bluuebunny/crossref_metadata_2025 huggingface dataset:
Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves
Authors: Gong W. , Taylor Peter A. , Dörnbrack Andreas
Published: April 2006

Results from a wind tunnel study of aerodynamically rough turbulent boundary-layer flow over a sinusoidal surface are presented. The waves had a maximum slope (ak) of 0.5 and two surface roughnesses were used. For the relatively rough surface the flow separated in the wave troughs while for the relatively smooth surface it generally remained attached. Over the relatively smooth-surfaced waves an organized secondary flow developed, consisting of vortex pairs of a scale comparable to the boundary-layer depth and aligned with the mean flow. Large-eddy simulation studies model the flows well and provide supporting evidence for the existence of this secondary flow.
The structure and development of a wing-tip vortex
Authors: Devenport William J. , Rife Michael C. , Liapis Stergios I. , Follin Gordon J.
Published: April 2006

Experiments have been performed on the tip vortex trailing from a rectangular NACA 0012 half-wing. Preliminary studies showed the vortex to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful velocity measurements could therefore be made using hot-wire probes.

Detailed analysis of the effects of wandering was performed to properly reveal the flow structure in the core region and to give confidence in measurements made outside the core. A theory has been developed to correct mean-velocity profiles for the effects of wandering and to provide complete quantitative estimates of its amplitude and contributions to Reynolds stress fields. Spectral decomposition was found to be the most effective method of separating these contributions from velocity fluctuations due to turbulence.

Outside the core the flow structure is dominated by the remainder of the wing wake which winds into an ever-increasing spiral. There is no large region of axisymmetric turbulence surrounding the core and little sign of turbulence generated by the rotational motion of the vortex. Turbulence stress levels vary along the wake spiral in response to the varying rates of strain imposed by the vortex. Despite this complexity, the shape of the wake spiral and its turbulent structure reach an approximately self-similar form.

On moving from the spiral wake to the core the overall level of velocity fluctuations greatly increases, but none of this increase is directly produced by turbulence. Velocity spectra measured at the vortex centre scale in a manner that implies that the core is laminar and that velocity fluctuations here are a consequence of inactive motion produced as the core is buffeted by turbulence in the surrounding spiral wake. Mean-velocity profiles through the core show evidence of a two-layered structure that dies away with distance downstream.
Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems
Authors: Severtson Yuan C. , Aidun Cyrus K.
Published: April 2006

To understand the physics of air entrainment in thin-film liquid coating and other applications, the stability characteristics of general stratified two-layer Poiseuille-Couette flow are examined in inclined channels. Only one mode of instability, the interfacial mode, is obtained in the long-wave asymptotic limit. The generalized eigenvalue problem, formed by spectral decomposition and solution of the general two-layer Orr-Sommerfeld equation, is solved to obtain all of the critical modes. Analysis of the air/liquid interface corresponding to experiments reveals that because of the large density variation between the two layers, the interfacial mode is the only mode of instability in air entrainment. Results from the stability analysis of the flow near the contact line where air entrainment occurs are consistent with previous experimental observations.
Torsional flow: elastic instability in a finite domain
Authors: Avagliano Aaron , Phan-Thien Nhan
Published: April 2006

A rotational shear flow is examined in the parallel plate geometry for the Oldroyd-B fluid. The Stokes solution is found to have eigenfunctions in an unbounded radial domain while it is unique for general boundary conditions in a finite radial domain. Critical conditions for the onset of an axisymmetric secondary flow are determined for the viscoelastic fluid, and we show that there is an almost linear relationship between the aspect ratio of the plates and the critical Deborah number for this model, especially at small values of the aspect ratio. The form of the initial secondary flow is also in agreement with experimental results obtained for a Boger fluid.
Global relationships between two-dimensional water wave potentials
Authors: McIver M.
Published: April 2006

When a body interacts with small-amplitude surface waves in an ideal fluid, the resulting velocity potential may be split into a part due to the scattering of waves by the fixed body and a part due to the radiation of waves by the moving body into otherwise calm water. A formula is derived which expresses the two-dimensional scattering potential in terms of the heave and sway radiation potentials at all points in the fluid. This result generalizes known reciprocity relations which express quantities such as the exciting forces in terms of the amplitudes of the radiated waves. To illustrate the use of this formula beyond the reciprocity relations, equations are derived which relate higher-order scattering and radiation forces. In addition, an expression for the scattering potential due to a wave incident from one infinity in terms of the scattering potential due to a wave from the other infinity is obtained.
Electrohydrodynamic stability of a highly viscous jet
Authors: Mestel A. J.
Published: April 2006

When a pendant drop of weakly conducting fluid is raised to a high electric potential, it frequently adopts the shape of a Taylor cone from whose apex a thin, charged jet is emitted. Such a jet can display surprising longevity, but eventually breaks up into fine droplets, a fact utilized in electro-spraying devices. This paper examines the linear stability of an incompressible cylindrical jet carrying surface charge q in a tangential electric field E, for various values of the permittivity ratio λ and the finite rate of charge relaxation, τ. The viscosity is assumed to be large. It is shown that all axisymmetric temporal modes can be stabilized for suitable values of (q, E), but sinuous modes with logarithmically large wavelengths are unstable. If these very long waves are excluded, the jet can sometimes be completely stabilized. It is also shown that an uncharged jet with low permittivity is unstable to sinuous waves for large E, contrary to previous belief.
An experimental study of a reactive plume in grid turbulence
Authors: Brown R. J. , Bilger R. W.
Published: April 2006

Experimental results for a reactive non-buoyant plume of nitric oxide (NO) in a turbulent grid flow doped with ozone (O3) are presented. The Damköhler number (ND) for the experiment is of order unity indicating the turbulence and chemistry have similar timescales and both affect the chemical reaction rate. Continuous measurements of two components of velocity using hot-wire anemometry and the two reactants using chemiluminescent analysers have been made. A spatial resolution for the reactants of four Kolmogorov scales has been possible because of the novel design of the experiment. Measurements at this resolution for a reactive plume are not found in the literature. The experiment has been conducted relatively close to the grid in the region where self-similarity of the plume has not yet developed. Statistics of a conserved scalar, deduced from both reactive and non-reactive scalars by conserved scalar theory, are used to establish the mixing field of the plume, which is found to be consistent with theoretical considerations and with those found by other investigators in non-reactive flows. Where appropriate the reactive species means and higher moments, probability density functions, joint statistics and spectra are compared with their respective frozen, equilibrium and reaction-dominated limits deduced from conserved scalar theory. The theoretical limits bracket reactive scalar statistics where this should be so according to conserved scalar theory. Both reactants approach their equilibrium limits with greater distance downstream. In the region of measurement, the plume reactant behaves as the reactant not in excess and the ambient reactant behaves as the reactant in excess. The reactant covariance lies outside its frozen and equilibrium limits for this value of ND. The reaction rate closure of Toor (1969) is compared with the measured reaction rate. The gradient model is used to obtain turbulent diffusivities from turbulent fluxes. Diffusivity of a non-reactive scalar is found to be close to that measured in non-reactive flows by others.
Linear and nonlinear dynamics of a differentially heated slot under gravity modulation
Authors: Farooq A. , Homsy G. M.
Published: April 2006

In this paper we consider the effect of sinusoidal gravity modulation of size ε on a differentially heated infinite slot in which a vertical temperature stratification is imposed on the walls. The slot problem is characterized by a Rayleigh number, Prandtl number, and the imposed uniform stratification on the walls. When ε is small, we show by regular perturbation expansion in ε that the modulation interacts with the natural mode of the system to produce resonances, confirming the results of Farooq & Homsy (1994). For ε ∼ O(1) we show that the modulation can potentially destabilize the longwave eigenmodes of the slot problem. This is achieved by projecting the governing equations onto the least-damped eigenmode, and investigating the resulting Mathieu equation via Floquet theory. No instability was found at large values of the Prandtl number and also low stratification, when there are no travelling modes present.

To understand the nonlinear saturation mechanisms of this growth, we consider a two-mode model of the slot problem with the primary mode being the least-damped travelling parallel-flow mode as before and a secondary mode of finite wavenumber. By projecting the governing equations onto these two modes we obtained the equations for temporal evolution of the two modes. For modulation amplitudes above critical, the growth of the primary mode is saturated resulting in a stable weak nonlinear synchronous oscillation of the primary mode. An unexpected and intriguing feature of the coupling is that the secondary mode exhibits very high-frequency bursts which appear once every cycle of the forcing frequency.
Second-order horizontal steady forces and moment on a floating body with small forward speed
Authors: Aranha J. A. P.
Published: April 2006

In a recent work, a simple formula was derived for the ‘wave drift damping’ in a two-dimensional floating body and the obtained expression is exact within the context of the related theory, where only leading-order terms in the forward speed are retained. This formula is now generalized for a three-dimensional problem and the coefficients of the ‘wave drift damping matrix’ are given explicitly in terms of the standard second-order steady forces and moment in the horizontal plane; Munk's yaw moment, related with the steady second-order potential and discussed in Grue & Palm (1993), is not analysed in this paper and the effect of an eventual small angular velocity around the vertical axis is also not considered.

Numerical results agree in general with the proposed formula although in a specific case a consistent disagreement has been observed, as discussed in §5.
Experimental and numerical study of the interaction between a planar shock wave and a square cavity
Authors: Igra O. , Falcovitz J. , Reichenbach H. , Heilig W.
Published: April 2006

The interaction of a planar shock wave with a square cavity is studied experimentally and numerically. It is shown that such a complex, time-dependent, process can be modelled in a relatively simple manner. The proposed physical model is the Euler equations which are solved numerically, using the second-order-accurate high-resolution GRP scheme, resulting in very good agreement with experimentally obtained findings. Specifically, the wave pattern is numerically simulated throughout the entire interaction process. Excellent agreement is found between the experimentally obtained shadowgraphs and numerical simulations of the various flow discontinuities inside and around the cavity at all times. As could be expected, it is confirmed that the highest pressure acts on the cavity wall which experiences a head-on collision with the incident shock wave while the lowest pressures are encountered on the wall along which the incident shock wave diffracts. The proposed physical model and the numerical simulation used in the present work can be employed in solving shock wave interactions with other complex boundaries.
Theory of low Mach number compressible flow in a channel
Authors: Shajii A. , Freidberg J. P.
Published: April 2006

The properties of a relatively uncommon regime of fluid dynamics, low Mach number compressible flow are investigated. This regime, which is characterized by an exceptionally large channel aspect ratio L/d ∼ 106 leads to highly subsonic flows in which friction dominates inertia. Even so, because of the large aspect ratio, finite pressure, temperature, and density gradients are required, implying that compressibility effects are also important. Analytical results are presented which show, somewhat unexpectedly, that for forced channel flow, steady-state solutions exist only below a critical value of heat input. Above this value the flow reverses against the direction of the applied pressure gradient causing fluid to leave both the inlet and outlet implying that the related concepts of a steady-state friction factor and heat transfer coefficient have no validity.
The influence of surface topography on rotating convection
Authors: Bell Peter I. , Soward Andrew M.
Published: April 2006

Busse's annulus is considered as a model of thermal convection inside the Earth's liquid core. The conventional tilted base and top are modified by azimuthal sinusoidal corrugations so that the effects of surface topography can be investigated. The annulus rotates rapidly about its axis of symmetry with gravity directed radially inwards towards the rotation axis. An unstable radial temperature gradient is maintained and the resulting Boussinesq convection is considered at small Ekman number. Since the corrugations on the boundaries cause the geostrophic contours to be no longer circular, strong geostrophic flows may be driven by buoyancy forces and damped by Ekman suction. When the bumps are sufficiently large, instability of the static state is dominated by steady geostrophic flow with the convection pattern locked to the bumps. As the bump size is decreased, oscillatory geostrophic flow is possible but the preferred mode is modulated on a long azimuthal length scale and propagates as a wave eastwards. This mode only exists in the presence of bumps and is not to be confused with the thermal Rossby waves which are eventually preferred as the bump height tends to zero. Like thermal Rossby waves, the new modes prefer to occupy the longest available radial length scale. In this long-length-scale limit, two finite-amplitude states characterized by uniform geostrophic flows can be determined. The small-amplitude state resembles Or & Busse's (1987) mean flow instability. On losing stability the solution jumps to the more robust large-amplitude state. Eventually, for sufficiently large Rayleigh number and bump height, it becomes unstable to a long-azimuthal-length-scale travelling wave. The ensuing finite-amplitude wave and the mean flow, upon which it rides, are characterized by a geostrophic flow, which is everywhere westward.
The structure of the vortices in freely decaying two-dimensional turbulence
Authors: Jiménez Javier , Moffatt H. K. , Vasco Carlos
Published: April 2006

The structure of a viscous two-dimensional vortex core in a imposed weak strain is analysed, in the same spirit as a similar analysis of strained columnar vortices (Moffatt, Kida & Ohkitani 1994). The analysis is recast in terms of a coordinate deformation, ensuring the uniform validity of the perturbation expansion up to the neighbourhood of a dividing streamline, beyond which it is not expected to work, and from where the exponentially weak vorticity is expected to be stripped to infinity. The orientation and ellipticity of the vorticity distribution of the cores is compared with the results of a numerical experiment in two-dimensional turbulence, and shown to agree. This is interpreted both as a confirmation of the theory and as an indication that the vortices of two-dimensional turbulence are sufficiently long-lived to be controlled by viscous diffusion, even at the relatively large Reynolds numbers of our simulation.
On laminar free convection in inclined rectangular enclosures
Authors: Sundström Lars-Göran , Kimura Shigeo
Published: April 2006

A class of problems of natural convection in tilted boxes is studied by analytical and numerical methods. The convection is assumed to be driven by uniform fluxes of heat (or mass) at two opposing walls, the remaining walls being perfect insulators. Disregarding end-region effects, an exact analytical solution is derived for the state which occurs after initial transients have decayed. This state is steady except for a spatially uniform, linear growth in the temperature (or the species concentration) which occurs whenever the fluxes are not equal. It is characterized by a uni-directional flow, a linear stratification and wall-to-wall temperature profiles which, except for the difference in absolute values due to the stratification, are the same at each crosssection. The mathematical problem is in essence nonlinear and multiple solutions are found in some parameter regions. The Bénard limit of horizontal orientation and heating from below is found to give a first bifurcation for which the steady states both before and after the bifurcation are obtained analytically. For a tilted Bénard-type problem, a steady state with top-heavy stratification is found to exist and compete with a more natural solution. The analytical solution is verified using numerical simulations and a known approximate solution for a vertical enclosure at high Rayleigh numbers. The presented solution admits arbitrary Rayleigh numbers, inclination angles and heat fluxes. Some restrictions on its validity are discussed in the paper.
Stability of a potential vorticity front: from quasi-geostrophy to shallow water
Authors: Boss E. , Paldor N. , Thompson L.
Published: April 2006

The linear stability of a simple two-layer shear flow with an upper-layer potential vorticity front overlying a quiescent lower layer is investigated as a function of Rossby number and layer depths. This flow configuration is a generalization of previously studied flows whose results we reinterpret by considering the possible resonant interaction between waves. We find that instabilities previously referred to as ‘ageostrophic’ are a direct extension of quasi-geostrophic instabilities.

Two types of instability are discussed: the classic long-wave quasi-geostrophic baroclinic instability arising from an interaction of two vortical waves, and an ageostrophic short-wave baroclinic instability arising from the interaction of a gravity wave and a vortical wave (vortical waves are defined as those that exist due to the presence of a gradient in potential vorticity, e.g. Rossby waves). Both instabilities are observed in oceanic fronts. The long-wave instability has length scale and growth rate similar to those found in the quasi-geostrophic limit, even when the Rossby number of the flow is O(1).

We also demonstrate that in layered shallow-water models, as in continuously stratified quasi-geostrophic models, when a layer intersects the top or bottom boundaries, that layer can sustain vortical waves even though there is no apparent potential vorticity gradient. The potential vorticity gradient needed is provided at the top (or bottom) intersection point, which we interpret as a point that connects a finite layer with a layer of infinitesimal thickness, analogous to a temperature gradient on the boundary in a continuously stratified quasi-geostrophic model.
Dynamics of drops in branched tubes
Authors: Manga Michael
Published: April 2006

The flow of two-dimensional deformable drops through branching (bifurcating) tubes is studied numerically using a boundary integral formulation. The undeformed drop diameter is assumed to be less than the tube diameter. Capillary numbers between 10−2 and 1 are considered. Flow in the branching tube is characterized by the fraction of fluid which enters each of the two downstream branches. The likelihood of drops entering the high-flow-rate branch increases as (i) the viscosity ratio between the drops and suspending fluid decreases, (ii) the capillary number increases, and (iii) the drop size increases. Hydrodynamic interactions between the suspended drops increase the number of drops which enter the low-flow-rate branch. The implications of these results for dispersion processes and local transport are explored. The disturbance flow created by drops passing over ‘dead-end’ pores or cavities results in fluid transfer between the pore and the free stream; suspensions may then be effective in improving the ‘cleaning’ of porous materials.
Nonlinear behaviour of contained inertia waves
Authors: Manasseh Richard
Published: April 2006

Rotating fluid-filled containers are systems which admit inertial oscillations, which at appropriate frequencies can be represented as inertia wave modes. When forced by a time-dependent perturbation, systems of contained inertia waves have been shown, in a number of experimental studies, to exhibit complex and varied breakdown phenomena. It is particularly hard to determine a forcing amplitude below which breakdowns do not occur but at which linear wave behaviour is still measurable. In this paper, experiments are presented where modes of higher order than the fundamental are forced. These modes exhibit more complex departures from linear inviscid behaviour than the fundamental mode. However, the experiments on higher-order modes show that instabilities begin at nodal planes. It is shown that even a weakly nonlinear contained inertia-wave system is one in which unexpectedly efficient interactions with higher-order modes can occur, leading to ubiquitous breakdowns. An experiment with the fundamental mode illustrates the system's preference for complex transitions to chaos.
Oscillations of a moderately underexpanded choked jet impinging upon a flat plate
Authors: Kuo Chih-Yu , Dowling Ann P.
Published: April 2006

The oscillation of a moderately underexpanded choked jet impinging upon a flat plate is investigated both analytically and numerically. The feedback mechanism between oscillations of the standoff-shock and the plate is clarified. Pressure waves produced by the motion of the shock are reflected by the plate. In addition, oscillations in the shock position lead to downstream entropy fluctuations, which generate pressure waves as they are convected through the stagnation flow near the plate. A linear stability analysis is used to investigate the stability threshold and frequencies of oscillation, as a function of jet pressure ratio and nozzle-to-plate distance. The analytical predictions are compared to results from a numerical simulation and to the experimental data of Powell (1988) and Mørch (1963, 1964).
Weakly nonlinear wave motions in a thermally stratified boundary layer
Authors: Denier James P. , Mureithi Eunice W.
Published: April 2006

We consider weakly nonlinear wave motions in a thermally stratified boundary layer. Attention is focused on the upper branch of the neutral stability curve, corresponding to small wavelengths and large Reynolds number. In this limit the motion is governed by a first harmonic/mean flow interaction theory in which the wave-induced mean flow is of the same order of magnitude as the wave component of the flow. We show that the flow is governed by a system of three coupled partial differential equations which admit finite-amplitude periodic solutions bifurcating from the linear, neutral points.
Large-eddy simulation of turbulent confined coannular jets
Authors: Akselvoll Knut , Moin Parviz
Published: April 2006

Large-eddy simulation (LES) was used to study mixing of turbulent, coannular jets discharging into a sudden expansion. This geometry resembles that of a coaxial jet-combustor, and the goal of the calculation was to gain some insight into the phenomena leading to lean blow-out (LBO) in such combustion devices. This is a first step in a series of calculations, where the focus is on the fluid dynamical aspects of the mixing process in the combustion chamber. The effects of swirl, chemical reactions and heat release were not taken into account. Mixing of fuel and oxidizer was studied by tracking a passive scalar introduced in the central jet. The dynamic subgrid-scale (DM) model was used to model both the subgrid-scale stresses and the subgrid-scale scalar flux. The Reynolds number was 38000, based on the bulk velocity and diameter of the combustion chamber. Mean velocities and Reynolds stresses are in good agreement with experimental data. Animated results clearly show that intermittent pockets of fuel-rich fluid (from the central jet) are able to cross the annular jet, virtually undiluted, into the recirculation zone. Most of the fuel-rich fluid is, however, entrained into the recirculation zone near the instantaneous reattachment point. Fuel trapped in the recirculation zone is, for the most part, entrained back into the step shear layer close to the base of the burner.
Near-wake structure of an oscillating cylinder: effect of controlled shear-layer vortices
Authors: Chyu C. K. , Rockwell D.
Published: April 2006

The instantaneous structure of the near wake of a cylinder subjected to small-amplitude perturbations is characterized using high-image-density particle image velocimetry. Emphasis is on control of the small-scale shear-layer vortices, which feed into the Kármán vortices. Modifications of the Kármán vortex formation are classified according to patterns of modulated and locked-on shear-layer vortices. The formation length of the Kármán vortices can be dramatically shortened and, in the limiting case, occur adjacent to the base of the cylinder when it is perturbed at the inherent instability frequency of the shear layer and its subharmonics. Moreover, the induced shear-layer vortices can lead to large-amplitude transverse undulations of the entire near-wake region during formation of the Kármán vortices.

These variations of the near-wake structure are further elucidated by considering the transient response of the wake, induced by abrupt cessation and onset of periodic motion of the cylinder. Distinctive intermediate states of the wake arise during relaxation to its asymptotic state; such relaxation requires a very large number of periods of the inherent instability of the shear layer.
Flow in an open channel capillary
Authors: Romero L. A. , Yost F. G.
Published: April 2006

The problem of capillary-driven flow in a V-shaped surface groove is addressed. A nonlinear diffusion equation for the liquid shape is derived from mass conservation and Poiseuille flow conditions. A similarity transformation for this nonlinear equation is obtained and the resulting ordinary differential equation is solved numerically for appropriate boundary conditions. It is shown that the position of the wetting front is proportional to (Dt)½ where D is a diffusion coefficient proportional to the ratio of the liquid-vapour surface tension to viscosity and the groove depth, and a function of the contact angle and the groove angle. For flow into the groove from a sessile drop source it is shown that the groove angle must be greater than the contact angle. Certain arbitrarily shaped grooves are also addressed.
On the wave excitation and the formation of recirculation eddies in an axisymmetric flow of uniformly rotating fluids
Authors: Hanazaki Hideshi
Published: April 2006

The inertial waves excited in a uniformly rotating fluid passing through a long circular tube are studied numerically. The waves are excited either by a local deformation of the tube wall or by an obstacle located on the tube axis. When the flow is subcritical, i.e. when the phase and group velocity of the fastest wave mode in their long-wave limit are larger than the incoming axial flow velocity, the excited waves propagate upstream of the excited position. The non-resonant waves have many linear aspects, including the upstream-advancing speed of the wave and the coexisting lee wavelength. When the flow is critical (resonant), i.e. when the long-wave velocity is nearly equal to the axial flow velocity, the large-amplitude waves are resonantly excited. The time development of these waves is described well by the equation derived by Grimshaw & Yi (1993). The integro-differential equation, which describes the strongly nonlinear waves until the axial flow reversal occurs, can predict the onset time and position of the recirculation eddies observed in the solutions of the Navier-Stokes equations. The numerical results and the theory both show that the flow reversal most probably occurs on the tube axis and also when the waves are excited by a contraction of the tube wall. The structure of the recirculation eddies obtained in the solutions of the Navier-Stokes equations at Re = 105 is similar to the axisymmetric or ‘bubble-type’ breakdown observed in the experiments of the vortex-breakdown which used a different non-uniform (Burgers-type) rotation. In uniformly rotating fluids the formation of the recirculation eddies has not been observed in the previous numerical studies of vortex breakdown where a straight tube was used and thus the inertial waves were not excited. This shows that the generation of the recirculation eddies in this study is genuinely explained by the topographically excited large-amplitude inertial ‘waves’ and not by other ‘instability’ mechanisms. Since the wave cannot be excited in a straight tube even in the non-uniformly rotating flows, the generation mechanism of the recirculation eddies in this study is different from the previous numerical studies for the vortex breakdown. The occurrence of the recirculation eddies depends not only on the Froude number and the strength of the excitation source but also on the Reynolds number since the wave amplitude generally decreases by the viscous effects. Some relations to the experiments of vortex breakdown, which have been exclusively done for non-uniformly rotating fluids but done in a ‘non-uniform tube’, are discussed. The flow states, which are classified as supercritical, subcritical or critical in hydraulic terminology, changes along the flow when the upstream flow is near resonant conditions and a non-uniform tube is used.
Forced convection in a fluid-saturated porous-medium channel with isothermal or isoflux boundaries
Authors: Nield D. A. , Junqueira S. L. M. , Lage J. L.
Published: April 2006

We present a fresh theoretical analysis of fully developed forced convection in a fluid-saturated porous-medium channel bounded by parallel plates, with imposed uniform heat flux or isothermal condition at the plates. As a preliminary step, we obtain an ‘exact’ solution of the Brinkman-Forchheimer extension of Darcy's momentum equation for flow in the channel. This uniformly valid solution permits a unified treatment of forced convection heat transfer, provides the means for a deeper explanation of the physical phenomena, and also leads to results which are valid for highly porous materials of current practical importance.
Effects of jet flow on jet noise via an extension to the Lighthill model
Authors: Ribner Herbert S.
Published: April 2006

The Lighthill formalism for jet noise prediction is extended to accommodate wave transport by the mean jet flow. The extended theory combines the simplicity of the Lighthill approach with the generality of the more complex Lilley approach. There is full allowance for ‘flow-acoustic’ effects: shielding, as well as the refractive ‘cone of (relative) silence’. A source term expansion yielda a convected wave equation that retains the basic Lighthill source term. This leads to a general formula for power spectral density emitted from unit volume as the Lighthill-based value multiplied by a squared ‘normalized’ Green's function. The Green's function, referred to a stationary point source, delineates the refraction dominated ‘cone of silence’. The convective motion of the sources, with its powerful amplifying effect, also directional, is accounted for in the Lighthill factor. Source convection and wave convection are thereby decoupled, in contrast with the Lilley approach: this makes the physics more transparent. Moreover, the normalized Green's function appears to be near unity outside the ‘cone of silence’. This greatly reduces the labour of calculation: the relatively simple Lighthill-based prediction may be used beyond the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected ‘point’ source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are coaxial or shrouding jets: in that case the difference from unity will quantify the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g. hot jets).
Dynamical flow characterization of transitional and chaotic regimes in converging–diverging channels
Authors: Guzmán A. M. , Amon C. H.
Published: April 2006

Numerical investigation of laminar, transitional and chaotic flows in converging–diverging channels are performed by direct numerical simulations in the Reynolds number range 10 < Re < 850. The temporal flow evolution and the onset of turbulence are investigated by combining classical fluid dynamics representations with dynamical system flow characterizations. Modern dynamical system techniques such as timedelay reconstructions of pseudophase spaces, autocorrelation functions, fractal dimensions and Eulerian Lyapunov exponents are used for the dynamical flow characterization of laminar, transitional and chaotic flow regimes. As a consequence of these flow characterizations, it is verified that the transitional flow evolves through intermediate states of periodicity, two-frequency quasi-periodicity, frequency-locking periodicity, and multiple-frequency quasi-periodicity before reaching a non-periodic unpredictable behaviour corresponding to low-dimensional deterministic chaos.

Qualitative and quantitative differences in Eulerian dynamical flow parameters are identified to determine the predictability of transitional flows and to characterize chaotic, weak turbulent flows in converging–diverging channels. Autocorrelation functions, pseudophase space representations and Poincaré maps are used for the qualitative identification of chaotic flows, assertion of their unpredictable nature, and recognition of the topological structure of the attractors for different flow regimes. The predictability of transitional flows is determined by analysing the autocorrelation functions and by representing their attractors in the reconstructed pseudophase spaces. The transitional flow behaviour is examined by the geometric visualization of the evolution of the attractors and Poincaré maps until the appearance of a strange attractor at the onset of chaos. Eulerian Lyapunov exponents and fractal dimensions are quantitative parameters to establish the onset of chaos, the persistence of chaotic flow behaviour, and the long-term persistent unpredictability of chaotic Eulerian flow regimes. Lastly, three-dimensional simulations for converging–diverging channel flow are performed to determine the effect of the spanwise direction on the route of transition to chaos.
Interaction of capillary waves with longer waves. Part 1. General theory and specific applications to waves in one dimension
Authors: Watson Kenneth M. , Buchsbaum Steven B.
Published: April 2006

A Hamiltonian formulation is used to investigate irrotational capillary wave dynamics. Dissipation is accounted for by putting the wave system in contact with a ‘heat bath’. The generation of short waves by longer waves is studied. It is found that millimetre-wavelength waves tend to be created on the forward face of a steep longer wave, while centimetre waves tend to form near the crest. Generation of capillary waves by wind waves is investigated. The results are compared with predictions of the Hasselmann transport equation. It is found that off-resonance interactions lead to significant corrections to the transport theory. The relative importance of three-wave and four-wave interactions is studied, as well as the role of triad resonances. For the capillary phenomena studied here, the four-wave terms in most cases lead to quantitative, but not qualitative, corrections to the three-wave only calculations. However, restricting interactions to the neighbourhood of triad resonances can give quite erroneous results. Use of a canonical transformation to pseudo-wave variables can greatly reduce numerical computation times.
Thermal convection in a magnetic fluid
Authors: Zebib Abdelfattah
Published: April 2006

A theoretical study of the character and stability of thermomagnetic flow in a microgravity environment is performed. Convection is driven owing to imposed radial magnetic and temperature gradients in a cylindrical shell containing a ferrofluid. Linear, nonlinear, and computational methods are employed. It is shown that convection sets in as a stable supercritical bifurcation. Results obtained for a specific shell configuration are in good agreement with experiments.
Atmospheric solitary waves: some applications to the morning glory of the Gulf of Carpentaria
Authors: Forbes Lawrence K. , Belward Shaun R.
Published: April 2006

A mathematical model is proposed to describe atmospheric solitary waves at the interface between a ‘shallow’ layer of fluid near the ground and a stationary upper layer of compressible air. The lower layer is in motion relative to the ground, perhaps as a result of a distant thunderstorm or a sea breeze, and possesses constant vorticity. The upper fluid is compressible and isothermal, so that its density and pressure both decrease exponentially with height. The profile and speed of the solitary wave are determined, for a wave of given amplitude, using a boundary-integral method. Results are discussed in relation to the ‘morning glory’, which is a remarkable meteorological phenomenon evident in the far north of Australia.
Multi-scalar triadic interactions in differential diffusion with and without mean scalar gradients
Authors: Yeung P. K.
Published: April 2006

The spectral mechanisms of the differential diffusion of pairs of passive scalars with different molecular diffusivities are studied in stationary isotropic turbulence, using direct numerical simulation data at Taylor-scale Reynolds number up to 160 on 1283 and 2563 grids. Of greatest interest are the roles of nonlinear triadic interactions between different scale ranges of the velocity and scalar fields in the evolution of spectral coherency between the scalars, and the effects of mean scalar gradients.

Analysis of single-scalar spectral transfer (extending the results of a previous study) indicates a robust local forward cascade behaviour at high wavenumbers, which is strengthened by both high diffusivity and mean gradients. This cascade is driven primarily by moderately non-local interactions in which two small-scale scalar modes are coupled via a lower-wavenumber velocity mode near the peak of the energy dissipation spectrum. This forward cascade is coherent, tending to increase the coherency between different scalars at high wavenumbers but to decrease it at lower wavenumbers. However, at early times coherency evolution at high wavenumbers is dominated by de-correlating effects due to a different type of non-local triad consisting of two scalar modes with a moderate scale separation and a relatively high-wavenumber velocity mode. Consequently, although the small-scale motions play little role in spectral transfer, they are responsible for the rapid de-correlation observed at early times. At later times both types of competing triadic interactions become important over a wider wavenumber range, with increased relative strength of the coherent cascade, so that the coherency becomes slow-changing. When uniform mean scalar gradients are present, a stationary state develops in the coherency spectrum as a result of a balance between a coherent mean gradient contribution (felt within about 1 eddy-turnover time) and the net contribution from scale interactions. The latter is made less de-correlating because of a strengthened coherent forward cascade, which is in turn caused by uniform mean gradients acting as a primarily low-wavenumber source of scalar fluctuations with the same spectral content as the velocity field.
Experiments on double-diffusive sugar–salt fingers at high stability ratio
Authors: Taylor John R. , Veronis George
Published: April 2006

In a series of laboratory experiments the growth of double-diffusive salt fingers from an initial configuration of two homogeneous reservoirs with salt in the lower and sugar in the upper layer was investigated. For most of the experiments the stability ratio was between 2.5 and 3, where the latter value is at the upper limit (the ratio of salt to sugar diffusivities) for which fingers can exist. In these experiments long slender fingers are generated at the interface. Essentially all theories or physical bases for models of salt fingers presuppose such a configuration of long fingers. Our measurements show that the length of fingers at high stability ratio increases with time like t1/2, with a coefficient that is consistent with the diffusive spread of the faster diffusing component (salt). When the initial stability ratio is closer to unity, fingers penetrate into the reservoirs very rapidly carrying with them large anomalies of salt and sugar which give rise to convective overturning of the reservoirs. The convection sweeps away the ends of the fingers, and when it is intense enough (as it is when the sugar anomaly is large) it can reduce the finger height to a value less than the width. After this initial phase the finger length grows linearly with time as has been found in previous studies. These results show that salt fingers can evolve in quite different ways depending on the initial stability ratio and must cast doubt on the use of simple similarity arguments to parameterize the heat and salt fluxes produced by fingers.
Numerical simulation of a concentrated emulsion in shear flow
Authors: Loewenberg M. , Hinch E. J.
Published: April 2006

A three-dimensional computer simulation of a concentrated emulsion in shear flow has been developed for low-Reynolds-number finite-capillary-number conditions. Numerical results have been obtained using an efficient boundary integral formulation with periodic boundary conditions and up to twelve drops in each periodically replicated unit cell. Calculations have been performed over a range of capillary numbers where drop deformation is significant up to the value where drop breakup is imminent. Results have been obtained for dispersed-phase volume fractions up to 30% and dispersed- to continuous-phase viscosity ratios in the range of 0 to 5. The results reveal a complex rheology with pronounced shear thinning and large normal stresses that is associated with an anisotropic microstructure that results from the alignment of deformed drops in the flow direction. The viscosity of an emulsion is only a moderately increasing function of the dispersed-phase volume fraction, in contrast to suspensions of rigid particles or undeformed drops. Unlike rigid particles, deformable drops do not form large clusters.
Vortex evolution in non-axisymmetric impulsive spin-up from rest
Authors: Henderson D. M. , Lopez J. M. , Stewart D. L.
Published: April 2006

The flow evolution of water in a completely filled rectangular container, impulsively rotated from rest to a steady angular speed, is investigated experimentally and numerically. The pathlines of the fluid from rest to solid-body rotation primarily follow one of two possible configurations that have been described previously in the literature. The first, consisting of two cyclones that form following the separation and roll-up of the sidewall boundary layers and an anticyclone that forms subsequently, results in a pattern on the path to spin-up of cyclonic–anticyclonic–cyclonic vorticity. In the second configuration the cyclones migrate into the interior of the container and merge, resulting in a pattern on the path to spin-up of anticyclonic–cyclonic–anticyclonic vorticity. The experiments provide a parameterization of the possible evolutionary configurations as a function of horizontal and vertical aspect ratios and Reynolds numbers. Critical Reynolds numbers for vortex merger are determined experimentally. Evolutionary configurations in addition to the primary two are observed; in particular symmetry breaking occurs at high Reynolds numbers causing complicated patterns of flow evolution. For some flow conditions at high Reynolds numbers, more than one evolutionary pattern is observed for the same external parameters. The experiments are conducted with a rigid lid showing that a free surface is not required for vortex merger. Numerical integrations of the two-dimensional Navier–Stokes equations (a situation corresponding to the limiting case of a container of infinite depth, where there are no effects from the top and bottom and all flow is horizontal) reproduce qualitatively many of the features of the experimental observations, in particular the merger events. The numerical results show that neither vertical flow due to Ekman boundary layers at the top and bottom nor a free surface are necessary for the observed vortex merger.
Oscillating flow of a heat-conducting fluid in a narrow tube
Authors: Bauwens Luc
Published: April 2006

Thermoacoustic refrigeration occurs in periodic flow in a duct with heat transfer within the fluid and to the tube. This study considers the periodic limit cycle with large pressure oscillations that is obtained in a tube when prescribed, phase-shifted, periodic velocities at the tube ends, at frequencies lower than acoustic eigenmodes, sweep a length comparable to the tube length. The temperature differences between the two ends are of arbitrary magnitude, heat transfer in the transverse direction within the fluid is assumed to be very effective and the thermal mass of the wall is large. The geometry is two-dimensional, axisymmetric, and conduction is accounted for, not only in the fluid, but also with and within the tube wall. A perturbation solution valid in a local near-isothermal limit determines the equilibrium longitudinal temperature profile that is reached at the periodic regime, the pressure field including longitudinal gradients, and the longitudinal enthalpy flux. Results are presented for tubes open at both ends and also with one end closed. In the latter case, a singularity occurs in the temperature at the closed end, with behaviour identical to Rott's result for acoustic flow with small pressure amplitude. Other new results obtained for tubes open at both ends show that when velocities at both ends are in opposite phase, internal singularities in the temperature profiles may occur.