region, and have a power-law solution in the y½ layer. The outer-region scaling precludes the usual ε-equation. The Clauser, constant-viscosity model is used in that region. An asymptotic expansion of the mean flow and matching between the three regions is carried out in order to determine the relation between skin friction and pressure gradient. Numerical calculations are done for self-similar flow. It is found that the surface shear stress is a double-valued function of the pressure gradient in a small range of pressure gradients.
Geostrophic adjustment in a channel: nonlinear and dispersive effects
Authors: Tomasson G. G. , Melville W. K.
Published: April 2006

We consider the general problem of geostrophic adjustment in a channel in the weakly nonlinear and dispersive (non-hydrostatic) limit. Governing equations of Boussinesq-type are derived, based on the assumption of weak nonlinear, dispersive and rotational effects, both for surface waves on a homogeneous fluid and internal waves in a two-layer system. Numerical solutions of the Boussinesq equations are presented, giving examples of the geostrophic adjustment in a channel for two different kinds of initial disturbances, both with non-zero perturbation potential vorticity. The timescales of rotational separation (that is, the separation of the Kelvin and Poincaré waves due to their dispersive properties) and that of nonlinear evolution are considered, with particular concern for the resonant interactions of nonlinear Kelvin waves and linear Poincaré waves described by Melville, Tomasson & Renouard (1989). A parameter measuring the ratio of the two timescales is used to predict when the free and forced Poincaré waves may be separated in the solution. It also distinguishes the cases in which the linear solutions are valid for the rotational separation from those requiring the full Boussinesq equations. Finally, solutions for the evolution of nonlinear internal waves in a sea strait are presented, and the effects of friction on the wavefront curvature of the nonlinear Kelvin waves are briefly considered.
A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes
Authors: Anderson K. G. , Jackson R.
Published: April 2006

In the past few years kinetic theory has been used to derive equations of motion for rapidly shearing granular materials, and there have been empirical extensions of these to take into account stress transmitted by sustained sliding and rolling contacts between particles. The equations are complicated and solutions have been generated only for very simple flows. In this paper three forms for the equations of motion are considered; one representing interaction by collisions only, one which is a high-density asymptotic form of this, and a third which includes terms representing the ‘frictional’ stresses associated with the sustained contacts referred to above. Solutions are found for fully developed flow under gravity down an inclined plane, and it is shown that the relation between the flow rate and the depth of the flowing layer predicted by the first two sets of equations is not in accord with observations. The third form appears to eliminate much of the discrepancy, but its predictions have not been explored over the whole parameter space. It is emphasized that the form of the solutions should be studied over a wide range of operating conditions in order to assess the usefulness of proposed equations.
Nonlinear oscillations of viscous liquid drops
Authors: Basaran Osman A.
Published: April 2006

A fundamental understanding of nonlinear oscillations of a viscous liquid drop is needed in diverse areas of science and technology. In this paper, the moderate- to large-amplitude axisymmetric oscillations of a viscous liquid drop, which is immersed in dynamically inactive surroundings, are analysed by solving the free boundary problem comprised of the Navier–Stokes system and appropriate interfacial conditions at the drop–ambient fluid interface. The means are the Galerkin/finite-element technique, an implicit predictor-corrector method, and Newton's method for solving the resulting system of nonlinear algebraic equations. Attention is focused here on oscillations of drops that are released from an initial static deformation. Two dimensionless groups govern such nonlinear oscillations: a Reynolds number, Re, and some measure of the initial drop deformation. Accuracy is attested by demonstrating that (i) the drop volume remains virtually constant, (ii) dynamic response to small-and moderate-amplitude disturbances agrees with linear and perturbation theories, and (iii) large-amplitude oscillations compare well with the few published predictions made with the marker-and-cell method and experiments. The new results show that viscous drops that are released from an initially two-lobed configuration spend less time in prolate form than inviscid drops, in agreement with experiments. Moreover, the frequency of oscillation of viscous drops released from such initially two-lobed configurations decreases with the square of the initial amplitude of deformation as Re gets large for moderate-amplitude oscillations, but the change becomes less dramatic as Re falls and/or the initial amplitude of deformation rises. The rate at which these oscillations are damped during the first period rises as initial drop deformation increases; thereafter the damping rate is lower but remains virtually time-independent regardless of Re or the initial amplitude of deformation. The new results also show that finite viscosity has a much bigger effect on mode coupling phenomena and, in particular, on resonant mode interactions than might be anticipated based on results of computations incorporating only an infinitesimal amount of viscosity.
The interaction between a high-frequency gust and a blade row
Authors: Peake N.
Published: April 2006

The ingestion of convected vorticity by a high-solidity rotating blade row is a potent noise source in modern aeroengines, due largely to the high level of mutual aerodynamic interactions between adjacent blades. In order to model this process we solve the problem of determining the unsteady lift on an infinite cascade of finite-chord flat plates due to an incident vorticity wave. The method of solution is the Wiener–Hopf technique, and we consider the case of the reduced frequency, Ω, being large, allowing application of asymptotic analysis in the formal limit Ω → ∞. This approach yields considerable simplification, both in allowing the truncation of an infinite reflection series to just two terms, and in allowing algebraic expressions for the Wiener–Hopf split functions to be found. The unsteady lift distribution is derived in closed form, and the accuracy of the asymptotic Wiener–Hopf factorization demonstrated for even modest values of Ω by comparison with exact (but less tractable) methods. Our formulae can easily be incorporated into existing noise prediction codes: the advantage of our scheme is that it handles a regime in which conventional numerical approaches become unwieldy, as well as providing significant physical insight into the underlying mechanisms.
Water waves in shallow channels of rapidly varying depth
Authors: Nachbin A. , Papanicolaou G. C.
Published: April 2006

We analyse the linear water-wave equations for shallow channels with arbitrary rapidly varying bottoms. We develop a theory for reflected waves based on an asymptotic analysis for stochastic differential equations when both the horizontal and vertical scales of the bottom variations are comparable to the depth but small compared to a typical wavelength so the shallow water equations cannot be used. We use the full, linear potential theory and study the reflection–transmission problem for time-harmonic (monochromatic) and pulse-shaped disturbances. For the monochromatic waves we give a formula for the expected value of the transmission coefficient which depends on depth and on the spectral density of the O(1) random depth perturbations. For the pulse problem we give an explicit formula for the correlation function of the reflection process. We compare our theory with numerical results produced using the boundary-element method. We consider several realizations of the bottom profile, let a Gaussian-shaped disturbance propagate over each topography sampled and record the reflected signal for each realization. Our numerical experiments produced reflected waves whose statistics are in good agreement with the theory.
Vortex structure and dynamics in the near field of a coaxial jet
Authors: Dahm WERNER J. A. , Frieler Clifford E. , Tryggvason Grétar
Published: April 2006

We present results from an experimental and numerical investigation into the structure of vortex patterns and the dynamics of their interactions for the incompressible flow in the near field of a round coaxial jet issuing into a quiescent ambient fluid. A two-colour planar laser-induced-fluorescence technique is used to document the flow field via still photographs and ciné sequences over a limited range of parameters. We examine the effects of varying the velocity ratio as well as the absolute velocities of the two coaxial streams for equal densities and for a single area ratio. Results show that a variety of widely differing near-field vortex patterns can arise, with very different interaction dynamics, which can depend both on the velocity ratio and on the absolute velocities of the two streams. The observed vortex structures and their dynamics are interpreted in terms of the instability of the initially cylindrical and concentric vorticity layers separating each of the fluid streams, and their subsequent rollup to form wake-like or shear-layer-like vortices. Our results show that in addition to the velocity jump across each of these vorticity layers, an accounting of the layer thicknesses and the wake defect within each layer can be essential to understanding the resulting near-field structure that occurs. Ensuing dynamical interactions between the vortices formed from each layer can produce a strong coupling between the development of the two layers. These resulting vortex structures and interaction dynamics are also seen to produce widely differing mixing patterns in the jet near field.
Stabilization and destabilization of turbulent shear flow in a rotating fluid
Authors: Tritton D. J.
Published: April 2006

We consider turbulent shear flows in a rotating fluid, with the rotation axis parallel or antiparallel to the mean flow vorticity. It is already known that rotation such that the shear becomes cyclonic is stabilizing (with reference to the non-rotating case), whereas the opposite rotation is destabilizing for low rotation rates and restabilizing for higher. The arguments leading to and quantifying these statement are heuristic. Their status and limitations require clarification. Also, it is useful to formulate them in ways that permit direct comparison of the underlying concepts with experimental data.

An extension of a displaced particle analysis, given by Tritton & Davies (1981) indicates changes with the rotation rate of the orientation of the motion directly generated by the shear/Coriolis instability occurring in the destabilized range.

The ‘simplified Reynolds stress equations scheme’, proposed by Johnston, Halleen & Lezius (1972), has been reformulated in terms of two angles, representing the orientation of the principal axes of the Reynolds stress tensor (αa) and the orientation of the Reynolds stress generating processes (αb), that are approximately equal according to the scheme. The scheme necessarily fails at large rotation rates because of internal inconsistency, additional to the fact that it is inapplicable to two-dimensional turbulence. However, it has a wide range of potential applicability, which may be tested with experimental data. αaand αbhave been evaluated from numerical data for homogeneous shear flow (Bertoglio 1982) and laboratory data for a wake (Witt & Joubert 1985) and a free shear layer (Bidokhti & Tritton 1992). The trends with varying rotation rate are notably similar for the three cases. There is a significant range of near equality of αaand αb. An extension of the scheme, allowing for evolution of the flow, relates to the observation of energy transfer from the turbulence to the mean flow.
Unsteady shock propagation in a steady flow nozzle expansion
Authors: Stalker R. J. , Mudford N. R.
Published: April 2006

The flow field produced when a strong shock wave propagates into a steady flow expansion has been investigated numerically, experimentally and analytically. The experiments were conducted with a shock tube which was modified to allow steady flow to be established in a hypersonic nozzle prior to arrival of the shock. It has been found that the axial density distribution associated with the prior steady flow allows the unsteady flow following the nozzle primary starting shock to accelerate from supersonic to hypersonic speeds, whereas a uniform density distribution causes it to decelerate to subsonic speeds. The prior steady flow also allows the starting shock system to propagate through the nozzle a t nearly the same velocity as the incident primary shock, and therefore provides a convenient method of ensuring rapid steady flow initiation in shock tunnel nozzles. The analysis shows that the flow behaviour can be understood in terms of two approximate models. The first is applicable to a wide range of flow conditions, and allows calculation of the trajectory of the centre of mass of the starting shock system. The second is applicable to cases involving a prior steady flow, and predicts detailed features of the flow structure.
Boundary conditions and linear analysis of finite-cell Rayleigh–Bénard convection
Authors: Chen Yih-Yuh
Published: April 2006

The linear stability of finite-cell pure-fluid Rayleigh–Bénard convection subject to any homogeneous viscous and/or thermal boundary conditions is investigated via a variational formalism and a perturbative approach. Some general properties of the critical Rayleigh number with respect to change of boundary conditions or system size are derived. It is shown that the chemical reaction–diffusion model of spatial-pattern-forming systems in developmental biology can be thought of as a special case of the convection problem. We also prove that, as a result of the imposed realistic boundary conditions, the nodal surfaces of the temperature of a nonlinear stationary state have a tendency to be parallel or orthogonal to the sidewalls, because the full fluid equations become linear close to the boundary, thus suggesting similar trend for the experimentally observed convective rolls.
The nonlinear evolution of a slowly growing wave on a laterally sheared baroclinic flow
Authors: Bell M. J.
Published: April 2006

Wave disturbances to baroclinic flows produce cyclones in the atmosphere and eddies in the oceans and have been extensively studied in laboratory experiments with differentially heated annuli of rotating fluid. Related analytical studies have concentrated mainly on the development of slowly growing waves on laterally uniform zonal flows. Neutral inviscid waves on such flows do not advect their own potential vorticity field whereas neutral waves on most laterally sheared baroclinic flows do. Scaling arguments suggest that on these laterally sheared flows the harmonics generated by the neutral waves play the dominant role in arresting the initial growth of weakly unstable waves. The arrest of a wave is chiefly accomplished by fully nonlinear advection within a critical layer centred on the wave's steering level whose depth is proportional to the wave's amplitude. Explicit numerical solutions illustrating these points are presented for a case in which the critical level is non-singular and the inviscid calculations comparatively straightforward. The stability of the solutions and the effects of diffusive fluxes on them are discussed. Potential vorticity diagnostics for a numerical simulation of a wave flow in a rotating annulus near the axisymmetric transition show that distortion of the wave's potential vorticity field is mainly confined to the vicinity of the steering level. Assumptions and approximations made in the explicit calculations which are of doubtful validity for this flow are highlighted.
An advanced experimental investigation of quasi-two-dimensional shear flow
Authors: Dolzhanskii F. V. , Krymov V. A. , Manin D. Yu.
Published: April 2006

Forced shear flows in a thin layer of an incompressible viscous fluid are studied experimentally. Streak photographs are used to obtain the stream function of vortical flow patterns arising after the primary shear flow loses stability. Various flow characteristics are determined and results are compared to the stability theory of quasi-two-dimensional flows. The applicability of the quasi-two-dimensional approximation is directly verified and the possibility of reconstruction of the driving force from the secondary flow pattern is demonstrated.
Stochastic backscatter in large-eddy simulations of boundary layers
Authors: Mason P. J. , Thomson D. J.
Published: April 2006

The ability of a large-eddy simulation to represent the large-scale motions in the interior of a turbulent flow is well established. However, concerns remain for the behaviour close to rigid surfaces where, with the exception of low-Reynolds-number flows, the large-eddy description must be matched to some description of the flow in which all except the larger-scale ‘inactive’ motions are averaged. The performance of large-eddy simulations in this near-surface region is investigated and it is pointed out that in previous simulations the mean velocity profile in the matching region has not had a logarithmic form. A number of new simulations are conducted with the Smagorinsky (1963) subgrid model. These also show departures from the logarithmic profile and suggest that it may not be possible to eliminate the error by adjustments of the subgrid lengthscale. An obvious defect of the Smagorinsky model is its failure to represent stochastic subgrid stress variations. It is shown that inclusion of these variations leads to a marked improvement in the near-wall flow simulation. The constant of proportionality between the magnitude of the fluctuations in stress and the Smagorinsky stresses has been empirically determined to give an accurate logarithmic flow profile. This value provides an energy backscatter rate slightly larger than the dissipation rate and equal to idealized theoretical predictions (Chasnov 1991).
Effects of horizontal gradients on thermohaline instabilities in infinite porous media
Authors: Sarkar Alok , Phillips O. M.
Published: April 2006

Thermohaline instabilities produced by horizontal gradients of temperature and salinity in a saturated homogeneous isotropic infinite porous medium are studied using linear stability analysis. In the basic state horizontal gradients of temperature and salinity are taken to be mutually compensating, so that the basic-state fluid density does not vary horizontally. It is found that under these conditions the fluid is always unstable. In a porous medium, assuming the solid matrix to be impervious to dissolved salts, the effective advection rates of heat and dissolved salts are different. Because of this difference any disturbance involving a horizontal component of displacement creates net horizontal density gradients, and thus destabilizes the predominantly hydrostatic force balance. When the vertical Rayleigh number is positive, the typical velocity field consists of almost vertical layers of fluid sliding past each other in opposite directions (salt fingers). When the vertical Rayleigh number is negative the fluid layers are almost horizontal, similar to the interleaving observed in Newtonian fluids. Resulting perturbation fluxes of heat and salt always tend to reduce the basic-state concentration gradients, and typically also the gravitational potential energy of the fluid. We also make some tentative estimates regarding properties of these instabilities at the fully developed state. It seems that thermohaline fine structures, similar to oceanic observations, are also possible in porous media.
Two-dimensional instabilities of steady double-diffusive interleaving
Authors: Kerr Oliver S.
Published: April 2006

The stability of finite-amplitude double–diffusive interleaving driven by linear gradients of salinity and temperature is considered. We show that as the sinusoidal interleaving predicted by linear analysis grows to finite amplitude it is subject to instabilities centred along the lines of minimum vertical density gradient and maximum shear. These secondary instabilities could lead to the step-like density profiles observed in experiments. We show that these instabilities can occur for large Richardson numbers and hence are not driven by shear, but are driven, by double-diffusive effects.
On the use of the method of matched asymptotic expansions in propeller aerodynamics and acoustics
Authors: Brouwer H. H.
Published: April 2006

The applicability of the method of matched asymptotic expansions to both propeller aerodynamics and acoustics is investigated. The method is applied to a propeller with blades of high aspect ratio, in a uniform axial flow. The first two terms of the inner expansion and the first three terms of the outer expansion are considered. The matching yields an expression for the spanwise distribution of the downwash velocity. A numerical application shows that the first two terms of the inner solution do not yield an acceptable approximation for the downwash velocity. However, recasting the analytical expressions into an integral equation, similar to Prandtl's lifting line equation for wings, yields results for both aerodynamic and acoustic quantities, which agree well with experimental results. The method thus constitutes a practical analysis method for conventional propellers.
The standing hydraulic jump: theory, computations and comparisons with experiments
Authors: Bowles R. I. , Smith F. T.
Published: April 2006

In this theoretical and computational study of the flow of a liquid layer, under the influence of surface tension and gravity most notably, the nonlinear equations governing an interaction between viscous effects and the effects of surface tension, gravity and streamline curvature for the limit of large Reynolds numbers are derived. The aim is to make a comparison between the predictions of this theory and the experiments of Craiket al.on the axisymmetric hydraulic jump. Such a jump is commonly encountered in the everyday context of the initial filling of a kitchen sink, for example, and it is found in the present work that initially all the effects listed above can play a primary role in practice in the local jump phenomenon. As a first step here, the flow of the layer over a small obstacle is considered. It is seen that as surface tension becomes increasingly significant the upstream influence becomes more wave-like. Second, calculations and analysis of the nonlinear free interaction are presented and show wave-like behaviour upstream, followed downstream by a depth profile not unlike that in the typical hydraulic jump. The effects of gravity dominate those of surface tension downstream. Finally, comparisons are made with the experiments and show fair quantitative agreement, supporting the present proposition that these hydraulic jumps are caused by boundary-layer separation due to a viscous–inviscid interaction forced by downstream boundary conditions on, in this case, a fully developed, high-Froude-number liquid layer.
The capillary instability of annular layers and liquid threads
Authors: Newhouse Lori A. , Pozrikidis C.
Published: April 2006

The capillary instability and break-up of an annular liquid layer coating the inner surface of a cylindrical tube while surrounding another core fluid is studied. In the limiting case where the thickness of the layer is almost equal to the radius of the tube, we obtain a thread of core fluid suspended in a virtually unbounded ambient liquid. The evolution of a layer or thread with a cylindrical or unduloidal interface subject to an axisymmetric perturbation is computed using a boundary integral method. It is shown that for large and moderate layer thicknesses the instability causes the core to transform into an alternating array of primary and secondary spherical drops along the centreline of the tube. The relative volume of the drops depends primarily on the ratio of the core radius to the tube radius, a/R, and the type of initial perturbation. The evolution of thin layers with a/R > 0.82 leads to formation of an array of lobes or collars. These results are used to assess the accuracy of previous approximate analyses based on lubrication flow and minimization of interfacial area.
Vortex shedding from slender cones at low Reynolds numbers
Authors: Papangelou A.
Published: April 2006

Wind-tunnel experiments on the flows created by a number of slightly tapered models of circular cross-section have shown the presence of spanwise cells (regions of constant shedding frequency) at Reynolds numbers of the order of 100. The experiments have also shown a number of other interesting features of these flows: the cellular flow configuration is dependent on the base Reynolds number and independent of the tip Reynolds number, the frequency jump between adjacent cells is a function of flow speed, taper angle and kinematic viscosity, but is constant along a cone's span, and the unsteady hot-wire anemometer signal is both amplitude and phase modulated. A mathematical model is proposed based on the complex Landau—Stuart equation with a spanwise diffusive coupling term. Numerical solutions of this equation have shown many of the qualitative features observed in the experiments.