bluuebunny/crossref_metadata_2025 huggingface dataset:
Temperature fluctuation spectrum in the dissipation range for statistically isotropic turbulent flow
Authors: Tatarskii V. I. , Dubovikov M. M. , Praskovsky A. A. , Karyakin M. Yu.
Published: April 2006

In the present paper we obtain a theoretical expression for the temperature fluctuation spectrum for a Prandtl number of approximately one and for the region where both viscosity and molecular heat conductivity are important. An asymptotic theory for very large wavenumbers of the temperature spectrum in the turbulent flow is developed. The assumption of smallness of the correlation coefficient between the product of small-scale components of velocities at two points and the corresponding product of small-scale components of temperatures is used. The results of simultaneous measurements of streamwise velocity fluctuations and temperature fluctuations carried out in the plane of symmetry of a two-dimensional wake behind a slightly heated cylinder (Rλ = 270) in a wind tunnel is consistent with this assumption.

The main result of the theory developed is the appearance of a bump in the temperature spectrum for a Prandtl number of approximately one.
Natural convection and dispersion in a tilted fracture
Authors: Woods Andrew W. , Linz Stefan J.
Published: April 2006

In many geophysical situations, fluid is contained in long narrow fractures embedded within an impermeable medium of different thermal conductivity: and there may be a uniform vertical temperature gradient imposed upon the system. We show that whenever the slot is tiled to the vertical, convection develops in the fluid, even if the background temperature increases with height. We then investigate the transport of passive material governed by this flow. The dispersion coefficient of a passive contaminant transported by this flow DT = f[R sin2ϕ] k2 cot2 ϕ/D, where k and D are the thermal and compositional diffusivities, ϕ is the angle of tilt and R is a Rayleigh number for the slot.

Using typical values for the physical properties of a water-filled fracture, we show that the Earth's geothermal gradient produces a convective flow in a fracture through the mechanism above; this has an associated dispersion coefficient DT ∼ 102-103D in fractures about a centimetre wide. We show that this shear dispersion could transport radioactive material, of half-life 104 years, tens of metres along the fracture within one half-life; without this dispersion, the material would only diffuse a few metres along the fracture within one half-life.

If there is a background salinity gradient along the slot in addition to the thermal gradient, analogous steady flow solutions exist; if the flow is stable, the salinity may either enhance or reduce the steady flow and associated dispersion of passive tracer.
Instability of unbounded uniform granular shear flow
Authors: Savage S. B.
Published: April 2006

The paper presents a linear stability analysis of cohesionless granular materials during rapid shear flow. The analysis is based on the governing equations developed in the kinetic theory of Lun et al. (1984) for granular flows of smooth, nearly elastic, uniform spherical particles. The primary flow is taken to be a uniform, simple shear flow and the effects of small perturbations in velocity components, granular temperature and solids fraction are considered. The inelasticity of the particles is characterized by a constant coefficient of restitution which is assumed to be close to unity. Some permissible solutions are sinusoidal plane waves in which the wavenumber vector is continuously turned by the mean shear flow and its magnitude varied as time proceeds. The initial growth (or decay) rates for these perturbations are sought. The resulting linearized equations for the flow perturbations turn out to be exceedingly long and complex; they are determined by the use of computer algebra. It is found that, in general, long wavelengths are the most unstable and that short wavelengths are dampened by ‘viscous action’. ‘Instability’ increases with decreasing coefficient of restitution. Numerical results for initial growth rates were obtained for several values of mean solids fraction and particle coefficient of restitution. Flows tend to be more stable at both high and very low concentrations than at moderate concentrations. These results appear to be consistent in the main with recent computer simulations of granular flows of disk-like particles by Hopkins & Louge (1991).
Frictional–collisional equations of motion for granular materials and their application to flow in aerated chutes
Authors: Nott P. , Jackson R.
Published: April 2006

Equations of motion and boundary conditions for a flowing granular material, developed in earlier publications, are here extended to allow for drag forces resulting from relative motion of the material and interstitial air. These are solved for fully developed flow down an inclined plane, through which a constant flow of air passes upward. The results are compared with measurements from an experimental aerated chute, in which the inclination of the chute, the flow rate of the granular material, and the flow of air are all varied. Using parameter values from independent measurements, as far as possible, the theory is found to give a good qualitative account of the observed behaviour. With a reasonable assigned value for the one parameter that cannot be determined independently the quantitative agreement is also satisfactory.
Magnetic field intermittency and fast dynamo action in random helical flows
Authors: Gilbert Andrew D. , Bayly B. J.
Published: April 2006

The evolution of passive magnetic fields is considered in random flows made up of single helical waves. In the absence of molecular diffusion the growth rates of all moments of a magnetic field are calculated analytically, and it is found that the field becomes increasingly intermittent with time. The evolution of normal modes of the ensemble-averaged field is determined; it is shown that the flows considered give fast dynamo action, and magnetic field modes with either sign of magnetic helicity may grow.
The shape of a magnetic liquid drop
Authors: Séro-Guillaume O. E. , Zouaoui D. , Bernardin D. , Brancher J. P.
Published: April 2006

The electromagnetic forces in a ferrofluid depend on the domain occupied by the fluid. We study here the equilibrium positions of a ferrofluid drop with a boundary which is partially or totally free. The method used is based on the minimization of the energy with respect to the shape of the drop. We show bifurcations of the solutions and hysteresis phenomena when the parameters vary.
Numerical experiments on two-dimensional foam
Authors: Herdtle Thomas , Aref Hassan
Published: April 2006

The statistical evolution of a two-dimensional polygonal, or ‘dry’, foam during diffusion of gas between bubbles lends itself to a very simple mathematical description by combining physical principles discovered by Young. Laplace, Plateau, and von Neumann over a period of a century and a half. Following a brief review of this ‘canonical’ theory, we report results of the largest numerical simulations of this system undertaken to date. In particular, we discuss the existence and properties of a scaling regime, conjectured on the basis of laboratory experiments on larger systems than ours by Glazier and coworkers, and corroborated in computations on smaller systems by Weaire and collaborators. While we find qualitative agreement with these earlier investigations, our results differ on important, quantitative details, and we find that the evolution of the foam, and the emergence of scaling, is very sensitive to correlations in the initial data. The largest computations we have performed follow the relaxation of a system with 1024 bubbles to one with O(10), and took about 30 hours of CPU time on a Cray-YMP supercomputer. The code used has been thoroughly tested, both by comparison with a set of essentially analytic results on the rheology of a monodisperse-hexagonal foam due to Kraynik & Hansen, and by verification of certain analytical solutions to the evolution equations that we found for a family of ‘fractal foams’.
Multiple equilibria in two-dimensional thermohaline circulation
Authors: Cessi Paola , Young W. R.
Published: April 2006

As a model of the thermohaline circulation of the ocean we study the two-dimensional Boussinesq equations forced by prescribing the surface temperature and the surface salinity flux. We simplify the equations of motion using an expansion based on the small aspect ratio of the domain. The result is an amplitude equation governing the evolution of the depth averaged salinity field. This amplitude equation has multiple, linearly stable equilibria. The simplified dynamics has a Lyapunov functional and this variational structure permits a simple characterization of the relative stability of the alternative steady solutions.

Even when the thermal and salinity surface forcing functions are symmetric about the equator there are asymmetric solutions, representing pole to pole circulations. These asymmetric solutions are stable to small perturbations and are always found in conjunction with symmetric solutions, also stable to small perturbations. Recent numerical solutions of the full two-dimensional equations have shown very similar flow patterns.
Uniformly travelling water waves from a dynamical systems viewpoint: some insights into bifurcations from Stokes’ family
Authors: Baesens C. , Mackay R. S.
Published: April 2006

Numerical work of many people on the bifurcations of uniformly travelling water waves (two-dimensional irrotational gravity waves on inviscid fluid of infinite depth) suggests that uniformly travelling water waves have a reversible Hamiltonian formulation, where the role of time is played by horizontal position in the wave frame. In this paper such a formulation is presented. Based on this viewpoint, some insights are given into bifurcations from Stokes’ family of periodic waves. It is demonstrated numerically that there is a ‘fold point’ at amplitude A0 ≈ 0.40222. Assuming non-degeneracy of the fold and existence of an associated centre manifold, this explains why a sequence of p/q-bifurcations occurs on one side of A0, with 0 < p/q [les ] ½, in the order of the rationals. Secondly, it explains why no symmetry-breaking bifurcation is observed at A0, contrary to the expectations of some. Thirdly, it explains why the bifurcation tree for periodic uniformly travelling waves looks so much like that for the area-preserving Hénon map. Fourthly, it leads to predictions of a rich variety of spatially quasi-periodic, heteroclinic and chaotic waves.
Jump conditions across normal shock waves in pure vapour–droplet flows
Authors: Guha A.
Published: April 2006

Closed-form analytical jump conditions across normal shock waves in pure vapour–droplet flows have been derived for different boundary conditions. They are equally applicable to partly and fully dispersed shock waves. Collectively they may be called the generalized Rankine–Hugoniot relations for wet vapour. A phase diagram is constructed which specifies the type of shock structure obtained in vapour–droplet flow given some overall parameters. It is shown that in addition to the partly and fully dispersed shock waves that are possible in any relaxing medium, there also exists a class of shock waves in wet vapour in which the two-phase relaxing medium reverts to a single-phase non-relaxing one. An analytical expression for the limiting upstream wetness fraction below which complete evaporation will take place inside a shock of specified strength has been deduced. A new theory has been formulated which shows that, depending on the upstream wetness fraction, a continuous transition exists for the shock velocity between its frozen and fully equilibrium values. The mechanisms of entropy production inside a shock are also discussed.
The effect of axial stretching on the three-dimensional stability of a vortex pair
Authors: Marshall J. S.
Published: April 2006

The stability of a pair of counter-rotating vortices to three-dimensional disturbances in the presence of a stretching flow is studied for vortices of small circular cross-section. The problem is reduced to a system of two first-order, linear ordinary differential equations, which can be integrated numerically to obtain the change in the perturbation of the vortex pair with time. The stability of the vortex pair depends upon four dimensionless constants, two of which characterize the stretching flow. Computations indicate that stretching usually exerts a stabilizing influence on the vortex pair, although in many cases the perturbation amplitude may initially increase and then decrease at some later time due to the effects of stretching. The results of the study are applied to investigate stability of hairpin vortices that are typically observed in turbulent shear flows. An estimate of the percentage increase in perturbation amplitude of a hairpin vortex in a homogeneous turbulent shear flow is given as a function of the stretch of the hairpin for different values of the dimensionless perturbation wavenumber and the microscale Reynolds number Reλ = λq/ν (based on the Taylor microscale λ and the turbulent kinetic energy ½q2). The maximum percentage growth of a perturbation of the legs of a hairpin vortex in a turbulent shear flow is found to decrease with increase in Reλ.
The structure of a turbulent free shear layer in a rotating fluid
Authors: Bidokhti A. A. , Tritton D. J.
Published: April 2006

An experimental investigation has been carried out on the effects of rotation on the development and structure of turbulence in a free shear layer, oriented so that its mean vorticity is parallel or antiparallel to the system vorticity. The effective local Rossby number extended down to about 1/3. The experimental methods were hydrogen-bubble flow visualization and hot-film anemometry.

In summarizing the results we refer to stabilized flow when the system vorticity has the same sign as the shear vorticity and destabilized and subsequently restabilized when it has the opposite sign (Tritton 1992). The roller eddy pattern, familiar in non-rotating flow, was observed in all stabilized flows, but was almost completely disrupted by even weak destabilization. Notable features of the quantitative results were: reorientation by Coriolis effects of the Reynolds stress tensor (inferred from the ratio of the cross-stream to longitudinal turbulence intensity and the normalized shear stress); changes in the ratio of spanwise to longitudinal intensity similar to but weaker than changes in the ratio of cross-stream to longitudinal; a gradual decrease, with increasing stabilization, of the Reynolds shear stress leading ultimately to its changing sign; an increase of the Reynolds shear stress in the destabilized range followed by rapid collapse to almost zero with restabilization. Absolute intensities did not change in line with the turbulence energy production, implying enhancement of dissipation in destabilized flow and inhibition in stabilized and restabilized. Correlation measurements indicated changes of lengthscale in the spanwise direction, and spectra indicated changes in the longitudinal direction that suggest that this enhancement and inhibition are associated with variations between fully three-dimensional and partially two-dimensional turbulence. Data for a wake in a rotating fluid (Witt & Joubert 1985) show similarities to some of the above observations and can be incorporated into the interpretation.
Plane turbulent jets in a bounded fluid layer
Authors: Dracos T. , Giger M. , Jirka G. H.
Published: April 2006

An experimental investigation of plane turbulent jets in bounded fluid layers is presented. The development of the jet is regular up to a distance from the orifice of approximately twice the depth of the fluid layer. From there on to a distance of about ten times the depth, the flow is dominated by secondary currents. The velocity distribution over a cross-section of the jet becomes three-dimensional and the jet undergoes a constriction in the midplane and a widening near the bounding surfaces. Beyond a distance of approximately ten times the depth of the bounded fluid layer the secondary currents disappear and the jet starts to meander around its centreplane. Large vortical structures develop with axes perpendicular to the bounding surfaces of the fluid layer. With increasing distance the size of these structures increases by pairing. These features of the jet are associated with the development of quasi two-dimensional turbulence. It is shown that the secondary currents and the meandering do not significantly affect the spreading of the jet. The quasi-two-dimensional turbulence, however, developing in the meandering jet, significantly influences the mixing of entrained fluid.
Nonlinear dynamics in Langmuir circulations with O(2) symmetry
Authors: Cox Stephen M. , Leibovich Sidney , Moroz Irene M. , Tandon Amit
Published: April 2006

A direct comparison is made between the dynamics obtained by weakly nonlinear theory and full numerical simulations for Langmuir circulations in a density-stratified layer having finite depth and infinite horizontal extent. In one limit, the mathematical formulation employed is analogous to that of double-diffusion phenonema with the flux of one diffusing quantity fixed at the boundaries of the layer. These problems have multiple bifurcation points, but their amplitude equations have no intrinsic (nonlinear) degeneracies, in contrast to ‘standard’ double-diffusion problems. The symmetry of the physical problem implies invariance with respect to translations and reflections in the horizontal direction normal to the applied wind stress (so-called O(2) symmetry). A multiple bifurcation at a double-zero point serves as an organizing centre for dynamics over a wide range of parameter values. This double zero, or Takens–Bogdanov, bifurcation leads to doubly periodic motions manifested as modulated travelling waves. Other multiple bifurcation points appear as double-Hopf bifurcations. It is believed that this paper gives the first quantitative comparison of dynamics of double-diffusive type predicted by rationally derived amplitude equations and by full nonlinear partial differential equations. The implications for physically observable natural phenomena are discussed. This problem has been treated previously, but the earlier numerical treatment is in error, and is corrected here. When the Stokes drift gradient due to surface waves is not constant, the analogy with the common formulations of double-diffusion problems is compromised. Our bifurcation analyses are extended here to include the case of exponentially decaying Stokes drift gradient.
The dimension of attractors underlying periodic turbulent Poiseuille flow
Authors: Keefe Laurence , Moin Parviz , Kim John
Published: April 2006

Using a coarse grained (16 × 33 × 8) numerical simulation, a lower bound on the Lyapunov dimension, Dλ, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 has been calculated to be approximately 352. These results were obtained on a spatial domain with streamwise and spanwise periods of 1.6π, and correspond to a wall-unit Reynolds number of 80. Comparison of Lyapunov exponent spectra from this and a higher-resolution (16 × 33 × 16) simulation on the same domain shows these spectra to have a universal shape when properly scaled. Using these scaling properties, and a partial exponent spectrum from a still higher-resolution (32 × 33 × 32) simulation, we argue that the actual dimension of the attractor underlying motion on the given computational domain is approximately 780. The medium resolution calculation establishes this dimension as a strong lower bound on this computational domain, while the partial exponent spectrum calculated at highest resolution provides some evidence that the attractor dimension in fully resolved turbulence is unlikely to be substantially larger. These calculations suggest that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier–Stokes equations in such flows. However, the magnitude of the dimension measured invalidates any notion that the global dynamics of such turbulence can be attributed to the interaction of a few degrees of freedom. Dynamical systems theory has provided the first measurement of the complexity of fully developed turbulence; the answer has been found to be dauntingly high.
Experimental investigation of the field of velocity gradients in turbulent flows
Authors: Tsinober A. , Kit E. , Dracos T.
Published: April 2006

We present results of experiments on a turbulent grid flow and a few results on measurements in the outer region of a boundary layer over a smooth plate. The air flow measurements included three velocity components and their nine gradients. This was done by a twelve-wire hot-wire probe (3 arrays × 4 wires), produced for this purpose using specially made equipment (micromanipulators and some other auxiliary special equipment), calibration unit and calibration procedure. The probe had no common prongs and the calibration procedure was based on constructing a calibration function for each combination of three wires in each array (total 12) as a three-dimensional Chebishev polynomial of fourth order. A variety of checks were made in order to estimate the reliability of the results.

Among the results the most prominent are the experimental confirmation of the strong tendency for alignment between vorticity and the intermediate eigenvector of the rate-of-strain tensor, the positiveness of the total enstrophy-generating term ωiωjsij (sij = ½(∂ui/∂xj+∂uj/∂xi), ωi = εijk∂uj/∂xk) even for rather short records and the tendency for alignment in the strict sense between vorticity and the vortex stretching vector Wi = ωjsij. An emphasis is put on the necessity to measure invariant quantities, i.e. independent of the choice of the system of reference (e.g. sijsij and ωiωjsij) as the most appropriate to describe physical processes. From the methodological point of view the main result is that the multi-hot-wire technique can be successfully used for measurements of all the nine velocity derivatives in turbulent flows, at least at moderate Reynolds numbers.
Nonlinear water waves in channels of arbitrary shape
Authors: Teng Michelle H. , Wu Theodore Y.
Published: April 2006

The generalized channel Boussinesq (gcB) two-equation model and the forced channel Korteweg–de Vries (cKdV) one-equation model previously derived by the authors are further analysed and discussed in the present study. The gcB model describes the propagation and generation of weakly nonlinear, weakly dispersive and weakly forced long water waves in channels of arbitrary shape that may vary both in space and time, and the cKdV model is applicable to unidirectional motions of such waves, which may be sustained under forcing at resonance of the system. These two models are long-wave approximations of a hierarchy set of section-mean conservation equations of mass, momentum and energy, which are exact for inviscid fluids. Results of these models are demonstrated with four specific channel shapes, namely variable rectangular, triangular, parabolic and semicircular sections, in which case solutions are obtained in closed form. In particular, for uniform channels of equal mean water depth, different cross-sectional shapes have a leading-order effect only on the variations of a k-factor of the coefficient of the term bearing the dispersive effects in the model equations. For this case, the uniform-channel analogy theorem enunciated here shows that long waves of equal (mean) height in different uniform channels of equal mean depth but distinct k-shape factors will propagate with equal velocity and with their effective wavelengths appearing k times of that in the rectangular channel, for which k = 1. It also shows that the further channel shape departs from the rectangular, the greater the value of k. Based on this observation, the solitary and cnoidal waves in a k-shaped channel are compared with experiments on wave profiles and wave velocities. Finally, some three-dimensional features of these solitary waves are presented for a triangular channel.
Instability of the equilibrium of a liquid below its vapour between horizontal heated plates
Authors: Huang Adam , Joseph Daniel D.
Published: April 2006

We study the stability of a motionless liquid below its vapour between heated horizontal plates. The temperature of the bottom plate is held below the vaporization temperature and the top plate is hotter than the vaporization temperature. A water film is on the cold plate and a vapour film on the hot plate. We find a basic solution depending only on the variable y normal to the plates, with steady distributions of temperature, a null velocity and no phase change. The linear stability of this basic state is studied in the frame of incompressible fluid dynamics, without convection, but allowing for phase change. An ambiguity in the choice of the conditions to be required of the temperature at the phase-change boundary is identified and discussed. It is shown that the basic state of equilibrium is overstable under conditions of large temperature gradient, when the other parameters have suitable values. An analysis of the energy of the most dangerous disturbance shows that the source of the instability is associated with change of phase.
Formal stability of circular vortices
Authors: Kloosterziel R. C. , Carnevale G. F.
Published: April 2006

The second variation of a linear combination of energy and angular momentum is used to investigate the formal stability of circular vortices. The analysis proceeds entirely in terms of Lagrangian displacements to overcome problems that otherwise arise when one attempts to use Arnol'd's Eulerian formalism. Specific attention is paid to the simplest possible model of an isolated vortex consisting of a core of constant vorticity surrounded by a ring of oppositely signed vorticity. We prove that the linear stability regime for this vortex coincides with the formal stability regime. The fact that there are formally stable isolated vortices could imply that there are provable nonlinearly stable isolated vortices. The method can be applied to more complicated vortices consisting of many nested rings of piecewise-constant vorticity. The equivalent expressions for continuous vorticity distributions are also derived.
Acoustic streaming about a cylinder in orthogonal beams
Authors: Riley N.
Published: April 2006

When orthogonal, plane sound waves of the same frequency, wavelength and amplitude, but with phase difference ½π, are incident upon a circular cylinder there is a time-independent streaming about the cylinder which is in the form of a potential vortex separated from the cylinder by a thin, viscous Stokes layer. As the amplitude of the waves in one of the beams decreases, an additional viscous boundary layer is involved until, when the amplitude is sufficiently small, this flow structure is destroyed as fluid erupts from the boundary layer. In the limit of a single beam it is known that this eruption results in opposing jets perpendicular to the wavefronts of the oncoming wave.
Instability of a solid-body rotating vortex in a two-layer model
Authors: Ripa P.
Published: April 2006

The instability of an anticyclonic solid-body rotating eddy embedded on a quiescent environment is studied, for all possible values of the parameters of the unperturbed state, i.e. the vortex's relative thickness and rotation rate. The Coriolis force is fundamental for the existence of the eddy (because the pressure force has a centrifugal direction) and therefore this analysis pertains to the study of mesoscale vortices in the ocean or the atmosphere, as well as those in other planets.

These eddies are known to be stable when the ‘second’ layer is assumed imperturbable (infinitely deep); however, here these vortices are found to be unstable in the more realistic case of an active environment layer, which may be arbitrarily thick.

Three basic types of instability are found, classified according to the dynamic structure of the growing perturbation field, in both layers: baroclinic instability (Rossby-like in both layers), Sakai instability (Poincaré-like in the vortex layer and Rossby-like in the environment), and Kelvin–Helmholtz instability (Poincaré-like in both layers). In addition, there is a hybrid instability, which goes continuously from the baroclinic to the Sakai types, as the rotation rate is increased.

The problem is constrained by the conservation of pseudoenergy and angular pseudomomentum, which are quadratic (to lowest order) in the perturbation. The requirement that both integrals of motion vanish for a growing disturbance, determines the structure of the latter in both layers. Furthermore, that constraint restricts the region, in parameter space, where each type of instability is present.
Viscous flows down an inclined plane from point and line sources
Authors: Lister John R.
Published: April 2006

The flow of a viscous fluid from a point or line source on an inclined plane is analysed using the equations of lubrication theory in which surface tension is neglected. At short times, when the gradient of the interfacial thickness is much greater than that of the plane, the fluid is shown to spread symmetrically from the source, as on a horizontal plane. At long times, the flow is predominantly downslope, with some cross-slope spreading for the case of a point source. Similarity solutions for the long-time behaviour of the governing nonlinear partial differential equations are found for the case in which the volume of fluid increases with time like tα, where α is a constant. The two-dimensional equations appropriate to a line source are hyperbolic in the self-similar regime and the similarity profile is found analytically to end abruptly at a downslope position which increases like t(2α+1)/3. Inclusion of higher-order terms in the analysis resolves this frontal shock into a boundary-layer structure of width comparable to the thickness of the current. Owing to the term representing cross-slope spreading, the mathematical structure of the equations is considerably more complex for flow from a point source and the similarity form is found numerically in this case. Though the downslope and cross-slope extents of the current again increase with time according to a power-law if α > 0, they also depend on a power of In t if α = 0. The leading-order near-source structure is shown to be that of steady flow from a constant-flux source of strength given by the instantaneous flow rate. For sources with α > 1, the contact line advances at all points on the perimeter of the flow and the entire plane is eventually covered by the flow; for sources with 0 < α < 1, only a portion of the contact line is advancing at any time and only that part of the plane with |y| [les ] cx3α/(4α+3) is eventually covered, where x and y are the downslope and cross-slope coordinates and c is a constant. The theoretical spreading relationships and planforms are found to be in good agreement with experimental measurements of constant-volume and constant-flux flows of viscous fluids from a point source on a plane. At very long times, however, the experimental flows are observed to be unstable to the formation of a capillary rivulet at the nose of the current.
Receptivity of a laminar boundary layer to the interaction of a three-dimensional roughness element with time-harmonic free-stream disturbances
Authors: Tadjfar M. , Bodonyi R. J.
Published: April 2006

Receptivity of a laminar boundary layer to the interaction of time-harmonic free-stream disturbances with a three-dimensional roughness element is studied. The three-dimensional nonlinear triple–deck equations are solved numerically to provide the basic steady-state motion. At high Reynolds numbers, the governing equations for the unsteady motion are the unsteady linearized three-dimensional triple-deck equations. These equations can only be solved numerically. In the absence of any roughness element, the free-stream disturbances, to the first order, produce the classical Stokes flow, in the thin Stokes layer near the wall (on the order of our lower deck). However, with the introduction of a small three-dimensional roughness element, the interaction between the hump and the Stokes flow introduces a spectrum of all spatial disturbances inside the boundary layer. For supercritical values of the scaled Strouhal number, S0 > 2, these Tollmien–Schlichting waves are amplified in a wedge-shaped region, 15° to 18° to the basic-flow direction, extending downstream of the hump. The amplification rate approaches a value slightly higher than that of two-dimensional Tollmien–Schlichting waves, as calculated by the linearized analysis, far downstream of the roughness element.
Dynamics and transport of a localized soluble surfactant on a thin film
Authors: Halpern D. , Grotberg J. B.
Published: April 2006

The flow induced by a localized droplet of soluble surfactant on the surface of a thin film is analysed, motivated by an interest in the interaction between inhaled droplets and the lung's thin liquid lining after an aerosol lands on its surface. The spreading is driven by gradients of surface tension and results in flow of the droplet and underlying liquid film. This induced flow field plays an important role in the transport of dissolved species from the droplet, through the film, and to the tissue for absorption.

Evolution equations for the film thickness, surface and bulk liquid concentrations are derived using lubrication theory, since the depth of the film is much smaller than the characteristic radius of the droplet. Solutions are obtained numerically using the method of lines for a variety of surface Péclet numbers.

We find that the effect of solubility is to decrease both film disturbances and surface concentrations, and to induce an absorption-driven backflow. In addition, there is a gravity-driven backflow from hydrostatics. At large surface Péclet numbers, large film disturbances are obtained and more surfactant is able to diffuse across the rigid permeable wall, while surface diffusion causes more rapid spreading and decreases film disturbances. Gravity acts as a restoring force by creating a bidirectional flow, and hence disenhances the vertical flux of surfactant across the air-liquid interface. This model may have implications for the delivery of drugs by aerosol inhalation.
Drag modifications for a sphere in a rotational motion at small, non-zero Reynolds and Taylor numbers: wake interference and possibly Coriolis effects
Authors: Davis A. M. J.
Published: April 2006

Matched asymptotic expansion methods are used to establish governing equations of Oseen type for a tethered sphere that describes a circular path and a stationary sphere subjected to a rotating fluid in an ‘antisedimentation’ tube. The two cases are shown to be significantly different, in contrast to an earlier presentation (Davis & Brenner 1986), because only the latter is subject to the Coriolis force. The evaluation of the force and torque coefficients is much improved, enabling better comparisons to be made with the classical rectilinear trajectory result of Proudman & Pearson (1957).
Distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate
Authors: Goldstein M. E. , Leib S. J. , Cowley S. J.
Published: April 2006

We consider a nominally uniform flow over a semi-infinite flat plate. Our analysis shows how a small streamwise disturbance in the otherwise uniform flow ahead of the plate is amplified by leading-edge bluntness effects and eventually leads to a small-amplitude but nonlinear spanwise motion far downstream from the leading edge of the plate. This spanwise motion is then imposed on the viscous boundary-layer flow at the surface of the plate – causing an order-one change in its profile shape. This ultimately reduces the wall shear stress to zero – causing the boundary layer to undergo a localized separation, which may be characterized as a kind of bursting phenomenon that could be related to the turbulent bursts observed in some flat-plate boundary-layer experiments.
AK—ε—γ equation turbulence model
Authors: Cho Ji Ryong , Chung Myung Kyoon
Published: April 2006

By considering the entrainment effect on the intermittency in the free boundary of shear layers, a set of turbulence model equations for the turbulent kinetic energyk, the dissipation rate ε, and the intermittency factor γ is proposed. This enables us to incorporate explicitly the intermittency effect in the conventionalK–ε turbulence model equations. The eddy viscosity νtis estimated by a function ofK, ε and γ. In contrast to the closure schemes of previous intermittency modelling which employ conditional zone averaged moments, the present model equations are based on the conventional Reynolds averaged moments. This method is more economical in the sense that it halves the number of partial differential equations to be solved. The proposedK–ε–γ model has been applied to compute a plane jet, a round jet, a plane far wake and a plane mixing layer. The computational results of the model show considerable improvement over previous models for all these shear flows. In particular, the spreading rate, the centreline mean velocity and the profiles of Reynolds stresses and turbulent kinetic energy are calculated with significantly improved accuracy.
Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number
Authors: Mei Renwei , Adrian Ronald J.
Published: April 2006

Unsteady flow over a stationary sphere with a small fluctuation in the free-stream velocity is considered at small Reynolds number, Re. A matched asymptotic solution is obtained for the frequency-dependent (or the acceleration-dependent) part of the unsteady flow at very small frequency, ω, under the restriction St [Lt ] Re [Lt ] 1, where St is the Strouhal number. The acceleration-dependent part of the unsteady drag is found to be proportional to St ∼ ω instead of the ω½ dependence predicted by Stokes’ solution. Consequently, the expression for the Basset history force is incorrect for large time even for very small Reynolds numbers. Present results compare well with the previous numerical results of Mei, Lawrence & Adrian (1991) using a finite-difference method for the same unsteady flow at small Reynolds number. Using the principle of causality, the present analytical results at small Re, the numerical results at finite Re for low frequency, and Stokes’ results for high frequency, a modified expression for the history force is proposed in the time domain. It is confirmed by comparing with the finite-difference results at arbitrary frequency through Fourier transformation. The modified history force has an integration kernel that decays as t−2, instead of t½, at large time for both small and finite Reynolds numbers.
Orbital flow around a circular cylinder. Part 1. Steady streaming in non-uniform conditions
Authors: Chaplin John R.
Published: April 2006

This work is concerned with the source of an important component of nonlinear loading on a horizontal cylinder beneath waves that is not present in conventional diffraction calculations. Earlier measurements (Chaplin 1984b) have suggested that circulation induced by steady streaming around the cylinder may be responsible for loading which in some cases reduces the perceived inertia force by 50%. The present work is aimed at studying the steady streaming around a cylinder in general non-uniform orbital flow, and determining whether in the particular case of wave-induced flow it could be related quantitatively to the loading.

The steady outer flow has been obtained numerically for cases where the steady streaming does not have a reversal, and for cases where a weak reversal is compatible with a uniform outer circulation. It is found that the outer circulation is closely related to the mean streaming velocity around the cylinder at the outer edge of the shear-wave layer. Results for conditions corresponding to previous measurements of force on a horizontal cylinder beneath waves suggest that separation, turbulence, transient effects and organized three-dimensional instabilities should also be considered.
Spin-up from rest of a compressible fluid in a rapidly rotating cylinder
Authors: Hyun Jae Min , Park Jun Sang
Published: April 2006

Spin-up flows of a compressible gas in a finite, closed cylinder from an initial state of rest are studied, The flow is characterized by small reference Ekman numbers, and the peripheral Mach number is O(1). Comprehensive numerical solutions have been obtained for the full, time-dependent compressible Navier-Stokes equations. The details of the flow, temperature, and density evolution are described. In the early phase of spin-up, owing to the thermoacoustic disturbances caused by the compressible Rayleigh effect, the flows are oscillatory, and this oscillatory behaviour is pronounced at higher Mach numbers. The principal dynamical role of the Ekman layer is dominant over moderate times of orders of the homogeneous spin-up timescales. Owing to the density stratification in the radial direction, the Ekman layer is thicker in the central region of the interior. The interior azimuthal flows are mainly uniform in the axial direction. As the Mach number increases, the rate of spin-up in the interior becomes slower, and the propagating shear front is more diffusive. Explicit comparisons with the results for an infinite cylinder are made to ascertain the contributions of the endwall disks. In contrast to the usual incompressible spin-up from rest, the viscous effects are relatively more important for the case of a compressible fluid.
Numerical study of an oscillating cylinder in uniform flow and in the wake of an upstream cylinder
Authors: Li Jing , Sun Jiong , Roux Bernard
Published: April 2006

Direct numerical simulation is carried out to study the response of an oscillating cylinder in uniform flow and in the wake of an upstream cylinder. It is found that the response of the cylinder wake is either a periodic (lock-in) or a quasi-periodic (non-lock-in) state. In the lock-in state, the vortex shedding frequency equals the forcing frequency. In the non-lock-in state, the shedding frequency shows a smooth variation with the driving frequency. For a cylinder oscillating in uniform flow, a lock-in diagram of different forcing amplitude is computed. However, no clear chaotic behaviour is detected near the lock-in boundary. For a cylinder oscillating in the wake of an upstream cylinder, the response state is strongly influenced by the distance between the two cylinders. By changing cylinder spacing, two different flow regimes are identified. In the ‘vortex formation regime’, found at large spacings, the vortex street develops behind both the upstream and downstream cylinders. The strength of the naturally produced oscillation upstream of the second cylinder becomes important compared to the forced oscillation and dominates the flow, leading to a very small or even indistinguishable zone of synchronization. However, in the ‘vortex suppression regime’, observed at small spacings, the oncoming flow to the downstream cylinder becomes so weak that it hardly affects its vortex wake, and therefore a large zone of synchronization is obtained. The numerical results are in good agreement with available experimental data.
Controlling chaos in a thermal convection loop
Authors: Wang Yuzhou , Singer Jonathan , Bau Haim H.
Published: April 2006

It is demonstrated experimentally and theoretically that through the use of an active (feedback) controller one can dramatically modify the nature of the flow in a toroidal thermal convection loop heated from below and cooled from above. In particular, we show how a simple control strategy can be used to suppress (laminarize) the naturally occurring chaotic motion or induce chaos in otherwise time-independent flow. The control strategy consists of sensing the deviation of fluid temperatures from desired values at a number of locations inside the loop and then altering the wall heating to either counteract or enhance such deviations.
A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence
Authors: Holt Steven E. , Koseff Jeffrey R. , Ferziger Joel H.
Published: April 2006

The structure and evolution of homogeneous stably stratified sheared turbulence have been investigated through direct numerical simulation. In these simulations the primary dimensionless parameter is the Richardson number which measures the relative importance of stratification and mean shear.

For Richardson numbers less than the transition value the Reynolds stress and vertical density flux are down-gradient. Some of the vertical kinetic energy gained indirectly through production is expended in creating potential energy. Included in this shear-dominated regime is the stationary Richardson number at which the turbulent kinetic energy is constant in time although the spectra are evolving. At low dimensionless shear rate the stationary Richardson number increases with increasing Reynolds number.

At the transition Richardson number the maximum anisotropy and energy partition are achieved. For larger Richardson numbers potential energy is released into vertical kinetic energy and the vertical density flux becomes counter-gradient. The associated production reversal enhances the decay rate of the turbulent kinetic energy.

The effects of other dimensionless parameters have been investigated. After initial transients the developed flow is rather insensitive to the presence of significant initial potential energy. An increase in the Schmidt number increases the effect of stable stratification, e.g. the counter-gradient vertical density flux occurs earlier.

In the shear dominated case the down-gradient fluxes are produced by the pumping of fluid through coherent hairpin-shaped vorticity. In the buoyancy dominated flow the counter-gradient fluid parcels induce helical vorticity structures as they move toward a position of neutral buoyancy.
The buoyancy-driven motion of a train of viscous drops within a cylindrical tube
Authors: Pozrikidis C.
Published: April 2006

The buoyancy-driven motion of a train of viscous drops settling or rising along the axis of a vertical cylindrical tube is investigated. Under the assumption of creeping flow, the evolution of the drops is computed numerically using a boundary integral method that employs the axisymmetric periodic Green's function for flow in a cylindrical tube. Given the drop volume and assuming that the viscosity of the drops is equal to that of the suspending fluid, the motion is studied as a function of the radius of the tube, the separation between the drops, and the Bond number. Two classes of drops are considered: compact drops whose effective radius is smaller than the radius of the tube, and elongated drops whose effective radius is larger than the radius of the tube. It is found that compact drops may have a variety of steady shapes including prolate and oblate, dimpled tops, and shapes containing pockets of entrained ambient fluid. When the surface tension is sufficiently small, compact drops become unstable, evolving to prolate rings with elongated tails. The terminal velocity of compact drops is discussed and compared with that predicted by previous asymptotic analyses for spherical drops. Steady elongated drops assume the shape of long axisymmetric fingers consisting of a nearly cylindrical main body and two curved ends. Relationships between the terminal velocity of elongated drops, the gap between the drops and the wall of the tube, and the Bond number are established. The results are discussed with reference to previous analyses and laboratory measurements for inviscid bubbles.