bluuebunny/crossref_metadata_2025 huggingface dataset:
Density fluctuation correlations in free turbulent binary mixing
Authors: Chassaing P. , Harran G. , Joly L.
Published: April 2006

This paper is devoted to the analysis of the turbulent mass flux and, more generally, of the density fluctuation correlation (d.f.c.) effects in variable-density fluid motion. The situation is restricted to the free turbulent binary mixing of an inhomogeneous round jet discharging into a quiescent atmosphere. Based on conventional (Reynolds) averaging, a ternary regrouping of the correlations occurring in the statistical averaging of the open equations is first introduced. Then an exact algebraic relationship between the d.f.c. terms and the second-order moments is demonstrated. Some consequences of this result on the global behaviour of variable-density jets are analytically discussed. The effects of the d.f.c. terms are shown to give a qualitative explanation of the influence of the ratio of the densities of the inlet jet and ambient fluid on the centerline decay rates of mean velocity and mass fraction, the entrainment rate and the restructuring of the jet. Finally, the sensitivity of second-order modelling to the d.f.c. terms is illustrated and it is suggested that such terms should be considered as independent variables in the closing procedure.
On the stability of Poiseuille flow of a Bingham fluid
Authors: Frigaard I. A. , Howison S. D. , Sobey I. J.
Published: April 2006

The stability to linearized two-dimensional disturbances of plane Poiseuille flow of a Bingham fluid is considered. Bingham fluids exhibit a yield stress in addition to a plastic viscosity and this description is typically applied to drilling muds. A non-zero yield stress results in an additional parameter, a Bingham number, and it is found that the minimum Reynolds number for linear instability increases almost linearly with increasing Bingham number.
Theoretical prediction and design for vortex generators in turbulent boundary layers
Authors: Smith F. T.
Published: April 2006

A theoretical study is presented of three-dimensional turbulent flow provoked in a boundary layer by an array of low-profile vortex generators (VGs) on the surface. The typical VG sits in the logarithmic region of the incident boundary layer, and the turbulence model used seems representative in this region. The governing equations yield a forward-marching three-dimensional vortex-type system, which is solved computationally and analytically for spanwise periodic VG arrays. Streamwise vortex patterns of various strengths are produced downstream, owing to three-dimensional distortion of the original logarithmic profile and to the turbulent stresses present. Predictions are given for certain basic VG shapes, e.g. triangular, with various spanwise spacings, and the predictions are found to agree favourably overall with recent experiments. In addition, the analytical formulae obtained prove useful in suggesting designs for favourable VG distributions, based on three factors: close spanwise packing, increased VG length, and suitably non-smooth spanwise shaping.
Plume formation and resonant bifurcations in porous-media convection
Authors: Graham Michael D. , Steen Paul H.
Published: April 2006

The classical boundary-layer scaling laws proposed by Howard for Rayleigh–Bénard convection at high Rayleigh number extend to the analogous case of convection in saturated porous media. We computationally study two-dimensional porous-media convection near the onset of this scaling behaviour. The main result of the paper is the observation and study of instabilities that lead to deviations from the scaling relations.

At Rayleigh numbers below the scaling regime, boundary-layer fluctuations born at a Hopf bifurcation strengthen and eventually develop into thermal plumes. The appearance of plumes corresponds to the onset of the boundary-layer scaling behaviour of the oscillation frequency and mean Nusselt number, in agreement with the classical theory. As the Rayleigh number increases further, the flow undergoes instabilities that lead to ‘bubbles’ in parameter space of quasi-periodic flow, and eventually to weakly chaotic flow. The instabilities disturb the plume formation process, effectively leading to a phase modulation of the process and to deviations from the scaling laws. We argue that these instabilities correspond to parametric resonances between the timescale for plume formation and the characteristic convection timescale of the flow.
Turbulence structural changes for a three-dimensional turbulent boundary layer in a 30° bend
Authors: Schwarz Walter R. , Bradshaw Peter
Published: April 2006

A three-dimensional turbulent boundary layer (3DTBL) was generated on the floor of a low-speed wind tunnel by the imposition of a cross-stream pressure gradient using a 30° bend in the horizontal plane. The surface streamlines were deflected by as much as 22° relative to the local tunnel centreline. Downstream of the bend, the 3DTBL gradually relaxed towards a 2DTBL; this was an impulse-and-recovery experiment which focused on the outer layer. Mean velocities were measured with a three-hole yawmeter and turbulence quantities, which included the Reynolds-stress tensor and the triple products, were measured with a cross-wire hot-wire anemometer. The experiment isolated the effects of crossflow from those of adverse streamwise pressure gradients, which may have clouded interpretations of previous 3DTBL experiments. In particular, the detailed developments of the cross-stream shear stress and of the stress/energy ratio become clearer. The shear-stress vector lagged behind the velocity-gradient vector as crossflow developed; however, the two vectors became more closely aligned downstream of the bend. Reductions in the stress/energy ratio implied that crossflow made shear-stress production less efficient. Another effect of three-dimensionality was a change of sign in the vertical transport of turbulent kinetic energy by turbulence, in the inner part of the boundary layer.
On the instability of wave-catalysed longitudinal vortices in strong shear
Authors: Phillips W.R.C. , Wu Z.
Published: April 2006

The inviscid instability of O(ε) two-dimensional periodic flows to spanwise-periodic longitudinal vortex modes in parallel O(1) shear flows is considered. In such cases, not only is the effect of fluctuations upon the mean state important but also the influence of the developing mean flow on the fluctuating part of the motion. The former is described by a generalized Lagrangian-mean formulation; the latter by a modified Rayleigh equation. Of specific interest is whether the spanwise distortion of the wave field feeds back to enhance or inhibit instability to longitudinal vortex form. Two cases are considered in detail: uniform shear between wavy walls and non-uniform shear beneath free-surface waves. In both cases wave distortion acts to inhibit, and in some circumstances curtail, instability for all but the shortest waves.
Analytical prediction of regular reflection over rigid porous surfaces in pseudo-steady flows
Authors: Li H. , Levy A. , Ben-Dor G.
Published: April 2006

An analytical model for solving the flow field associated with regular reflections of straight shock waves over porous layers has been developed. The governing equations of the gas inside the porous material were obtained by simplifying the general macroscopic balance equations which were obtained by an averaging process over a representative elementary volume of the microscopic balance equations as originally done by Bear & Bachmat (1990). The analytical predictions of the proposed model were compared to experimental results of Skews (1992) and Kobayashi, Adachi & Suzuki (1993). Very good to excellent agreement was evident.
The bath-plug vortex
Authors: Forbes Lawrence K. , Hocking Graeme C.
Published: April 2006

Steady flow with constant circulation into a vertical drain is considered. The precise details of the outflow are simplified by assuming that the drain is equivalent to a distributed volume sink, into which the fluid flows with uniform downward speed. It is shown that a maximum outflow rate exists, corresponding to no fluid circulation and vertical entry into the drain hole. Numerical solutions to the full nonlinear problem are computed, using the method of fundamental solutions. An approximate analysis, based on the use of the shallow-water equations, is presented for flows in which the free surface enters the drain. There is, in addition, a second type of solution, having a stagnation point at the free surface and no fluid circulation. These flows are also computed numerically, and results are presented.
Boundary layer flow of air over water on a flat plate
Authors: Nelson John J. , Alving Amy E. , Joseph Daniel D.
Published: April 2006

A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x), away from the leading edge. We derive a simple non-similar analytic solution of the problem for which the interface height is proportional to x1/4 and the water and air flow satisfy the Blasius boundary layer equations, with a linear profile in the water and a Blasius profile in the air. Numerical studies of the initial value problem suggest that this asymptotic non-similar air–water boundary layer solution is a global attractor for all initial conditions.
The time-dependent free surface flow induced by a submerged line source or sink
Authors: Sozer E. M. , Greenberg M. D.
Published: April 2006

The unsteady nonlinear potential flow induced by a submerged line source or sink is studied by a vortex sheet method, both to trace the free surface evolution and to explore the possible existence of steady-state solutions. Only steady-state flows have been considered by other investigators, and these flows have been insensitive to whether they are generated by a source or sink, except with respect to the flow direction along the streamlines. The time-dependent solution permits an assessment of the stability of previously found steady solutions, and also reveals differences between source and sink flows: for the infinite-depth case, steady stagnation-point-type solutions are found both for source flows and sink flows, above the critical value reported by other investigators; finally, it is shown that streamline patterns of steady stagnation-point flows are identical for source and sink flows only in the limiting case of infinite depth.
Barotropic quasi-geostrophic f-plane flow over anisotropic
topography
Authors: Carnevale G. F. , Purini R. , Orlandi P. , Cavazza P.
Published: April 2006

For an anisotropic topographic feature in a large-scale flow, the
orientation of the topography with respect to the flow will affect the
vorticity production that results from the topography–flow interaction. This
in turn affects the amount of form drag that the ambient flow experiences.
Numerical simulations and perturbation theory are used to explore these
effects of change in topographic orientation. The flow is modelled as a
quasi-geostrophic homogeneous fluid on an
f-plane. The topography is taken to be a hill of
limited extent, with an elliptical cross-section in the horizontal. It is
shown that, as a result of a basic asymmetry of the quasi-geostrophic flow,
the strength of the form drag depends not only on the magnitude of the angle
that the topographic axis makes with the oncoming stream, but also on the
sign of this angle. For sufficiently low topography, it is found that a
positive angle of attack leads to a stronger form drag than that for the
corresponding negative angle. For strong topography, this relation is
reversed, with the negative angle then resulting in the stronger form
drag.
Free-surface flow due to impulsive motion of a submerged circular cylinder
Authors: Tyvand Peder A. , Miloh Touvia
Published: April 2006

The impulsively starting motion of a circular cylinder submerged horizontally below a free surface is studied analytically using a small-time expansion. The series expansion is taken as far as necessary to include the leading gravitational effects for two cases: constant velocity and constant acceleration, both commencing from rest. The hydrodynamic force on the cylinder and the surface elevation are calculated and expressed in terms of bipolar coordinates. Comparisons are also made with earlier theoretical and experimental work. The theory is valid for arbitrary value of submergence depth to cylinder radius.
Wall pressure and coherent structures in a turbulent boundary layer on a cylinder in axial flow
Authors: Snarski Stephen R. , Lueptow Richard M.
Published: April 2006

Measurements of wall pressure and streamwise velocity fluctuations in a turbulent boundary layer on a cylinder in an axial air flow (δ/a = 5.04, Reθ = 2870) have been used to investigate the turbulent flow structures in the cylindrical boundary layer that contribute to the fluctuating pressure at the wall in an effort to deduce the effect of transverse curvature on the structure of boundary layer turbulence. Wall pressure was measured at a single location with a subminiature electret condenser microphone, and the velocity was measured throughout a large volume of the boundary layer with a hotwire probe. Auto- and cross-spectral densities, cross-correlations, and conditional sampling of the pressure and streamwise velocity indicate that two primary groups of flow disturbances contribute to the fluctuating pressure at the wall: (i) low-frequency large-scale structures with dynamical significance across the entire boundary layer that are consistent with a pair of large-scale spanwise-oriented counter-rotating vortices and (ii) higher frequency small-scale disturbances concentrated close to the wall that are associated with the burst-sweep cycle and are responsible for the short-duration large-amplitude wall pressure fluctuations. A bidirectional relationship was found to exist between both positive and negative pressure peaks and the temporal derivative of u near the wall. Because the frequency of the large-scale disturbance observed across the boundary layer is consistent with the bursting frequency deduced from the average time between bursts, the burst-sweep cycle appears to be linked to the outer motion. A stretching of the large-scale structures very near the wall, as suggested by space-time correlation convection velocity results, may provide the coupling mechanism. Since the high-frequency disturbance observed near the wall is consistent with the characteristic frequency deduced from the average duration of bursting events, the bursting process provides the two characteristic time scales responsible for the bimodal distribution of energy near the wall. Because many of the observed structural features of the cylindrical boundary layer are similar to those observed in flat-plate turbulent boundary layers, transverse curvature appears to have little effect on the fundamental turbulent structure of the boundary layer for the moderate transverse curvature ratio used in this investigation. From differences that exist between the turbulence intensity, skewness, and spectra of the streamwise velocity, however, it appears that transverse curvature may enhance (i.e. energize) the large-scale motion owing to the reduced constraint imposed on the flow by the smaller cylindrical wall.
Surface-tension-driven flows at low Reynolds number arising in optoelectronic technology
Authors: Yarin A. L.
Published: April 2006

Some methods of formation of preforms for drawing of polarization-maintaining optical fibres are based on utilization of the surface tension of glass in the liquid state. Under the action of surface tension non-circular glass articles begin to flow, which results in formation of an anisotropic internal structure of the preforms. The hydrodynamic analysis of two such methods is given in the paper. Analytical solutions of the Stokes equations with linearized boundary conditions for the corresponding creeping surface-tension-driven flows of liquid glass are obtained. By means of these solutions a processing strategy may be predetermined with a view to a specific internal structure of the fibre, as well as to the required value of birefringence. The theoretical results are compared with experimental data and agreement is fairly good.
An investigation of turbulent plane Couette flow at low Reynolds numbers
Authors: Bech Knut H. , Tillmark Nils , Alfredsson P. Henrik , Andersson Helge I.
Published: April 2006

The turbulent structure in plane Couette flow at low Reynolds numbers is studied using data obtained both from numerical simulation and physical experiments. It is shown that the near-wall turbulence structure is quite similar to what has earlier been found in plane Poiseuille flow; however, there are also some large differences especially regarding Reynolds stress production. The commonly held view that the maximum in Reynolds stress close to the wall in Poiseuille and boundary layer flows is due to the turbulence-generating events must be modified as plane Couette flow does not exhibit such a maximum, although the near-wall coherent structures are quite similar. For two-dimensional mean flow, turbulence production occurs only for the streamwise fluctuations, and the present study shows the importance of the pressure—strain redistribution in connection with the near-wall coherent events.
The development of Long's vortex
Authors: Drazin P.G. , Banks W.H.H. , Zaturska M.B.
Published: April 2006

This paper describes the solution of Long's problem for steady rotationally symmetric swirling jets in a uniform viscous fluid. Long found these vortices in 1958 by assuming a similarity form of solution, and in 1961 solved the consequent problem in the boundary-layer limit, finding dual solutions. The overall pattern of the solutions to the problem for general values of the Reynolds number is described. The linear spatial stability of the flows to small steady disturbances is analysed and a few results presented. In particular, details of the solutions and their stability are given asymptotically for small and large values of the Reynolds number. The asymptotic results for the basic flow are linked by direct numerical integration of the flow at several finite positive values of the Reynolds number.
The occurrence of moist ‘anticonvection’ in a water–air system
Authors: Perestenko Oleg V. , Ingel Lev Kh.
Published: April 2006

A non-Rayleigh mechanism of instability in horizontally homogeneous hydrodynamic systems consisting of two iimmiscible fluids and heated uniformly from above, i.e. ‘anticonvection’, was first investigated theoretically by Welander (1964) and more recently (and independently) by Gershuni & Zhukhovitsky (1980). This paper discusses the possibility of ‘anticonvection’ occurring in a water–air system, taking into account evaporation, stratification with respect to moisture, thermocapillary effects and the presence of a surface heat source at the water–air interface. For this purpose, a linear problem of stability is solved, in which the Rayleigh number analogues in each of the fluids are its eigenvalues in one case and the increments of disturbances in the other. It has been shown that taking into account evaporation and stratification with respect to moisture in the air reveals a new feedback in the system resulting in the disappearance of one of the previously known areas of anticonvection and the formation of new areas of instability. The mechanism of the oscillatory regime of the loss of stability in the system under study was found and considered in detail. Increments and wavelengths of the growing modes are calculated, and the possibility of experimental investigation of moist anticonvection in laboratory and field conditions is discussed.
Interaction of a potential vortex with a local roughness on a smooth surface
Authors: Ryzhov Oleg S. , Timofeev Sergey V.
Published: April 2006

Disturbances generated by a potential vortex moving past a small hump or dent on the otherwise smooth flat plate are considered. Features peculiar to this problem derive from the fact that the vortex is stuck with a fixed fluid particle; hence the nonlinear dependence of the pressure on the induced velocity field ensues even if the vortex intensity tends to zero. Formulation of the problem on a flow in the viscous wall sublayer given in canonical variables involves four similarity parameters for any particular shape of a roughness. The parallels between the process at hand and sound scattering from a boundary layer with a small obstacle at the bottom are indicated. Results from numerical integration of the boundary-value problem posed allow us to trace the evolution of the wave-packet structure depending on the potential vortex intensity. Overlapping of the peak wings and formation of an almost continuous spectrum in the Fourier decomposition of the signal serve as a guide for explaining the explosive development of the wave packet as distinct from the Tollmien–Schlichting wavetrain that has been registered experimentally.

The theory developed is applied to discussing the so-called bypass mode of transition provoked by external turbulence. Special emphasis is laid on flows in gas turbine engines where bypass transition plays a dominant role owing to extremely high free-stream turbulence levels.
A mathematical analysis of the steady response of floating ice to the uniform motion of a rectangular load
Authors: Milinazzo F. , Shinbrot Marvin , Evans N. W.
Published: April 2006

In this article, we considered the steady response of an infinite unbroken floating ice sheet to the uniform motion of a rectangular load. It is assumed that the ice sheet is supported below by water of finite uniform depth. The ice displacement is expressed as a Fourier integral and the method of residues is combined with a numerical quadrature scheme to calculate the displacement of the surface. In addition, asymptotic estimates of the displacement are given for the far field and for the case where the aspect ratio of the load is large. The far-field approximation provides a good description of the surface displacement at distances greater than about one or two wavelengths away from the load. The behaviour of the steady solution at the two critical speeds Um, where the phase speed takes on its minimum, and Ug, the speed of gravity waves on shallow water, observed in Schulkes & Sneyd (1988) for an impulsively started line load is examined to see if these speeds are critical for two-dimensional loads. Unlike the steady part of the solution in Schulkes & Sneyd (1988), the solution is everywhere finite at the critical speed Ug. However, at the load speed Um, the solution is unbounded. At all load speeds the change in surface displacement is greatest near the load. A comparison with the experimental observations of Takizawa (1985) is made. Our calculations show a significant dependence of the amplitude of the ice displacement on the aspect ratio of the load. For wide loads the surface deflection has much more structure than does the surface displacement corresponding to loads of smaller aspect ratios.
Numerical and theoretical solutions for a drop spreading below a free fluid surface
Authors: Koch Dorothy M. , Koch Donald L.
Published: April 2006

Numerical solutions are derived for a viscous, buoyant drop spreading below a free fluid surface. The drop has zero interfacial tension, and we consider viscosity contrasts 0.1 < λ < 10 with the surrounding fluid half-space. The density contrast between the drop and outer fluid is assumed to be small compared with the density contrast at the fluid surface. The numerical solutions for the approach and initial spread of the drop below the fluid surface are obtained using the boundary integral method. To facilitate an investigation over a larger range of viscosity contrasts and for longer time periods, we solve for the motion of gravity currents at the fluid surface. For this geometry we also solve the boundary integral equations for the cases λ = 0 and 1/λ = 0.

For extensive drop spreading, the motion is described by asymptotic solutions. Three asymptotic solutions are derived, which apply for different values of the viscosity contrast relative to the aspect ratio ((radial extent R)/(drop thickness a)). For very low-viscosity drops (λ [Lt ] a/R[ln(R/a)]-1), the greatest resistance to spreading occurs at the drop rim, and the asymptotic solution is found using slender body theory. Drops with intermediate viscosity contrast (a/R [Lt ] λ [Lt ] R/a) are slowed primarily by shear stresses at the lower drop surface, and a lubrication solution (Lister & Kerr 1989) applies. The greatest resistance to the spread of very viscous drops (λ [Gt ] R/a) comes from the radial stresses within the drop, and the asymptotic solution is independent of the outer fluid. All drops having 0 [Lt ] λ [Lt ] ∞ will eventually spread according to lubrication theory, when their aspect ratio becomes sufficiently large relative to viscosity contrast.

Theoretical results are compared with numerical and experimental results for drops and gravity currents spreading at a fluid surface. The solutions can be applied to aspects of planetary mantle flow where temperature variations cause significant viscosity contrasts. The low-viscosity solution has been applied to study the encounter of a hot, low-viscosity upwelling plume with a planet surface (Koch 1994). Here we apply the high-viscosity asymptotic solution to study how cold downwelling slabs spread at a depth of neutral buoyancy in the Earth's mantle.
The flow field downstream of a hydraulic jump
Authors: Hornung Hans G. , Willert Christian , Turner Stewart
Published: April 2006

A control-volume analysis of a hydraulic jump is used to obtain the mean vorticity downstream of the jump as a function of the Froude number. To do this it is necessary to include the conservation of angular momentum. The mean vorticity increases from zero as the cube of Froude number minus one, and, in dimensionless form, approaches a constant at large Froude number. Digital particle imaging velocimetry was applied to travelling hydraulic jumps giving centre-plane velocity field images at a frequency of 15 Hz over a Froude number range of 2–6. The mean vorticity determined from these images confirms the control-volume prediction to within the accuracy of the experiment. The flow field measurements show that a strong shear layer is formed at the toe of the wave, and extends almost horizontally downstream, separating from the free surface at the toe. Various vorticity generation mechanisms are discussed.
Mechanics of collisional motion of granular materials. Part 2. Wave propagation through vibrofluidized granular layers
Authors: Goldshtein Alexander , Shapiro Michael , Moldavsky Leonid , Fichman Mati
Published: April 2006

According to numerous experimental observations and theoretical models vibrated layers composed of large granules behave like a solid plastic body. In contrast, in this study experimental data are presented that reveal that, for constant vibration amplitudes A ≥ 1 cm with the frequency ω increasing from zero, all layers pass through three vibrational states, with the respective behaviours being as of (i) a solid plastic body, (ii) a liquid, (iii) a gas. In the liquid-like vibrational state transverse waves propagating along the layer width were observed. These waves were shown to be gravitational resonance waves, with the corresponding frequencies well correlated by the known formula for incompressible liquids. In the gas-like vibrational state compression (shock) and expansion waves propagating across the layer height, were observed.

A theoretical model for time-periodic collisional vibrational regimes was developed on the basis of the Euler-like equations of a granular gas composed of inelastic spheres. The model shows that the vibrational granular state (bed porosity, shock wave speed, granular pressure and kinetic energy) is inter alia governed by the dimensionless parameter V = (Aω)/(hmg)1/2, with g, hm being the gravitational acceleration and the height of the resting layer, respectively. This is in contrast with the previous studies, where the behaviour of vibrated granular layers was interpreted in terms of the dimensionless acceleration Δ = (Aω2)/g. The proposed model was tested by processing the data obtained from photographs of the particle distribution within vibrated layers. Theoretical predictions of the particle average concentration compared favourably with the experimental data.

Other phenomena observed in vibrated granular layers include the formation of caverns, circulatory motion of granules and synchronized periodic motion of two adjacent vibrated layers of different widths. The importance of the observed phenomena in relation to various technological processes involving bulk materials (vibromixing, vibroseparation, etc.) is discussed.
Stability of large-amplitude geostrophic flows localized in a thin layer
Authors: Benilov E. S.
Published: April 2006

In this paper the dynamics of geostrophic flows localized in a thin layer of continuously stratified fluid, which overrides a thick homogeneous layer are studied. The displacement of isopycnal surfaces is assumed large; the β-effect is strong, i.e.
\[(R_0/R_e)\cot\theta\gtrsim\epsilon, \]
where ε is the Rossby number, θ is the latitude; Re is the Earth's radius, and R0 is the deformation radius based on the total depth of the ocean. An asymptotic system of equations is derived and used to study the stability of zonal currents. Three sufficient conditions of stability are obtained, which restrict the slope of the interface between the stratified and non-stratified layers. The results obtained are applied to the subtropical and subarctic frontal currents in the Northern Pacific: the former was found to be stable, the latter was found to be unstable. However, the growth rate of the instability is very small (the effective time of growth is about 2 years).
Three-dimensional vortex dynamics in a rectangular sudden expansion
Authors: Hertzberg J. R. , Ho C. M.
Published: April 2006

A detailed experimental study of flow in a rectangular sudden expansion using both active and passive forcing techniques has been made. The configuration consists of a 2:1-aspect-ratio rectangular channel which undergoes a sudden expansion such that the backward-facing step height (h) is uniform, and equal to the minor side of the inlet channel. Passive forcing was provided by the system geometry; the rectangular vortex rings formed in the shear layer of the expanding jet undergo self-induction, deforming the jet cross-section and introducing transverse velocities not found in plane or axisymmetric configurations. Active forcing was induced by periodic fluctuations in the system flow rate at the jet natural frequency. This served to enhance the unusual three-dimensional effects and phase-lock the flow for ensemble analysis. The results presented here include a description of the evolution of an isolated vortex in this configuration obtained from flow visualization of a suddenly started jet, as well as forced steady-state three-component velocity measurements which are used to characterize the flow field. The evolution of a rectangular vortex ring in the jet shear layer is traced, and both fluctuating and time-constant transverse velocities are related to the passage of the vortex structures.
Transition to turbulence in constant-mass-flux pipe flow
Authors: Darbyshire A. G. , Mullin T.
Published: April 2006

We report the results of an experimental study of the transition to turbulence in a pipe under the condition of constant mass flux. The transition behaviour and structures observed in this experiment were qualitatively the same as those described in previous reported studies performed in pressure-driven systems. A variety of jet and suction devices were used to create repeatable disturbances which were then used to test the stability of developed Poiseuille flow. The Reynolds number (Re) and the parameters governing the disturbances were varied and the outcome, whether or not transition occurred some distance downstream of the injection point, was recorded. It was found that a critical amplitude of disturbance was required to cause transition at a given Re and that this amplitude varied in a systematic way with Re. This finite, critical level was found to be a robust feature, and was relatively insensitive to the form of disturbance. We interpret this as evidence for disconnected solutions which may provide a pointer for making progress in this fundamental, and as yet unresolved, problem in fluid mechanics.
The evolution of a localized vortex disturbance in external shear flows. Part 1. Theoretical considerations and preliminary experimental results
Authors: Levinski Vladimir , Cohen Jacob
Published: April 2006

The evolution of a finite-amplitude three-dimensional localized disturbance embedded in external shear flows is addressed. Using the fluid impulse integral as a characteristic of such a disturbance, the Euler vorticity equation is integrated analytically, and a system of linear equations describing the temporal evolution of the three components of the fluid impulse is obtained. Analysis of this system of equations shows that inviscid plane parallel flows as well as high Reynolds number two-dimensional boundary layers are always unstable to small localized disturbances, a typical dimension of which is much smaller than a dimensional length scale corresponding to an O(1) change of the external velocity. Since the integral character of the fluid impulse is insensitive to the details of the flow, universal properties are obtained. The analysis predicts that the growing vortex disturbance will be inclined at 45° to the external flow direction, in a plane normal to the transverse axis. This prediction agrees with previous experimental observations concerning the growth of hairpin vortices in laminar and turbulent boundary layers. In order to demonstrate the potential of this approach, it is applied to Taylor-Couette flow, which has additional dynamical effects owing to rotation. Accordingly, a new instability criterion associated with three-dimensional localized disturbances is found. The validity of this criterion is supported by our experimental results.
The formation of drops through viscous instability
Authors: Cardoso Silvana S. S. , Woods Andrew W.
Published: April 2006

The stability of an immiscible layer of fluid bounded by two other fluids of different viscosities and migrating through a porous medium is analysed, both theoretically and experimentally. Linear stability analyses for both one-dimensional and radial flows are presented, with particular emphasis upon the behaviour when one of the interfaces is highly stable and the other is unstable. For one-dimensional motion, it is found that owing to the unstable interface, the intermediate layer of fluid eventually breaks up into drops.

However, in the case of radial flow, both surface tension and the continuous thinning of the intermediate layer as it moves outward may stabilize the system. We investigate both of these stabilization mechanisms and quantify their effects in the relevant parameter space. When the outer interface is strongly unstable, there is a window of instability for an intermediate range of radial positions of the annulus. In this region, as the basic state evolves to larger radii, the linear stability theory predicts a cascade to higher wavenumbers. If the growth of the instability is sufficient that nonlinear effects become important, the annulus will break up into a number of drops corresponding to the dominant linear mode at the time of rupture.

In the laboratory, a Hele-Shaw cell was used to study these processes. New experiments show a cascade to higher-order modes and confirm quantitatively the prediction of drop formation. We also show experimentally that the radially spreading system is stabilized by surface tension at small radii and by the continual thinning of the annulus at large radii.
Gravity current flow over obstacles
Authors: Lane-Serff G. F. , Beal L. M. , Hadfield T. D.
Published: April 2006

When a gravity current meets an obstacle a proportion of the flow may continue over the obstacle while the rest is reflected back as a hydraulic jump. There are many examples of this type of flow, both in the natural and man-made environment (e.g. sea breezes meeting hills, dense gas and liquid releases meeting containment walls). Two-dimensional currents and obstacles, where the reflected jump is in the opposite direction to the incoming current, are examined by laboratory experiment and theoretical analysis. The investigation concentrates on the case of no net flow, so that there is a return flow in the (finite depth) upper layer. The theoretical analysis is based on shallow-water theory. Both a rigid lid and a free surface condition for the top of the upper layer are considered. The flow may be divided into several regions: the inflow conditions, the region around the hydraulic jump, the flow at the obstacle and the flow downstream of the obstacle. Both theoretical and empirical inflow conditions are examined; the jump conditions are based on assuming that the energy dissipation is confined to the lower layer; and the flow over the obstacle is described by hydraulic control theory. The predictions for the proportion of the flow that continues over the obstacle, the speed of the reflected jump and the depth of the reflected flow are compared with the laboratory experiments, and give reasonable agreement. A shallower upper layer (which must result in a faster return velocity in the upper layer) is found to have a significant effect, both on the initial incoming gravity current and on the proportion of the flow that continues over the obstacle.
An experimental investigation of Taylor vortex flow between conical cylinders
Authors: Wimmer Manfred
Published: April 2006

Viscous flows and instabilities between conical cylinders are described which result from rotating an inner cone while the outer one is at rest. Both cones have the same apex angle resulting in a constant width of the gap between the bodies. The laminar basic flow is tree-dimensional. Owing to different centrifugal forces on the cone's surface one obtains regions of sub- and supercritical flows in the annulus. The Taylor vortices generated can be steady or unsteady, so that toroidal or helical vortices travel through the closed system, depending on different initial and boundary conditions. Furthermore, combinations of steady toroidal and unsteady helical vortices are possible. The influence of the governing parameters, like acceleration rate, gap width, end plates and so on is discussed. A comparison with available calculations is made.
Rotating free-shear flows. Part 2. Numerical simulations
Authors: Métais Olivier , Flores Carlos , Yanase Shinichiro , Riley James J. , Lesieur Marcel
Published: April 2006

The three-dimensional dynamics of the coherent vortices in periodic planar mixing layers and in wakes subjected to solid-body rotation of axis parallel to the basic vorticity are investigated through direct (DNS) and large-eddy simulations (LES). Initially, the flow is forced by a weak random perturbation superposed on the basic shear, the perturbation being either quasi-two-dimensional (forced transition) or three-dimensional (natural transition). For an initial Rossby number Ro(i), based on the vorticity at the inflexion point, of small modulus, the effect of rotation is to always make the flow more two-dimensional, whatever the sense of rotation (cyclonic or anticyclonic). This is in agreement with the Taylor–Proudman theorem. In this case, the longitudinal vortices found in forced transition without rotation are suppressed.

It is shown that, in a cyclonic mixing layer, rotation inhibits the growth of three-dimensional perturbations, whatever the value of the Rossby number. This inhibition exists also in the anticyclonic case for |Ro(i)| ≤ 1. At moderate anticyclonic rotation rates (Ro(i) < −1), the flow is strongly destabilized. Maximum destabilization is achieved for |Ro(i) ≈ 2.5, in good agreement with the linear-stability analysis performed by Yanase et al. (1993). The layer is then composed of strong longitudinal alternate absolute vortex tubes which are stretched by the flow and slightly inclined with respect to the streamwise direction. The vorticity thus generated is larger than in the nonrotating case. The Kelvin–Helmholtz vortices have been suppressed. The background velocity profile exhibits a long range of nearly constant shear whose vorticity exactly compensates the solid-body rotation vorticity. This is in agreement with the phenomenological theory proposed by Lesieur, Yanase & Métais (1991). As expected, the stretching is more efficient in the LES than in the DNS.

A rotating wake has one side cyclonic and the other anticyclonic. For |Ro(i)| ≤ 1, the effect of rotation is to make the wake more two-dimensional. At moderate rotation rates (|Ro(i)| > 1), the cyclonic side is composed of Kármán vortices without longitudinal hairpin vortices. Karman vortices have disappeared from the anticyclonic side, which behaves like the mixing layer, with intense longitudinal absolute hairpin vortices. Thus, a moderate rotation has produced a dramatic symmetry breaking in the wake topology. Maximum destabilization is still observed for |Ro(i)| ≈ 2.5, as in the linear theory.

The paper also analyses the effect of rotation on the energy transfers between the mean flow and the two-dimensional and three-dimensional components of the field.
Experimental study of convection in a mushy layer during directional solidification
Authors: Chen C. F.
Published: April 2006

Results of experiments using a number of techniques to study the nature of convection in a mushy layer generated by directional solidification of aqueous ammonium chloride solutions are reported. The techniques include flow visualization using a dye tracing method to study convection within the mushy layer before and after the onset of plume convection, and X-ray tomography to measure the solid fraction of a growing mush. The principal results are as follows. (i) Prior to the onset of chimneys, there is no convective motion in the mush, in spite of the vigorous finger convection at the mush-liquid interface. (ii) When the plume convection is fully developed, the flow of fluid in the mush consists of a nearly uniform downward motion toward the bottom of the tank, horizontal motion along the bottom toward the chimneys, then upward plume motion through the chimneys in the liquid region above the mush. (iii) The solid fraction of a growing mush as determined by X-ray tomography shows a significant decrease toward the bottom of the tank after the chimneys are fully developed. As a result, the concomitant increase in the local permeability can be as much as 50%. Some of the results reported herein confirm theoretical predictions of Worster (1992) and Amberg & Homsey (1993). Others reveal phenomena not observed heretofore.
Observations and scaling of travelling bubble cavitation
Authors: De Chizelle Y. Kuhn , Ceccio S. L. , Brennen C. E.
Published: April 2006

Recent observations of growing and collapsing bubbles in flows over axisymmetric headforms have revealed the complexity of the ‘micro-fluid-mechanics’ associated with these bubbles (van der Meulen & van Renesse 1989; Briancon-Marjollet et al. 1990; Ceccio & Brennen 1991). Among the complex features observed were the bubble-to-bubble and bubble-to-boundary-layer interactions which leads to the shearing of the underside of the bubble and alters the collapsing process. All of these previous tests, though, were performed on small headform sizes. The focus of this research is to analyse the scaling effects of these phenomena due to variations in model size, Reynolds number and cavitation number. For this purpose, cavitating flows over Schiebe headforms of different sizes (5.08, 25.4 and 50.8 cm in diameter) were studied in the David Taylor Large Cavitation Channel (LCC). The bubble dynamics captured using high-speed film and electrode sensors are presented along with the noise signals generated during the collapse of the cavities.

In the light of the complexity of the dynamics of the travelling bubbles and the important bubble/bubble interactions, it is clear that the spherical Rayleigh-Plesset analysis cannot reproduce many of the phenomena observed. For this purpose an unsteady numerical code was developed which uses travelling sources to model the interactions between the bubble (or bubbles) and the pressure gradients in the irrotational flow outside the boundary layer on the headform. The paper compares the results of this numerical code with the present experimental results and demonstrates good qualitative agreement between the two.
The effect of blade sweep on the reduction and enhancement of supersonic propeller noise
Authors: Parry A. B.
Published: April 2006

An asymptotic frequency-domain approach is used to describe the radiation from a supersonic swept propeller within the framework of linear acoustics. With this approach the radiation of singularities, their points of origin on the blades, and their relation to blade geometry and loading are easily obtained. In particular, it is shown that a swept propeller with a completely subsonic leading edge can still radiate singularities, if the leading edge is blunt, due to a supersonic edge effect at the blade tips. In addition, the radiation from a family of ‘critical’ swept-blade designs is shown to be more singular than that from a straight-bladed design. Numerical and asymptotic results for such designs show that the peak radiation is, typically, increased by 5–10 dB.
Hysteresis in Faraday resonance
Authors: Decent S. P. , Craik A. D. D.
Published: April 2006

Faraday waves arise on the surface of a liquid in a container that is undergoing vertical periodic oscillations. Hysteresis occurs when both finite-amplitude solutions and the flat-surface solution are available. We derive a nonlinear model of Faraday resonance, extending the Lagrangian method of Miles (1976). The model is used to investigate hysteresis. The theoretical results are compared to previous experimental studies and to some new observations. It is found necessary to retain damping and forcing terms up to third-order in wave amplitude, and also the fifth-order conservative frequency shift, in order to achieve agreement with experiments. The latter fifth-order term was omitted from all previous studies of Faraday waves. The lower hysteresis boundary in forcing-frequency space is found in most cases to be defined by the lower boundary above which non-trivial stationary points exist. However, the stability of stationary points and the existence of limit cycles are also found to be factors in determining the lower hysteresis boundary. Our results also suggest an indirect method for estimating the coefficient of cubic damping, which is difficult to obtain either experimentally or theoretically.