bluuebunny/crossref_metadata_2025 huggingface dataset:
A supersonic turbulent boundary layer in an adverse pressure gradient
Authors: Fernando Emerick M. , Smits Alexander J.
Published: April 2006

This investigation describes the effects of an adverse pressure gradient on a flat plate supersonic turbulent boundary layer (Mf ≈ 2.9, βx ≈ 5.8, Reθ, ref ≈ 75600). Single normal hot wires and crossed wires were used to study the Reynolds stress behaviour, and the features of the large-scale structures in the boundary layer were investigated by measuring space–time correlations in the normal and spanwise directions. Both the mean flow and the turbulence were strongly affected by the pressure gradient. However, the turbulent stress ratios showed much less variation than the stresses, and the essential nature of the large-scale structures was unaffected by the pressure gradient. The wall pressure distribution in the current experiment was designed to match the pressure distribution on a previously studied curved-wall model where streamline curvature acted in combination with bulk compression. The addition of streamline curvature affects the turbulence strongly, although its influence on the mean velocity field is less pronounced and the modifications to the skin-friction distribution seem to follow the empirical correlations developed by Bradshaw (1974) reasonably well.
Velocity, scalar and transfer spectra in numerical turbulence
Authors: Kerr Robert M.
Published: April 2006

Velocity and passive-scalar spectra for turbulent fields generated by a forced three-dimensional simulation with 1283 grid points and Taylor-microscale Reynolds numbers up to 83 are shown to have convective and diffusive spectral regimes. One-and three-dimensional spectra are compared with experiment and theory. If normalized by the Kolmogorov dissipation scales and scalar dissipation, velocity spectra and scalar spectra for given Prandtl numbers collapse to single curves in the dissipation regime with exponential tails. If multiplied by k⅗ the velocity spectra show an anomalously high Kolmogorov constant that is consistent with low Reynolds number experiments. When normalized by the Batchelor scales, the scalar spectra show a universal dissipation regime that is independent of Prandtl numbers from 0.1 to 1.0. The time development of velocity spectra is illustrated by energy-transfer spectra in which distinct pulses propagate to high wavenumbers.
Stability of stationary barotropic modons by Lyapunov's direct method
Authors: Sakuma H. , Ghil M.
Published: April 2006

A new Lyapunov stability condition is formulated for the shallow-water equations, using a gauge-variable formalism. This sufficient condition is derived for the class of perturbations that conserve the total mass. It is weaker than existing stability criteria, i.e. it applies to a wider class of flows. Formal stability to infinitesimally small perturbations of arbitrary shape is obtained for two classes of large-scale geophysical flows: pseudo-eastward flow with constant shear, and localized coherent structures of modon type.
The three-dimensional stability of finite-amplitude convection in a layered porous medium heated from below
Authors: Rees D. A. S. , Riley D. S.
Published: April 2006

Landau–Ginzburg equations are derived and used to study the three-dimensional stability of convection in a layered porous medium of infinite horizontal extent. Criteria for the stability of convection with banded or square planform are determined and results are presented for two-layer and symmetric three-layer systems. In general the neutral curve is uni-modal and parameter space is divided into regions where either rolls or square cells are stable. For certain ranges of parameters, however, the neutral curve is bimodal and there exists a locus of parameters where two modes with different wavenumbers have simultaneous onset.
The influence of wave breaking on the surface pressure distribution in wind—wave interactions
Authors: Banner Michael L.
Published: April 2006

In reviewing the current status of our understanding of the mechanisms underlying wind-wave generation, it is apparent that existing theories and models are not applicable to situations where the sea surface is disturbed by breaking waves, and that the available experimental data on this question are sparse. In this context, this paper presents the results of a detailed study of the effects of wave breaking on the aerodynamic surface pressure distribution and consequent wave-coherent momentum flux, as well as its influence on the total wind stress.

Two complementary experimental configurations were used to focus on the details and consequences of the pressure distribution over breaking waves under wind forcing. The first utilized a stationary breaking wave configuration and confirmed the presence of significant phase shifting, due to air flow separation effects, between the surface pressure and surface elevation (and slope) distributions over a range of wind speeds. The second configuration examined the pressure distribution, recorded at a fixed height above the mean water surface just above the crest level, over short mechanically triggered waves which were induced to break almost continuously under wind forcing. This allowed a very detailed comparison of the form drag for actively breaking waves and for waves of comparable steepness just prior to breaking (‘incipiently’ breaking waves). For these propagating steep-wave experiments, the pressure phase shifts and distributions closely paralleled the stationary configuration findings. Moreover, a large increase (typically 100%) in the total windstress was observed for the breaking waves, with the increase corresponding closely to the comparably enhanced form drag associated with the actively breaking waves.

In addition to further elucidating some fundamental features of wind-wave interactions for very steep wind waves, this paper provides a useful data set for future model calculations of wind flow over breaking waves. The results also provide the basis for a parameterization of the wind input source function applicable for a wave field undergoing active breaking, an important result for numerical modelling of short wind waves.
On the stability of circular Couette flow with radial heating
Authors: Ali Mohamed , Weidman P. D.
Published: April 2006

The stability of circular Couette flow with radial heating across a vertically oriented annulus with inner cylinder rotating and outer cylinder stationary is investigated using linear stability theory. Infinite aspect ratio and constant fluid properties are assumed and critical stability boundaries are calculated for a conduction-regime base flow. Buoyancy is included through the Boussinesq approximation and stability is tested with respect to both toroidal and helical disturbances of uniform wavenumber. Symmetries of the linearized disturbance equations based on the sense of radial heating and the sense of cylinder rotation and their effect on the kinematics and morphology of instability waveforms are presented. The numerical investigation is primarily restricted to radius ratios 0.6 and 0.959 at Prandtl numbers 4.35, 15 and 100. The results follow the development of critical stability from Taylor cells at zero heating through a number of asymmetric modes to axisymmetric cellular convection at zero rotation. Increasing the Prandtl number profoundly destabilizes the flow in both wide and narrow gaps and the number of contending critical modes increases with increasing radius ratio. Specific calculations made to compare with the stability measurements of Snyder & Karlsson (1964) and Sorour & Coney (1979) exhibit good agreement considering the idealizations built into the linear stability analysis.
Absolute and convective instability of a liquid sheet
Authors: Lin S. P. , Lian Z. W. , Creighton B. J.
Published: April 2006

The linear stability of a viscous liquid sheet in the presence of ambient gas is investigated. It is shown that there are two independent modes of instability, sinuous and varicose. The large-time asymptotic amplitude of sinuous disturbances is found to be bounded but non-vanishing for all calculated values of Reynolds numbers and the gas-to-liquid density ratios when the Weber number is greater than one half. The Weber numberWeis defined as the ratio of the surface tension force to the inertia force per unit area of the gas–liquid interface. WhenWeis smaller than one half, the sinuous mode is stable if the gas-to-liquid density ratio is zero, otherwise it is convectively unstable. The varicose mode is always convectively unstable unless the density ratio,Q, is zero. Then it is asymptotically stable. The spatial growth rate of the varicose mode is smaller than that of the sinuous mode for the same flow parameters. The wavelength of the most amplified waves in both modes is found to scale with the product of the sheet thickness andQ/We. It is shown, by use of the energy equation, that the mechanism of instability is a capillary rupture whenWe[ges ] 0.5, and the convective instability is due to the interfacial pressure fluctuation whenWe< 0.5.
Thermocapillary convection in long horizontal layers of low-Prandtl-number melts subject to a horizontal temperature gradient
Authors: Hadid Hamda Ben , Roux Bernard
Published: April 2006

Thermocapillary convection arising in small-depth layers (long horizontal cavities) subject to a horizontal temperature gradient is studied numerically. A broad range of values of the Reynolds-Marangoni number,Re, is considered for three values of the aspect ratio (A= length/height). For the largest aspect ratio considered,A= 25, the fully developed Poiseuille-Couette solution is reached, but only for moderateRe. The limitingRevalue for the observability of such a fully developed solution is derived as a function of A(Re[les ] 20A). ForRe[les ] 20A, the flow exhibits three distinct regimes, in the upwind, central and downwind regions, respectively. The Poiseuille-Couette solution (when it exists) fills the central region, and the flow is accelerated, in the upwind region, to reach this Poiseuille-Couette solution at a distance that is proportional toRe.In the downwind region, where the flow is deflected by the endwall, a multi-roll structure is exhibited forRe[ges ] 1330. The number of rolls increases withRe.WhenRe> 20A, the upwind and downwind regions coalesce and some of the downwind rolls can be suppressed. Most of the computations concern interfacial conditions (with fixed temperature distribution) for which the dynamical solution is decoupled from the thermal one. A few thermal solutions are given herein, forPr= 0.015 only.
Linear stability of natural convection in spherical annuli
Authors: Gardner David R. , Douglass Rod W. , Trogdon Steven A.
Published: April 2006

Natural convection in a Boussinesq fluid filling the narrow gap between two isothermal, concentric spheres at different temperatures depends strongly on radius ratio, Prandtl number, and Grashof number. When the inner sphere has a higher temperature than the outer sphere, and for fixed values of radius ratio and Prandtl number, experiments show the flow to be steady and axisymmetric for sufficiently small Grashof number and quasi-periodic and axisymmetric for Grashof numbers greater than a critical value. It is our hypothesis that the observed transition is a flow bifurcation. This hypothesis is examined by solving an appropriate eigenvalue problem. The critical Grashof number, critical eigenvalues, and corresponding eigenvectors are obtained as functions of the radius ratio, Prandtl number, and longitudinal wavenumber. Critical Grashof numbers range from 1.18 × 104 to 2.63 × 103 as Prandtl number Pr increases from zero to 0.7, for radius ratios of 0.900 and 0.950. A transitional Prandtl number Prt exists such that for Pr < Prt the bifurcation is time-periodic and axisymmetric. For Pr > Prt the bifurcation is steady and non-axisymmetric with wavenumber two

A first approximation to the bifurcated flow is obtained using the critical eigenvectors. For Pr < Prt the bifurcation sets in as a cluster of relatively strong cells with alternating directions of rotation. The cells remain fixed in location, but pulsate with time. The cluster moves toward the top of the annulus as Pr increases toward Prt. An important feature of the non-axisymmetric bifurcation for Pr > Prt is a set of four cells located at each pole of the annulus in which the radial velocity alternates direction in moving from any one cell to an adjacent one. For fixed radius ratio, the average Nusselt number at criticality varies only slightly with Prandtl number.
Mixed nonlinearity and double shocks in superfluid helium
Authors: Cramer M. S. , Sen R.
Published: April 2006

We examine weak second-sound waves in He II at temperatures and pressures near one of the zeros of the Khalatnikov steepening parameter Γ. An extension of the reductive perturbation scheme of Taniuti & Wei is employed to derive the cubic Burgers’ equation governing these waves. It is shown that mixed nonlinearity may occur in disturbances in which the local value of Γ remains strictly positive or strictly negative. Further new results include expressions for the shock speed, shock structure and the conditions under which the shock thickness increases, rather than decreases, with strength. The fundamental existence conditions for temperature shocks are also delineated and related to the shock disintegration process observed in experimental studies.
The extended Korteweg-de Vries equation and the resonant flow of a fluid over topography
Authors: Marchant T. R. , Smyth N. F.
Published: April 2006

The extended Korteweg-de Vries equation which includes nonlinear and dispersive terms cubic in the wave amplitude is derived from the water-wave equations and the Lagrangian for the water-wave equations. For the special case in which only the higher-order nonlinear term is retained, the extended Korteweg-de Vries equation is transformed into the Korteweg-de Vries equation. Modulation equations for this equation are then derived from the modulation equations for the Korteweg-de Vries equation and the undular bore solution of the extended Korteweg-de Vries equation is found as a simple wave solution of these modulation equations. The modulation equations are also used to extend the solution for the resonant flow of a fluid over topography. This resonant flow occurs when, in the weakly nonlinear, long-wave limit, the basic flow speed is close to a linear long-wave phase speed for one of the long-wave modes. In addition to the effect of higher-order terms, the effect of boundary-layer viscosity is also considered. These solutions (with and without viscosity) are compared with recent experimental and numerical results.
Time-dependent helical waves in rotating pipe flow
Authors: Landman Michael J.
Published: April 2006

The Navier-Stokes equations for flow in a rotating circular pipe are solved numerically, subject to imposing helical symmetry on the velocity fieldv=v(r, θ + αz,t). The helical symmetry is exploited by writing the equations of motion in helical variables, reducing the problem to two dimensions. A limited study of the pipe flow is made in the parameter space of the wavenumber α, and the axial and azimuthal Reynolds numbers. The steadily rotating waves previously studied by Toplosky & Akylas (1988), which arise from the linear instability of the basic steady flow, are found to undergo a series of bifurcations, through periodic to aperiodic time dependence. The relevance of these results to the mechanism of laminar-turbulent transition in a stationary pipe is discussed.
Supersonic gas-particle two-phase flow around a sphere
Authors: Ishii R. , Hatta N. , Umeda Y. , Yuhi M.
Published: April 2006

This paper describes supersonic flows of a gas-particle mixture around a sphere. The Euler equations for a gas-phase interacting with a particle one are solved by using a TVD (Total Variation Diminishing) scheme developed by Chakravarthy & Osher, and the particle phase is solved by applying a discrete particle-cloud model. First, steady two-phase flows with a finite loading ratio are simulated. By comparing in detail the dusty results with the dust-free ones, the effects of the presence of particles on the flow field in the shock layer are clarified. Also an attempt to correlate the particle behaviours is made with universal parameters such as the Stokes number and the particle loading ratio. Next, non-steady two-phase flows are treated. Impingement of a large particle-cloud on a shock layer of a dust-free gas in front of a sphere is numerically simulated. The effect of particles rebounded from the sphere is taken into account. It is shown that a temporal reverse flow region of the gas is induced near the body axis in the shock layer, which is responsible for the appearance of the gas flow region where the pressure gradient becomes negative along the body surface. These phenomena are consistent with the previous experimental observations. It will be shown that the present results support a flow model for the particle-induced flow field postulated in connection with ‘heating augmentation’ found in the heat transfer measurement in hypersonic particle erosion environments. The particle behaviour in such flows is so complicated that it is almost impossible to treat the particle phase as an ordinary continuum medium.
On near-wall turbulent flow modelling
Authors: Lai Y. G. , So R. M. C.
Published: April 2006

The characteristics of near-wall turbulence are examined and the result is used to assess the behaviour of the various terms in the Reynolds-stress transport equations. It is found that all components of the velocity-pressure-gradient correlation vanish at the wall. Conventional splitting of this second-order tensor into a pressure diffusion part and a pressure redistribution part and subsequent neglect of the pressure diffusion term in the modelled Reynolds-stress equations leads to finite near-wall values for two components of the redistribution tensor. This, therefore, suggests that, in near-wall turbulent flow modelling, the velocity-pressure-gradient correlation rather than pressure redistribution should be modelled. Based on this understanding, a methodology to derive an asymptotically correct model for the velocity-pressure-gradient correlation is proposed. A model that has the property of approaching the high-Reynolds-number model for pressure redistribution far away from the wall is derived. A similar analysis is carried out on the viscous dissipation term and asymptotically correct near-wall modifications are proposed. The near-wall closure based on the Reynolds-stress equations and a conventional low-Reynolds-number dissipation-rate equation is used to calculate fully-developed turbulent channel and pipe flows at different Reynolds numbers. A careful parametric study of the model constants introduced by the near-wall closure reveals that one constant in the dissipation-rate equation is Reynolds-number dependent, and a preliminary expression is proposed for this constant. With this modification, excellent agreement with near-wall turbulence statistics, measured and simulated, is obtained, especially the anisotropic behaviour of the normal stresses. On the other hand, it is found that the dissipation-rate equation has a significant effect on the calculated Reynolds-stress budgets. Possible improvements could be obtained by using available direct simulation data to help formulate a more realistic dissipation-rate equation. When such an equation is available, the present approach can again be used to derive a near-wall closure for the Reynolds-stress equations. The resultant closure could give improved predictions of the turbulence statistics and the Reynolds-stress budgets.
On curve and surface stretching in isotropic turbulent flow
Authors: Etemadi N.
Published: April 2006

Cocke (1969) showed that, on average, infinitesimal material lines and surfaces are stretched in incompressible isotropic turbulence. We have extended those results to obtain upper and lower bounds for the stretching of such infinitesimal elements in terms of the eigenvalues of the Green deformation tensor. These bounds are in turn used to find bounds for the stretching of finite material lines and surfaces.
Wave forces on three-dimensional floating bodies with small forward speed
Authors: Nossen Jan , Grue John , Palm Enok
Published: April 2006

A boundary-integral method is developed for computing first-order and mean second-order wave forces on floating bodies with small forward speed in three dimensions. The method is based on applying Green's theorem and linearizing the Green function and velocity potential in the forward speed. The velocity potential on the wetted body surface is then given as the solution of two sets of integral equations with unknowns only on the body. The equations contain no water-line integral, and the free-surface integral decays rapidly. The Timman-Newman symmetry relations for the added mass and damping coefficients are extended to the case when the double-body flow around the body is included in the free-surface condition. The linear wave exciting forces are found both by pressure integration and by a generalized far-field form of the Haskind relations. The mean drift force is found by far-field analysis. All the derivations are made for an arbitrary wave heading. A boundary-element program utilizing the new method has been developed. Numerical results and convergence tests are presented for several body geometries. It is found that the wave exciting forces and the mean drift forces are most influenced by a small forward speed. Values of the wave drift damping coefficient are computed. It is found that interference phenomena may lead to negative wave drift damping for bodies of complicated shape.
Particle dynamics and mixing in a viscously decaying shear layer
Authors: Meiburg E. , Newton P. K.
Published: April 2006

We study the mixing of fluid in a viscously decaying row of point vortices. To this end, we employ a simplified model based on Stuart's (1967) one-parameter family of solutions to the steady Euler equations. Our approach relates the free parameter to a vortex core size, which grows in time according to the exact solution of the Navier-Stokes equations for an isolated vortex. In this way, we approach an exact solution for small values of t/Re. We investigate how the growing core size leads to a shrinking of the cat's eye and hence to fluid leaking out of the trapped region into the free streams. In particular, we observe that particles initially located close to each other in neighbouring intervals along the streamwise direction escape from the cat's eye near opposite ends. The size of these intervals scales with the inverse square root of the Reynolds number. We furthermore examine the particle escape times and observe a self-similar blow-up for the particles near the border between two adjacent intervals. This can be explained on the basis of a simple stagnation-point flow. An investigation of interface generation shows that viscosity leads to an additional factor proportional to time in the growth rates. Numerical simulations confirm the above results and give a detailed picture of the underlying mixing processes.
The stability of countercurrent mixing layers in circular jets
Authors: Strykowski P. J. , Niccum D. L.
Published: April 2006

A spatially developing countercurrent mixing layer was established experimentally by applying suction to the periphery of an axisymmetric jet. A laminar mixing region was studied in detail for a velocity ratio R = ΔU/2U between 1 and 1.5, where ΔU describes the intensity of the shear across the layer and U is the average speed of the two streams. Above a critical velocity ratio Rr = 1.32 the shear layer displays energetic oscillations at a discrete frequency which are the result of very organized axisymmetric vortex structures in the mixing layer. The spatial order of the primary vortices inhibits the pairing process and dramatically alters the spatial development of the shear layer downstream. Consequently, the turbulence level in the jet core is significantly reduced, as is the decay rate of the mean velocity on the jet centreline. The response of the shear layer to controlled external forcing indicates that the shear layer oscillations at supercritical velocity ratios are self-excited. The experimentally determined critical velocity ratio of 1.32, established for very thin axisymmetric shear layers, compares favourably with the theoretically predicted value of 1.315 for the transition from convective to absolute instability in plane mixing layers (Huerre & Monkewitz 1985).
Flame balls stabilized by suspension in fluid with a steady linear ambient velocity distribution
Authors: Buckmaster J. , Joulin G.
Published: April 2006

The ignition of lean H2/air mixtures under microgravity (μg) conditions can lead to the formation of spherical premixed flames (flame balls) with small Péclet number (Pe). A central question concerning these structures is the existence of appropriate stationary stable solutions of the combustion equations. In this paper we examine an individual flame ball that is suspended in a fluid whose velocity far from the flame is steady and varies linearly in space. Detailed results are obtained for simple shear flows and simple straining flows, both axisymmetric and plane.

Convection enhances the flux of heat from the flame and the flux of mixture to the flame, but because the Lewis number (Le) is less than unity the relative impact on the former is greater than on the latter. Consequently, there is a net loss of energy from the flame to the far field, and if large enough this will quench the flame. For values of shear or strain less than the quenching value there are two possible stationary solutions, but one of these is unstable to spherically symmetric disturbances of the flame ball. The radius of the other solution is unbounded as Pe goes to zero. Examination of a class of three-dimensional disturbances reveals no additional instability when the energy losses are due only to convection, but sufficiently large flame balls are unstable when volumetric heat losses from radiation are accounted for. This last result is in agreement with previous results that have been obtained for zero Pe, albeit with inadequate accounting for the flow field generated by the perturbations.
Particle pressures in gas-fluidized beds
Authors: Campbell Charles S. , Wang David G.
Published: April 2006

The particle pressure is the surface force that is exerted due to the motion of particles and their interactions. This paper describes measurements of the particle pressure exerted on the sidewall of a gas-fluidized bed. As long as the bed remains in a packed state, the particle pressure decreases with increasing gas velocity as progressively more of the bed is supported by fluid forces. It appropriately reaches a minimum fluidization and then begins to rise again when the bed is fluidized, reflecting the agitation of the bed by bubbles. In this fully fluidized region, the particle pressure scales with the particle density and the bubble size.
Short-time Lyapunov exponent analysis and the transition to chaos in Taylor–Couette flow
Authors: Vastano John A. , Moser Robert D.
Published: April 2006

Short-time Lyapunov exponent analysis is a new approach to the study of the stability properties of unsteady flows. At any instant in time the Lyapunov perturbations are the set of infinitesimal perturbations to a system state that will grow the fastest in the long term. Knowledge of these perturbations can allow one to determine the instability mechanisms producing chaos in the system. This new method should prove useful in a wide variety of chaotic flows. Here it is used to elucidate the physical mechanism driving weakly chaotic Taylor–Couette flow.

Three-dimensional, direct numerical simulations of axially periodic Taylor–Couette flow are used to study the transition from quasi-periodicity to chaos. A partial Lyapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. The axial wavelength and the particular quasi-periodic state are chosen to correspond to the most complete experimental studies of this transition. The computational results are consistent with available experimental data, both for the flow characteristics in the quasi-periodic regime and for the Reynolds number at which transition to chaos is observed.

The dimension of the chaotic attractor near onset is estimated from the Lyapunov exponent spectrum using the Kaplan–Yorke conjecture. This dimension estimate supports the experimental observation of low-dimensional chaos, but the dimension increases more rapidly away from the transition than is observed in experiments. Reasons for this disparity are given. Short-time Lyapunov exponent analysis is used to show that the chaotic state studied here is caused by a Kelvin–Helmholtz-type instability of the outflow boundary jet of the Taylor vortices.
Velocities and concentrations in oscillatory flow over beds of sediment
Authors: Dick J. E. , Sleath J. F. A.
Published: April 2006

Measurements are reported of the velocity and concentration distributions both within and above two beds of sediment in oscillatory flow. The experiments were carried out in an oscillatory flow water tunnel, the velocities were measured with a laser-Doppler anemometer and the concentrations of sediment with resistance probes operating through the sidewall of the tunnel. The sediments studied consisted of nylon granules of median diameter 4.0 mm and Perspex of median diameter 0.7 mm. Most of the beds were plane for the tests with the 0.7 mm sediment and rippled for those with the 4 mm sediment.

The measured velocity profile could be divided into three regions: a central region in which the amplitude and phase of the velocity increased almost linearly with height and two outer regions in which the variation in velocity with height was much less rapid. It is suggested that at very high sediment transport rates the central region covers almost the entire depth of the moving bed but that at lower transport rates the outer regions are more significant.

The effect of sediment movement on the velocity distribution above the bed is very marked. Bed roughness length is increased and the velocity amplitude falls off more slowly with height than for fixed beds under similar conditions.

Within the bed the shear stress increases almost linearly with depth. Apparent viscosity also increases steadily with depth below the surface of the bed.

The measurements of concentrations are in good agreement with the results of other investigators in the region above the moving bed. Within the bed the time-mean concentration rises steadily, with distance below the initial bed surface, towards the limiting value for a stationary bed. The concentration record also shows a fluctuation during the course of the cycle at twice the frequency of the fundamental oscillation. The amplitude of this fluctuation in concentration decreases with depth below the initial bed level. The phase variation with height is close to that of zero velocity gradient, within the moving bed.
The axisymmetric thermocapillary motion of a fluid particle in a tube
Authors: Chen Jinnan , Dagan Zeev , Maldarelli Charles
Published: April 2006

The thermocapillary migration of a fluid particle in a tube, owing to an imposed axial temperature gradient, is studied theoretically for the case of steady, axisymmetric, creeping, translation in the absence of thermal convection and fluid particle distortion from sphericity, and for an insulated tube. Formulated with these assumptions, the migration is a linear Stokes flow which is separable into two fixed-fluid particle flow idealizations. One is the fluid motion in a quiescent continuous phase, owing only to the thermocapillary surface stress. This stress causes fluid streaming which exerts a lift force on the fluid particle in the direction of the warmer fluid described by a lift coefficient. The second idealization is uniform flow in the absence of thermocapillary forces. The force on the fluid particle owing to this flow represents the hydrodynamic resistance to the forward motion of the fluid particle in the presence of the tube wall, and is described in terms of a drag coefficient. Numerical solutions for the lift and drag coefficients are obtained by a boundary collocation technique.

The migration velocity in the tube relative to that under identical conditions in an infinite medium is computed from the ratio of the lift and drag coefficients. The calculations show that for a fixed ratio of the sphere to the tube diameter, as the conductivity of the fluid particle phase decreases relative to that of the continuous phase, a greater proportion of energy is conducted through the gap between the insulated tube wall and the fluid particle. This conduction pattern creates a larger surface temperature gradient, and causes the relative migration velocity to increase. The enhancement in migration for decreasing fluid particle conductivity at a fixed ratio of the sphere to the tube diameter becomes more pronounced as the later ratio increases and the surface gradient intensifies. However, as the gap distance between the sphere and the tube decreases, hydrodynamic retarding forces develop, and these forces are overriding in the sense that the relative migration velocity in the tube decreases monotonically from the value of one as the gap thickness decreases, and therefore the migration velocity in the tube never exceeds the value in an infinite medium.
Elliptic jets. Part 2. Dynamics of coherent structures: pairing
Authors: Husain Hyder S. , Hussain Fazle
Published: April 2006

The dynamics of coherent structure interactions, in particular the jet column mode of vortex pairing, in the near field of an elliptic jet have been investigated using hotwire measurements and flow visualization. A 2:1 aspect-ratio jet with an initially laminar boundary layer and aconstantmomentum thickness all around the nozzle exit perimeter is used for this study. While detailed hot-wire measurements were made in air at a Reynolds numberReDe(≡UeDe/ν) = 3.2 × 104, flow visualization was performed in water at a lowerReDe= 1.7 × 104; hereUeis the exit speed andDeis the equivalent diameter of the nozzle exit cross-section. Excitation at the stable pairing mode induced successive pairings to occur periodically at the same location, allowing phase-locked measurements using a local trigger sensor. Coherent structures were educed at different phases of pairing in the planes of both the major and minor axes. These are compared with corresponding data in a circular jet, educed similarly.

Pairing interactions are found to be quite different from those in a circular jet. Owing to non-planar and non-uniform self-induction of elliptical vortical structures and the consequent effect on mutual induction, pairing of elliptic vortices in the jet column does not occur uniformly around the entire perimeter, unlike in a circular jet. Merger occurs only in the initial major-axis plane through an entanglement process, while in the initial minor-axis plane, the trailing vortex rushes through the leading vortex without pairing and then breaks down violently. These motions produce considerably greater entrainment and mixing than in circular or plane jets. From distributions of dynamical properties over the extent of coherent structures, the production mechanism is explained in terms of the longitudinal vortices (orribs) connecting the elliptic structures. Time-average measures and their modification by controlled excitation are also discussed in terms of coherent structure dynamics. A significant space in this paper is devoted to documenting phase-dependent and time-average flow measures; these new results should serve as target data for numerical simulations. Further details are given in Husain (1984).
Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres
Authors: Lun C. K. K.
Published: April 2006

A general set of conservation equations and constitutive integrals for the dynamic properties of the rapid flow of a granular material consisting of slightly inelastic and slightly rough spherical particles is derived by following an approach used in the kinetic theory of dense gases. By taking moments of the translational and rotational particle velocities in the general transport moment equation and making the Enskog approximation, the singlet velocity distribution function is determined. As a result, the constitutive relations and coefficients such as stresses, energy fluxes, rates of translational and rotational energy interchanges, shear viscosity, spin viscosity, bulk viscosity and ‘thermal’ conductivities are obtained. The present theory incorporates the kinetic as well as the collisional contributions for stresses and energy fluxes. Thus, it is appropriate for dilute as well as dense concentrations of solids. For the case of simple shear flow, there is favourable agreement between the theoretical predictions of stresses and both the experimental measurements and the results from computer simulations.
Nonlinear evolution of spiral density waves generated by the instability of the shear layer in a rotating compressible fluid
Authors: Shukhman I. G.
Published: April 2006

In a previous paper we considered the nonlinear stability of a cylindrical mixing layer in an incompressible fluid at large Reynolds numbers. Nonlinear evolution results in the formation of vortex structures in the vicinity of the corotation radius rc. This paper considers the same model but in a compressible fluid. A fundamental difference implied by the presence of compressibility is the possibility of the generation of disturbances which are no longer localized near the shear layer but embrace the entire region. These are acoustic waves generated in the region of corotation resonance and emitted into the periphery. In the r > rc region lines of equal density are trailing spirals. The nonlinear evolution of such disturbances is determined by redistribution of the mean flow inside the critical layer (CL). It is shown that only two possible types of CL, viscous and unsteady, can be realized here. For both types of these regimes, evolution equations describing the dynamics of a spiral density wave amplitude are obtained and their solutions analysed. It appears that at any values (provided that they are small enough) of initial supercriticality of the flow, an explosive growth of amplitude occurs which continues as long as values comparable with background ones are reached.
Observations of the dynamics and acoustics of travelling bubble cavitation
Authors: Ceccio S. L. , Brennen C. E.
Published: April 2006

Individual travelling cavitation bubbles generated on two axisymmetric headforms were detected using a surface electrode probe. The growth and collapse of the bubbles were studied photographically, and these observations are related to the pressure fields and viscous flow patterns associated with each headform. Measurements of the acoustic impulse generated by the bubble collapse are analysed and found to correlate with the maximum volume of the bubble for each headform. These results are compared to the observed bubble dynamics and numerical solutions of the Rayleigh–Plesset equation. Finally, the cavitation nuclei flux was measured and predicted cavitation event rates and bubble maximum size distributions are compared with the measurements of these quantities.
Low-Reynolds-number turbulent boundary layers
Authors: Erm Lincoln P. , Joubert Peter N.
Published: April 2006

An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Rθ varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations with Rθ, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rθ ≈ 1020 and above, indicating an absence of dependence on flow history for this Rθ range. These types of measurements were also compared at both Rθ ≈ 1020 and Rθ ≈ 2175 to see if they were dependent on how Rθ was formed (i.e. the combination of velocity and momentum thickness used to determine Rθ). There were noticeable differences for Rθ ≈ 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rθ ≈ 2175.
On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation
Authors: Dussan V. E. B. , Ramé Enrique , Garoff Stephen
Published: April 2006

Over the past decade and a half, analyses of the dynamics of fluids containing moving contact lines have specified hydrodynamic models of the fluids in a rather small region surrounding the contact lines (referred to as the inner region) which necessarily differ from the usual model. If this were not done, a singularity would have arisen, making it impossible to satisfy the contact-angle boundary condition, a condition that can be important for determining the shape of the fluid interface of the entire body of fluid (the outer region). Unfortunately, the nature of the fluids within the inner region under dynamic conditions has not received appreciable experimental attention. Consequently, the validity of these novel models has yet to be tested.

The objective of this experimental investigation is to determine the validity of the expression appearing in the literature for the slope of the fluid interface in the region of overlap between the inner and outer regions, for small capillary number. This in part involves the experimental determination of a constant traditionally evaluated by matching the solutions in the inner and outer regions. Establishing the correctness of this expression would justify its use as a boundary condition for the shape of the fluid interface in the outer region, thus eliminating the need to analyse the dynamics of the fluid in the inner region.

Our experiments consisted of immersing a glass tube, tilted at an angle to the horizontal, at a constant speed, into a bath of silicone oil. The slope of the air–silicone oil interface was measured at distances from the contact line ranging between O.O13a. and O.17a, where a denotes the capillary length, the lengthscale of the outer region (1511 μm). Experiments were performed at speeds corresponding to capillary numbers ranging between 2.8 × 10-4 and 8.3 × 10-3. Good agreement is achieved between theory and experiment, with a systematic deviation appearing only at the highest speed. The latter may be a consequence of the inadequacy of the theory at that value of the capillary number.
Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers
Authors: Joo S. W. , Davis S. H. , Bankoff S. G.
Published: April 2006

A layer of volatile viscous liquid drains down a uniformly heated inclined plate. Long-wave instabilities of the uniform film are studied by deriving an evolution equation for two-dimensional disturbances. This equation incorporates viscosity, gravity, surface tension, thermocapillarity, and evaporation eifects. The linear theory derived from this describes the competition among the instabilities. Numerical solution of the evolution equation describes the finite-amplitude behaviour that determines the propensity for dryout of the film. Among the phenomena that appear are the tendency to wave breaking, the creation of secondary structures, and the preemption of dryout by mean flow.
Stokes drift in two-dimensional wave flumes
Authors: Hudspeth Robert T. , Sulisz Wojciech
Published: April 2006

A complete second-order solution is presented for the two-dimensional wave motion forced by a generic planar wavemaker. The wavemaker is doubly articulated and includes both piston and hinged wavemakers of variable draught. It is shown that the first-order evanescent eigenseries cannot be neglected when computing the amplitude of the second-order free wave. A previously neglected, time-independent solution that is required to satisfy an inhomogeneous kinematic boundary condition on the wavemaker as well as an mhomogeneous Neumann boundary condition on the free surface is examined in detail for the first time. This time-independent solution is found to accurately estimate the mean return flow in a closed wave flume computed by the Eulerian method. This mean return current due to Stokes drift is usually estimated using the principle of kinematic conservation of mass flux. Even though the first-order eigenseries will converge for any geometry of a generic planar wavemaker, the second-order solutions obtained from Stokes perturbation expansions will not converge for all planar wavemaker geometries.
Numerical investigation of three-dimensionally evolving jets subject to axisymmetric and azimuthal perturbations
Authors: Martin J. E. , Meiburg E.
Published: April 2006

We study the inviscid mechanisms governing the three-dimensional evolution of an axisymmetric jet by means of vortex filament simulations. The spatially periodic calculations provide a detailed picture of the processes leading to the concentration, reorientation, and stretching of the vorticity. In the purely axisymmetric case, a wavy perturbation in the streamwise direction leads to the formation of vortex rings connected by braid regions, which become depleted of vorticity. The curvature of the jet shear layer leads to a loss of symmetry as compared to a plane shear layer, and the position of the free stagnation point forming in the braid region is shifted towards the jet axis. As a result, the upstream neighbourhood of a vortex ring is depleted of vorticity at a faster rate than the downstream side. When the jet is also subjected to a sinusoidal perturbation in the azimuthal direction, it develops regions of counter-rotating streamwise vorticity, whose sign is determined by a competition between global and local induction effects. In a way very similar to plane shear layers, the streamwise braid vorticity collapses into counter-rotating round vortex tubes under the influence of the extensional strain. In addition, the cores of the vortex rings develop a wavy dislocation. As expected, the vortex ring evolution depends on the ratio R/θ of the jet radius and the jet shear-layer thickness. When forced with a certain azimuthal wavenumber, a jet corresponding to R/θ = 22.6 develops vortex rings that slowly rotate around their unperturbed centreline, thus preventing a vortex ring instability from growing. For R/θ = 11.3, on the other hand, we observe an exponentially growing ring waviness, indicating a vortex ring instability. Comparison with stability theory yields poor agreement for the wavenumber, but better agreement for the growth rate. The growth of the momentum thickness is much more dramatic in the second case. Furthermore, it is found that the rate at which streamwise vorticity develops is strongly affected by the ratio of the streamwise and azimuthal perturbation amplitudes.