bluuebunny/crossref_metadata_2025 huggingface dataset:
Boundary-layer separation of rotating flows past surface-mounted obstacles
Authors: Richards K. J. , Smeed D. A. , Hopfinger E. J. , D'Hières G. Chabert
Published: April 2006

This paper describes laboratory experiments on the flow over a three-dimensional hill in a rotating fluid. The experiments were carried out in towing tanks, placed on rotating tables. Rotation is found to have a strong influence on the separation behind the hill. The topology of the separation is found to be the same for all the flows examined. The Rossby number R in the experiments is of order 1, the maximum value being 6. The separated flow is dominated by a single trailing vortex. In the majority of cases the surface stress field has a single separation line and there are no singular points. In a few experiments at the highest Rossby numbers the observations suggest more complex stress fields but the results are inconclusive.

A criterion for flow separation is sought. For values of D/L > 1, where D is the depth of the flow and L the lengthscale of the hill, separation is found to be primarily dependent on R. At sufficiently small values of R separation is suppressed and the flow remains fully attached.

Linear theory is found to give a good estimate for the critical value of R for flow separation. For hills with a moderate slope (slope ≤ 1) this critical value is around 1, decreasing with increasing slope. It is postulated that the existence of a single dominant trailing vortex is due to the uplifting and subsequent turning of transverse vorticity generated by surface pressure forces upstream of the separation line.
The effects of curvature on sheared turbulence
Authors: Holloway A. G. L. , Tavoularis S.
Published: April 2006

The present experiments are an extension of previous studies on nearly homogeneous, parallel, shear flows and represent an attempt to study the effects of curvature on sheared turbulence in relative isolation from wall and entrainment effects. Uniformly sheared turbulence was allowed to reach a state of transverse statistical homogeneity in a straight rectangular duct: it was then passed into a curved duct, also of rectangular cross-section. The near homogeneity of the turbulence and the near uniformity of the shear were preserved. In the present experiments, the parameter S = (Uc/Rc)(dU/dn) spanned a wide range, from approximately -0.50 to over 1.0 (Uc is the centreline velocity, dU/dn the mean shear and Rc the radius of curvature on the centreline of the duct). Variation of S was achieved by using two curved tunnel sections as well as by adjusting the shear. Measurements indicate that the growth of the turbulent stresses and lengthscales was enhanced for S < 0 and suppressed for S > 0. For S > 0.05, the stresses decayed. In cases where sufficiently large total strain was achieved, the stresses seemed to grow or decay roughly exponentially and to develop in a quasi-self-preserving manner. The magnitude of the dimensionless shear stress decreased monotonically with increasing S, while, for sufficiently large positive values of S, this quantity reversed sign, to achieve the same sense as the mean shear. Measurements of the integral lengthscales and the Taylor microscales are presented and their dependence upon curvature discussed. The results in ‘mildly curved’ flows are used to derive approximate expressions for the dependence upon S of the various terms in the Reynolds stress equations, including the pressure-strain rate covariance tensor.
Three-dimensional boundary-layer instability and separation induced by small-amplitude streamwise vorticity in the upstream flow
Authors: Goldstein M. E. , Leib S. J.
Published: April 2006

We consider the effects of a small-amplitude, steady, streamwise vorticity field on the flow over an infinitely thin flat plate in an otherwise uniform stream. We show how the initially linear perturbation, ultimately leads to a small-amplitude but nonlinear cross-flow far downstream from the leading edge. This motion is imposed on the boundary-layer flow and eventually causes the boundary layer to separate. The streamwise velocity profiles within the boundary layer become inflexional in localized spanwise regions just upstream of the separation point. The flow in these regions is therefore susceptible to rapidly growing inviscid instabilities.
The laminar interactions of a pair of vortex tubes with a free surface
Authors: Dommermuth Douglas G.
Published: April 2006

A fully nonlinear numerical method is developed to study the viscous interactions of a pair of vortex tubes rising toward a free surface. The numerical theory uses Helmholtz's decomposition to treat the irrotational and vortical components of the flow as separate nonlinearly coupled equations. The laminar interactions of a pair of vortex tubes with a clean free surface at intermediate Froude and Weber numbers and a low Reynolds number show two distinct phases. During the rise phase of the vortex pairs, instabilities lead to the formation of helical vorticity. The rotation of the helical vorticity around the primary vortex tubes causes an unsteady oscillation in the free-surface elevation. During the reconnection phase, the helical vortex sheets get narrower and attach themselves to the free surface. The normal connections of cross-axis vorticity with the free surface give whirls. The free-surface elevation is well correlated with the vortical pressure. The numerical results agree qualitatively with experimental measurements.
On the response of a reservoir sidearm to diurnal heating and cooling
Authors: Farrow D. E. , Patterson J. C.
Published: April 2006

During the day, the shallower regions of a reservoir sidearm absorb more heat per unit volume than the deeper parts, leading to a horizontal pressure gradient that drives a circulation in the sidearm. At night, the shallow regions cool more rapidly, leading to a circulation in the opposite direction. Since the spin-up time of a typical sidearm is at least of the same order as a day, the flow within a diurnally forced sidearm is principally an inertia–buoyancy balance. In this paper, a diurnally forced sidearm is modelled by periodically forced natural convection in a triangular cavity. The periodic forcing enters the model via an internal heating/cooling term in the temperature equation. Reservoir sidearms typically have small bottom slopes and this fact can be exploited to obtain asymptotic solutions of the resulting equations. These solutions clearly demonstrate the transition from the viscous-dominated flow in the shallows to the inertia-dominated flow in the deeper parts. In the inertia-dominated region, the flow response significantly lags the forcing. Numerical solutions of the full nonlinear problem are consistent with the asymptotic solutions.
Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet
Authors: Panchapakesan N. R. , Lumley J. L.
Published: April 2006

A turbulent round jet of air discharging into quiescent air was studied experimentally. Some × -wire hot-wire probes mounted on a moving shuttle were used to eliminate rectification errors due to flow reversals in the intermittent region of the jet. Moments of velocity fluctuations up to fourth order were measured to characterize turbulent transport in the jet and to evaluate current models for triple moments that occur in the Reynolds stress equations. Fourth moments were very well described in terms of second moments by the quasi-Gaussian approximation across the entire jet including the intermittent region. Profiles of third moments were found to be significantly different from earlier measurements: 〈uv2〉, 〈uw2〉 and 〈u2v〉 are found to be negative near the axis of the jet. TheBasictriple moment model that included turbulent production and models for the dissipation and the return-to-isotropy part of the pressure correlations was found to be unsatisfactory. When mean-strain production and a model for rapid pressure correlations were also included, predictions were satisfactory in the fully turbulent region. The consistency of the measurements with the equations of motion was assessed: momentum flux across the jet was found to be within ±5% of the nozzle input and the integral of radial diffusive flux of turbulent kinetic energy across the jet calculated from the measured third moments was found to be close to zero.
Turbulence measurements in axisymmetric jets of air and helium. Part 2. Helium jet
Authors: Panchapakesan N. R. , Lumley J. L.
Published: April 2006

A turbulent round jet of helium was studied experimentally using a composite probe consisting of an interference probe of the Way–Libby type and an × -probe. Simultaneous measurements of two velocity components and helium mass fraction concentration were made in the x/d range 50–120. These measurements are compared with measurements in an air jet of the same momentum flux reported in Part 1. The jet discharge Froude number was 14000 and the measurement range was in the intermediate region between the non-buoyant jet region and the plume region. The measurements are consistent with earlier studies on helium jets. The mass flux of helium across the jet is within ±10% of the nozzle input. The mean velocity field along the axis of the jet is consistent with the scaling expressed by the effective diameter but the mean concentration decay constant exhibits a density-ratio dependence. The radial profiles of mean velocity and mean concentration agree with earlier measurements, with the half-widths indicating a turbulent Schmidt number of 0.7. Significantly higher intensities of axial velocity fluctuations are observed in comparison with the air jet, while the intensities of radial and azimuthal velocity fluctuations are virtually identical with the air jet when scaled with the half-widths. Approximate budgets for the turbulent kinetic energy, scalar variance and scalar fluxes are presented. The ratio of mechanical to scalar timescales is found to be close to 1.5 across most of the jet. Current models for triple moments involving scalar fluctuations are compared with measurements. As was observed with the velocity triple moments in Part 1, the performance of the Full model that includes all terms except advection was found to be very good in the fully turbulent region of the jet.
Note on formulas for the drag of a sphere
Authors: Benjamin T. Brooke
Published: April 2006

Standard approximations expressing the drag of a sphere as a function of Reynolds number are reappraised in the light of the evident requirement that drag reverses with the direction of motion. It is thereby highlighted that the relation between the drag and the velocity of a sphere is not analytic. Another, simpler example is cited to illustrate a non-analytic relation between physical properties, which is appreciated to be a common feature of hydrodynamic models that rely on the abstract notion of an infinite incompressible fluid.
The asymptotic theory of hypersonic boundary-layer stability
Authors: Grubin S. E. , Trigub V. N.
Published: April 2006

In this paper the linear stability of the hypersonic boundary layer is considered in the local-parallel approximation. It is assumed that the Prandtl-number ½ < σ < 1 and the viscosity-temperature law is a power function: μ/μ∞ = (T/T∞)ω. The asymptotic theory in the limit M∞ → ∞ is developed.

Smith & Brown found for the Blasius base flow and Balsa & Goldstein for the mixing layer that, in this limit, the disturbances of the vorticity mode are located in the thin region between the boundary layer and the external flow. The gas model with σ = 1, ω = 1 was exploited in these studies. Here it is demonstrated that the vorticity mode also exists for gas with ½ < σ 1, ω < 1, but its structure and characteristics are considerably different. The nomenclature is discussed, i.e. what an acoustic mode and a vorticity mode are. The numerical solution of the inviscid instability problem for the vorticity mode is obtained for helium and compared with the solution of the complete Rayleigh equation at finite Mach numbers.

The limit M∞ → ∞ in the local-parallel approximation for the Blasius base flow is considered so as to understand the viscous structure of the vorticity mode. The viscous stability problem for the vorticity mode is formulated under these assumptions. The problem contains only a single similarity parameter which is a function of the Mach and Reynolds numbers, the temperature factor and wave inclination angle. This problem is numerically solved for helium. The universal upper branch of the neutral curve is obtained as a result. The asymptotic results are compared with the numerical solutions of the complete problem.
Spin-up from rest of a mixture: numerical simulation and asymptotic theory
Authors: Amberg Gustav , Ungarish Marius
Published: April 2006

Spin-up from rest of a separating fluid–particle mixture is studied. A cylindrical container, filled with a stationary mixture of initially uniform particle volume fraction, is instantaneously set into rapid rotation. The viscous forces.on the walls introduce a secondary Ekman-layer circulation which causes the fluid motion to gradually approach a state of solid-body rotation. While the mixture acquires angular momentum, separation starts under the action of the local centrifugal effects: the dispersed particles – assumed here to be lighter than the fluid – tend to concentrate around the centre, leaving behind a peculiarly shaped domain of pure fluid. This process is simulated by a finite difference version of the ‘mixture model’ equations. The numerical results are in good agreement with previous asymptotical predictions but also illuminate some aspects of the flow field that have been covered by the analytical approach.
Turbulent boundary layers subjected to multiple curvatures and pressure gradients
Authors: Bandyopadhyay Promode R. , Ahmed Anwar
Published: April 2006

The effects of abruptly applied cycles of curvatures and pressure gradients on turbulent boundary layers are examined experimentally. Two two-dimensional curved test surfaces are considered: one has a sequence of concave and convex longitudinal surface curvatures and the other has a sequence of convex and concave curvatures. The choice of the curvature sequences were motivated by a desire to study the asymmetric response of turbulent boundary layers to convex and concave curvatures. The relaxation of a boundary layer from the effects of these two opposite sequences has been compared. The effect of the accompanying sequences of pressure gradient has also been examined but the effect of curvature dominates. The growth of internal layers at the curvature junctions have been studied. Measurements of the Górtler and corner vortex systems have been made. The boundary layer recovering from the sequence of concave to convex curvature has a sustained lower skin friction level than in that recovering from the sequence of convex to concave curvature. The amplification and suppression of turbulence due to the curvature sequences have also been studied.
On the nonlinear development of the most unstable Görtler vortex mode
Authors: Denier James P. , Hall Philip
Published: April 2006

The nonlinear development of the most unstable Görtler vortex mode in boundary-layer flows over curved walls is investigated. The most unstable Görtler mode is confined to a viscous wall layer of thickness O(G−1/5) and has spanwise wavelength O(G−1/5); it is, of course, most relevant to flow situations where the Görtler number G [Gt ] 1. The nonlinear equations governing the evolution of this mode over an O(G−3/5) streamwise lengthscale are derived and are found to be of a fully non-parallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Görtler equations valid for O(1) Görtler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite-difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flow field as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.
Flow in deformable porous media. Part 2 Numerical analysis – the relationship between shock waves and solitary waves
Authors: Spiegelman Marc
Published: April 2006

Using numerical schemes, this paper demonstrates how viscous resistance to volume changes modifies the simplest shock wave solutions presented in Part 1. For an initial condition chosen to form a step-function shock, viscous resistance causes the shock to disperse into a rank-ordered wavetrain of solitary waves. Large obstructions in flux produce large-amplitude, slow-moving wavetrains while smaller shocks shed small-amplitude waves. While the viscous resistance term is initially important over a narrow boundary layer, information about obstructions in the flux can propagate over many compaction lengths through the formation of non-zero wavelength porosity waves. For large-amplitude shocks, information can actually propagate backwards relative to the matrix. The physics of dispersion is discussed and a physical argument is presented to parameterize the amplitude of the wavetrain as a function of the amplitude of the predicted shock. This quantitative relationship between the prediction of shocks and the development of solitary waves also holds when mass transfer between solid and liquid is included. Melting causes solitary waves to decrease in amplitude but the process is reversible and freezing can cause small perturbations in the fluid flux to amplify into large-amplitude waves. These model problems show that the equations governing volume changes of the matrix are inherently time dependent. Perturbations to steady-state solutions propagate as nonlinear waves and these problems demonstrate several initial conditions that do not relax to steady state. If these equations describe processes such as magma migration in the Earth, then these processes should be inherently episodic in space and time.
On some kinematic versus dynamic properties of homogeneous turbulence
Authors: Shtilman L. , Spector M. , Tsinober A.
Published: April 2006

A comparison is made between a number of properties of a quasi-homogeneous isotropic turbulent field obtained from a direct numerical simulation of the Navier–Stokes equation and its random counterpart with the same energy spectrum. It is demonstrated that some effects in a real flow have a considerable contribution of a kinematic nature (e.g. reduction of nonlinearity), while others are mostly dynamical (e.g. alignment between vorticity and eigenvectors of the rate of strain).
The motion and stability of a vortex array above a pulsed surface
Authors: Acton E. , Dhanak M. R.
Published: April 2006

A model inviscid and incompressible flow problem is studied in which an infinite array of equi-spaced identical rectilinear line vortices moves in a uniform stream over a wall in which is embedded an equi-spaced array of discrete line sources of variable strength. It is shown that for a suitable choice of source spacing and strength, a flow that is periodic both in time and in the streamwise direction is possible. The flow is shown to be stable to small two-dimensional disturbances for a range of values of vortex height above the wall and source strength. The implications for the corresponding viscous problem and active flow control are discussed.
Flow generated by a small oscillating cylinder in a mixing layer
Authors: Balsa Thomas F.
Published: April 2006

We study the flow generated by a small circular cylinder in a mixing layer. The cylinder is executing an oscillatory translation whose frequency is within the range of unstable frequencies of the shear layer. The smallness of the cylinder is measured by the ratio of its radius to the characteristic thickness of the layer. This (small) ratio serves as the expansion parameter for our theory; the flow naturally divides into inner and outer regions. The former is in the immediate vicinity of the cylinder and the latter is the far field which contains the instability waves. The solution to this problem is obtained by the method of matched asymptotic expansion. One objective is to study the dependence of this solution on various parameters such as the frequency of oscillation, velocity ratio, etc., and thus shed light on the associatedreceptivity. Other objectives deal with a restatement of causality and with the hydrodynamic field near the streamwise location of the cylinder. We find that receptivity is a strong function of frequency and velocity ratio and that the local hydrodynamic field may be quite large. Causality is restated in terms of the well-known exponential integral.
Elliptic jets. Part 3. Dynamics of preferred mode coherent structure
Authors: Husain Hyder S. , Hussain Fazle
Published: April 2006

The dynamics of the preferred mode structure in the near field of an elliptic jet have been investigated using hot-wire measurements. A 2:1 aspect ratio jet with an initially turbulent boundary layer and a constant momentum thickness all around the nozzle exit perimeter was used for this study. Measurements were made in air at a Reynolds number ReDe (≡ UeDe/v) = 3.5 × 104. Controlled longitudinal excitation at the preferred mode frequency (StDe ≡ fDe/Ue = 0.4) induced periodic formation of structures, allowing phase-locked measurements with a local trigger hot wire. The dynamics of the organized structure are examined from educed fields of coherent vorticity and incoherent turbulence in the major and minor symmetry planes at five successive phases of evolution, and are also compared with corresponding data for a circular jet. Unlike in a circular jet, azimuthally fixed streamwise vortices (ribs) form without the aid of azimuthal forcing. The three-dimensional deformation of elliptic vortical structures and the rib formation mechanism have also been studied through direct numerical simulation. Differential self-induced motions due to non-uniform azimuthal curvature and the azimuthally fixed ribs produce greater mass entrainment in the elliptic jet than in a circular jet. The turbulence production mechanism, entrainment and mixing enhancement, and time-average measures and their modification by excitation are also discussed in terms of coherent structure dynamics and the rib-roll interaction. Various phase-dependent and time-average turbulence measures documented in this paper should serve as target data for validation of numerical simulations and turbulence modelling, and for design and control purposes in technological applications. Further details are given by Husain (1984).
The interaction between a steady jet flow and a supersonic blade tip
Authors: Peake N.
Published: April 2006

The potentially high level of noise generated by modern counter-rotation propellers has attracted considerable interest and concern, and one of the most potent mechanisms involved is the unsteady interaction between the tip vortex shed from the tips of the forward blade row and the rear row. In this paper a model problem is considered, in which the tip vortex is represented by a jet of constant axial velocity, which is convected at right angles to itself by a uniform supersonic mean flow, and which is cut by a rigid airfoil with its chord aligned along the mean flow direction. Ffowcs Williams & Guo have previously considered this problem for an infinite-span airfoil and a circular jet; in this paper we extend their analysis to include the effects of the presence of the second-row blade tip on the interaction, by considering a semi-infinite-span airfoil. As a first attempt, the case of a highly compact jet, represented by a delta-function upwash on the airfoil, is considered, and both the total lift on the airfoil and the radiation are investigated. The presence of the airfoil corner and side edge is seen to cause the lift to decay in time from its infinite-span value towards zero, due to a spanwise motion round the side edge; whilst the radiation is shown to be composed of two Signals, the first received directly from the interaction between the jet and the leading edge, and the second resulting from the diffraction of sound waves emanating from the leading edge by the side edge. The effect of choosing a more diffuse upwash distribution is then considered, in which case it becomes clear that the first signal has a considerably larger amplitude, and shorter duration, than the second, diffracted signal.
The plane Symmetric sudden-expansion flow at low Reynolds numbers
Authors: Durst F. , Pereira J. C. F. , Tropea C.
Published: April 2006

Detailed velocity measurements and numerical predictions are presented for the flow through a plane nominally two-dimensional duct with a Symmetric sudden expansion of area ratio 1:2. Both the experiments and the predictions confirm a symmetry-breaking bifurcation of the flow leading to one long and one short Separation zone for channel Reynolds numbers above 125, based on the upstream channel height and the maximum flow velocity upstream. With increasing Reynolds numbers above this value, the short separated region remains approximately constant in length whereas the long region increases in length.

The experimental data were obtained using a one-component laser-Doppler anemometer at many Reynolds number values, with more extensive measurements being performed for the three Reynolds numbers 70, 300 and 610. Predictions were made using a finite volume method and an explicit quadratic Leith type of temporal discretization. In general, good agreement was found between measured and predicted velocity profiles for all Reynolds numbers investigated.
On Faraday waves
Authors: Miles John
Published: April 2006

The standing waves of frequency ω and wavenumber κ that are induced on the surface of a liquid of depthdthat is subjected to the vertical displacementaocos 2wtare determined on the assumptions that: the effects of lateral boundaries are negligible; ε =ka0tanhkd[Lt ] 1 and 0 < ε−δ = O(δ3), where δ is the linear damping ratio of a free wave of frequency ω; the waves form a square pattern (which follows from observation). This problem, which goes back to Faraday (1831), has recently been treated by Ezerskiiet al.(1986) and Milner (1991) in the limit of deep-water capillary waves (kd, kl*[Gt ] 1, wherel*is the capillary length). Ezerskiiet al.show that the square pattern is unstable for sufficiently large ε—δ, and Milner shows that nonlinear damping is necessary for equilibration of the square pattern. The present formulation extends those of Ezerskiiet al.and Milner to capillary–gravity waves and finite depth and incorporates third-order parametric forcing, which is neglected in these earlier formulations but is comparable with third-order damping. There are quantitative differences in the resulting evolution equations (forkd, kl*[Gt ] 1), which appear to reflect errors in the earlier work.

These formulations determine a locus of admissible waves, but they do not select a particular wave. The hypothesis that the selection process maximizes the energy-transfer rate to the Faraday wave selects the maximum of the resonance curve in a frequency-amplitude plane.
The structure of a three-dimensional turbulent boundary layer
Authors: Degani A. T. , Smith F. T. , Walker J. D. A.
Published: April 2006

The three-dimensional turbulent boundary layer is shown to have a self-consistent two-layer asymptotic structure in the limit of large Reynolds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a defect-function form in the outer layer which is adjusted to zero at the wall through an inner wall layer. An asymptotic expansion accurate to two orders is required for the cross-stream velocity which is shown to exhibit a logarithmic form in the overlap region. The inner wall-layer flow is collateral to leading order but the influence of the pressure gradient, at large but finite Reynolds numbers, is not negligible and can cause substantial skewing of the velocity profile near the wall. Conditions under which the boundary layer achieves self-similarity and the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is matched asymptotically to an inner wall-layer solution and the composite profiles so formed describe the flow throughout the entire boundary layer. The effects of Reynolds number and cross-stream pressure gradient on the cross-stream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overlap region.
A mechanism for bypass transition from localized disturbances in wall-bounded shear flows
Authors: Henningson Dan S. , Lundbladh Anders , Johansson Arne V.
Published: April 2006

The linear, nonlinear and breakdown stages in the transition of localized disturbances in plane Poiseuille flow is studied by direct numerical simulations and analysis of the linearized Navier–Stokes equations. Three-dimensionality plays a key role and allows for algebraic growth of the normal vorticity through the linear lift-up mechanism. This growth primarily generates elongated structures in the streamwise direction since it is largest at low streamwise wavenumbers. For finite-amplitude disturbances such structures will be generated essentially independent of the details of the initial disturbance, since the preferred nonlinear interactions transfer energy to low streamwise wavenumbers. The nonlinear interactions also give a decrease in the spanwise scales. For the stronger initial disturbances the streamwise vorticity associated with the slightly inclined streaks was found to roll up into distinct streamwise vortices in the vicinity of which breakdown occurred. The breakdown starts with a local rapid growth of the normal velocity bringing low-speed fluid out from the wall. This phenomenon is similar to the low-velocity spikes previously observed in transition experiments. Soon thereafter a small turbulent spot is formed. This scenario represents a bypass of the regular Tollmien–Schlichting, secondary instability process. The simulations have been carried out with a sufficient spatial resolution to ensure an accurate description of all stages of the breakdown and spot formation processes. The generality of the observed processes is substantiated by use of different types of initial disturbances and by Blasius boundary-layer simulations. The present results point in the direction of universality of the observed transition mechanisms for localized disturbances in wall-bounded shear flows.
Nonlinear evolution of waves on a vertically falling film
Authors: Chang H.-C. , Demekhin E. A. , Kopelevich D. I.
Published: April 2006

Wave formation on a falling film is an intriguing hydrodynamic phenomenon involving transitions among a rich variety of spatial and temporal structures. Immediately beyond an inception region, short, near-sinusoidal capillary waves are observed. Further downstream, long, near-solitary waves with large tear-drop humps preceded by short, front-running capillary waves appear. Both kinds of waves evolve slowly downstream such that over about ten wavelengths, they resemble stationary waves which propagate at constant speeds and shapes. We exploit this quasi-steady property here to study wave evolution and selection on a vertically falling film. All finite-amplitude stationary waves with the same average thickness as the Nusselt flat film are constructed numerically from a boundary-layer approximation of the equations of motion. As is consistent with earlier near-critical analyses, two travelling wave families are found, each parameterized by the wavelength or the speed. One family γ1travels slower than infinitesimally small waves of the same wavelength while the other family γ2and its hybrids travel faster. Stability analyses of these waves involving three-dimensional disturbances of arbitrary wavelength indicate that there exists a unique nearly sinusoidal wave on the slow family γ1with wavenumber αs(or α2) that has the lowest growth rate. This wave is slightly shorter than the fastest growing linear mode with wavenumber αmand approaches the wave on γ1with the highest flow rate at low Reynolds numbers. On the fast γ2family, however, multiple bands of near-solitary waves bounded below by αfare found to be stable to two-dimensional disturbances. This multiplicity of stable bands can be interpreted as a result of favourable interaction among solitary-wave-like coherent structures to form a periodic train. (All waves are unstable to three-dimensional disturbances with small growth rates.) The suggested selection mechanism is consistent with literature data and our numerical experiments that indicate waves slow down immediately beyond inception as they approach the short capillary wave with wavenumber α2of the slow γ1family. They then approach the long stable waves on the γ2family further downstream and hence accelerate and develop into the unique solitary wave shapes, before they succumb to the slowly evolving transverse disturbances.
Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow
Authors: Chang K. S. , Olbricht W. L.
Published: April 2006

An experimental study is reported of the motion, deformation, and breakup of a synthetic capsule that is freely suspended in Couette flow. The capsule is a liquid drop surrounded by a thin polymeric membrane. The shape and orientation of the capsule are measured in steady flow and following the start-up of Couette flow. Results are compared with predictions of the small-deformation theory of Barthes-Biesel and co-workers. The data suggest that the capsule membrane is viscoelastic, and comparisons with theory yield values of the membrane elastic modulus and the membrane viscosity. The values of the elastic modulus of the capsule membrane deduced from the flow data are compared with independent measurements for the same capsule.

When the flow-induced deformation becomes sufficiently large, the capsules break. Breakup begins at points on the membrane surface near the principal strain axis of the undisturbed flow. By examining the local deformation within the membrane, it is shown that breakup is correlated with local thinning of the membrane and is initiated at points where the thickness is a minimum.
Trapped modes of internal waves in a channel spanned by a submerged cylinder
Authors: Kuznetsov Nikolay
Published: April 2006

A horizontal channel of infinite length and depth and of constant width contains inviscid, incompressible, two-layer fluid under gravity. The upper layer has constant finite depth and is occupied by a fluid of constant density ρ*. The lower layer has infinite depth and is occupied by a fluid of constant density ρ > ρ*. The parameter ε = (ρ/ρ*)–1 is assumed to be small. The lower fluid is bounded internally by an immersed horizontal cylinder which extends right across the channel and has its generators normal to the sidewalls. The free, time-harmonic oscillations of fluid, which have finite kinetic and potential energy (such oscillations are called trapped modes), are investigated. Trapped modes in homogeneous fluid above submerged cylinders and other obstacles are well known. In the present paper it is shown that there are two sets of frequencies of trapped modes for the two-layer fluid. The frequencies of the first finite set are close to the frequencies of trapped modes in the homogeneous fluid (when ρ* = ρ). They correspond to the trapped modes of waves on the free surface of the upper fluid. The frequencies of the second finite set are proportional to ε, and hence, are small. These latter frequencies correspond to the trapped modes of internal waves on the interface between two fluids. To obtain these results the perturbation method for a quadratic operator family was applied. The quadratic operator family with bounded, symmetric, linear, integral operators in the space L2(−∞, +∞) arises as a result of two reductions of the original problem. The first reduction allows to consider the potential in the lower fluid only. The second reduction is the same as used by Ursell (1987).
Buoyancy-induced flow in porous media generated near a drilled oil well. Part 1. The accumulation of filtrate at a horizontal impermeable boundary
Authors: Dussan V. E. B. , Auzerais François M.
Published: April 2006

A substantial amount of drilling fluid can invade a permeable bed during the drilling of an oil well. The presence of this fluid, often referred to as filtrate, can greatly influence the performance of instruments lowered into the wellbore for the purpose of locating these permeable beds. The invaded filtrate can also substantially alter the physical properties of the porous rock. For these reasons, it is of great interest to known where the filtrate goes upon entering the bed. The objective of this study is to quantify the influence of the difference in density between the filtrate and the naturally occurring formation fluid on the shape of the filtrate front as the filtrate invades the formation. This type of phenomenon is often referred to as buoyancy or gravity segregation. In this study, Part 1, we determine the behaviour of the filtrate as it accumulates (and spreads out) at a horizontal impermeable barrier within the formation. This is a combined theoretical and experimental study in which an X-ray CT scanner is extensively used to determine the appropriateness and limitations of the simplifying assumptions used in the theory. In Part 2, the flow of the invading filtrate within the entire bed will be presented. The problem addressed in Part 1 may be viewed from the broader, more fundamental, perspective, as a well-defined model fluid mechanics problem for flow in porous media. One fundamental issue infrequently addressed concerns the consequence on the dynamics of the fluids of heterogeneities, always present to some degree, in consolidated porous solids. The X-ray CT scanner enables the assessment of the appropriateness of modelling such porous solids as spatially homogeneous, a very popular assumption. This study also addresses the limitation of the small-slope approximation when a fluid–fluid interface occurs in a porous solid, an approximation which has enjoyed great success in free-surface fluid mechanics problems when no porous media is present.
The effect of a weak heterogeneity of a porous medium on natural convection
Authors: Braester Carol , Vadasz Peter
Published: April 2006

The results of an investigation on the effect of a weak heterogeneity of a porous medium on natural convection are presented. A medium heterogeneity is represented by spatial variations of the permeability and of the effective thermal conductivity. As a general rule the existence of horizontal thermal gradients in heterogeneous porous media provides a sufficient condition for the occurrence of natural convection. The implications of this condition are investigated for horizontal layers or rectangular domains subject to isothermal top and bottom boundary conditions. Results lead to a restriction on the classes of thermal conductivity functions which allow a motionless solution. Analytical solutions for rectangular weak heterogeneous porous domains heated from below, consistent with a basic motionless solution, are obtained by applying the weak nonlinear theory. The amplitude of the convection is obtained from an ordinary non-homogeneous differential equation, with a forcing term representative of the medium heterogeneity with respect to the effective thermal conductivity. A smooth transition through the critical Rayleigh number is obtained, thus removing a bifurcation which usually appears in homogeneous domains with perfect boundaries, at the critical value of the Rayleigh number. Within a certain range of slightly supercritical Rayleigh numbers, a symmetric thermal conductivity function is shown to reinforce a symmetrical flow while antisymmetric functions favour an antisymmetric flow. Except for the higher-order solutions, the weak heterogeneity with respect to permeability plays a relatively passive role and does not affect the solutions at the leading order. In contrast, the weak heterogeneity with respect to the effective thermal conductivity does have a significant effect on the resulting flow pattern.
Gas bubbles bursting at a free surface
Authors: Boulton-Stone J. M. , Blake J. R.
Published: April 2006

When a small air bubble bursts from an equilibrium position at an air/water interface, a complex motion ensues resulting in the production of a high-speed liquid jet. This free-surface motion following the burst is modelled numerically using a boundary integral method. Jet formation and liquid entrainment rates from jet breakup into drops are calculated and compared with existing experimental evidence. In order to investigate viscous effects, a boundary layer is included in the calculations by employing a time-stepping technique which allows the boundary mesh to remain orthogonal to the surface. This allows an approximation of the vorticity development in the region of boundary-layer separation during jet formation. Calculated values of pressure and energy dissipation rates in the fluid indicate a violent motion, particularly for smaller bubbles. This has important implications for the biological industry where animal cells in bioreactors have been found to be killed by the presence of small bubbles.
The role of acoustics in flame/vortex interactions
Authors: Jackson T. L. , Macaraeg Michéle G. , Hussaini M. Y.
Published: April 2006

The role of acoustics in flame/vortex interactions is examined via asymptotic analysis and numerical simulation. The model consists of a one-step, irreversible Arrhenius reaction between initially unmixed species occupying adjacent half-planes which are allowed to mix and react by convection and diffusion in the presence of an acoustic field or a time-varying pressure field of small amplitude. The main emphasis is on the influence of the acoustics on the ignition time and flame structure as a function of vortex Reynolds number and initial temperature differences of the reactants.
A numerical investigation of the coherent vortices in turbulence behind a backward-facing step
Authors: Neto Aristeu Silveira , Grand Dominique , Métais Olivier , Lesieur Marcel
Published: April 2006

This paper presents a statistical and topological study of a complex turbulent flow over a backward-facing step by means of direct and large-eddy simulations. Direct simulations are first performed for an isothermal two-dimensional case. In this case, shedding of coherent vortices in the mixing layer is demonstrated. Both direct and large-eddy simulations are then carried out in three dimensions. The subgrid-scale model used is the structure-function model proposed by Métais & Lesieur (1992). Lowstep computations corresponding to the geometry of Eaton & Johnston's (1980) laboratory experiment give turbulence statistics in better agreement with the experimental data than both Smagorinsky's method and K-ε modelling. Furthermore, calculations for a high step show that the eddy structure of the flow presents striking analogies with forced plane mixing layers: large billows are shed behind the step with intense longitudinal vortices strained between them.
Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence
Authors: Wang Lian-Ping , Maxey Martin R.
Published: April 2006

The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, has been shown to differ from that in still fluid owing to a bias from the particle inertia (Maxey 1987). Previous numerical results for particles in a random flow field, where the flow dynamics were not considered, showed an increase in the average settling velocity. Direct numerical simulations of the motion of heavy particles in isotropic homogeneous turbulence have been performed where the flow dynamics are included. These show that a significant increase in the average settling velocity can occur for particles with inertial response time and still-fluid terminal velocity comparable to the Kolmogorov scales of the turbulence. This increase may be as much as 50% of the terminal velocity, which is much larger than was previously found. The concentration field of the heavy particles, obtained from direct numerical simulations, shows the importance of the inertial bias with particles tending to collect in elongated sheets on the peripheries of local vortical structures. This is coupled then to a preferential sweeping of the particles in downward moving fluid. Again the importance of Kolmogorov scaling to these processes is demonstrated. Finally, some consideration is given to larger particles that are subject to a nonlinear drag force where it is found that the nonlinearity reduces the net increase in settling velocity.
Acoustic forcing of oblique wave resonance in the far wake
Authors: Williamson C. H. K. , Prasad A.
Published: April 2006

In this paper, we investigate to what extent the far-wake ‘signature’ of the near-wake vortex dynamics of a nominally two-dimensional bluff body is affected by the character of the free-stream noise. We confirm the existence of an oblique wave resonance (at frequency, fK–fT), which is caused by nonlinear ‘quadratic’ interactions between primary oblique shedding waves (fK) and secondary two-dimensional waves (fT), which are amplified from free-stream disturbances. In this work, oblique wave resonance is induced by acoustic forcing of two-dimensional waves. The use of acoustic forcing reveals a set of higher-order oblique wave resonances corresponding to frequencies (fK–nfT), where n is an integer. We find from visualization that, even when the secondary two-dimensional waves have the same frequency as the oblique waves, it is the oblique waves that are preferentially amplified. Oblique wave angles up to 74° have been observed. The response of the wake to a large range of forcing frequencies shows a broad region of peak response, centred around F = (fT/fK) = 0.55, and is in reasonable agreement with predictions from linear stability analysis. A similar broad response is found for each of the higher-order oblique wave modes. Simple equations for the oblique waves yield approximate conditions for maximum wake response, with a frequency for peak response given by Fmax = 1/2n = 1/2, 1/4, 1/6,…, and an oblique wave angle given by θmax = 2θK, where θK is the angle of oblique vortex shedding. An increase in forcing amplitude has the effect of bringing the nonlinear wave interactions, leading to oblique wave resonance, further upstream. Paradoxically, the effect of an increase in amplitude (A) of the two-dimensional wave forcing is to further amplify the oblique waves in preference to the two-dimensional waves and, under some conditions, to inhibit the appearance of prominent two-dimensional waves where they would otherwise appear. With a variation in forcing amplitude, the amplitude of oblique wave response is found to be closely proportional to A½. In summary, this investigation confirms the surprising result that it is only through the existence of noise in the free stream that the far wake is ‘connected’ to the near wake.