bluuebunny/crossref_metadata_2025 huggingface dataset:
On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet
Authors: Liu Shewen , Meneveau Charles , Katz Joseph
Published: April 2006

The properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number ofRλ≈ 310. Measurements are performed using two-dimensional particle displacement velocimetry. Three elements of the subgrid-scale stress tensor are calculated using planar filtering of the data. Usinga prioritesting, eddy-viscosity closures are shown to display very little correlation with the real stresses, in accord with earlier findings based on direct numerical simulations at lower Reynolds numbers. Detailed analysis of subgrid energy fluxes and of the velocity field decomposed into logarithmic bands leads to a new similarity subgrid-scale model. It is based on the ‘resolved stress’ tensorLij, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale. The correlation coefficient of this model with the real stress is shown to be substantially higher than that of the eddy-viscosity closures. It is shown that mixed models display similar levels of correlation. During thea prioritest, care is taken to only employ resolved data in a fashion that is consistent with the information that would be available during large-eddy simulation. The influence of the filter shape on the correlation is documented in detail, and the model is compared to the original similarity model of Bardinaet al.(1980). A relationship betweenLijand a nonlinear subgrid-scale model is established. In order to control the amount of kinetic energy backscatter, which could potentially lead to numerical instability, anad hocweighting function that depends on the alignment betweenLijand the strain-rate tensor, is introduced. A ‘dynamic’ version of the model is shown, based on the data, to allow a self-consistent determination of the coefficient. In addition, all tensor elements of the model are shown to display the correct scaling with normal distance near a solid boundary.
Instability of wind-forced inertial oscillations
Authors: Treguier A. M. , Klein P.
Published: April 2006

An instability mechanism that can amplify wind-forced inertial oscillations in the upper ocean is investigated. This forced instability happens because of the phase relationship between the mixed-layer depth and the surface current. It allows the inertial oscillations propagating against the wind to extract energy from it and amplify. The key ingredients for the instability to work are (a) a non-zero mean wind stress, (b) a spatial variability of the oscillations in the direction of the wind stress. The amplification is demonstrated using a simple shallow-water model in a few situations: the dispersion of a localized disturbance with steady and time-varying wind forcing, generation of inertial waves at a coast, and spatial variability induced by mesoscale eddies. Estimates of the growth rate are provided for both dissipative and non-dissipative cases.
A theory of steady breakers
Authors: Cointe Raymond , Tulin Marshall P.
Published: April 2006

The mechanics of the quasi-steady breaking wave created above a submerged hydrofoil, first studied experimentally by Duncan (1981), is elucidated here. It is an example of a flow wherein the resistance of the body manifests itself in a detached separation eddy located away from the body (i.e. on the free surface). As we show, the conditions for inception of separation and the prediction of the breaking configuration follow from simple considerations, without extensive calculation.

The physical model of the breaker, based on observations, consists of an essentially stagnant eddy riding on the forward face of the leading wave in the wave train behind the hydrofoil. This eddy is sustained by turbulent stresses acting in the shear zone separating the eddy and the underlying flow. These stresses result in a trailing turbulent wake just beneath the water surface. The breaker eddy contains air entrained at breaking, and the degree of aeration is a parameter of the problem.

The eddy—breaker model is quantified utilizing independent measurements of turbulent shear stress in shear zones. It is then shown that the hydrostatic pressure acting on the dividing streamline underneath the eddy creates a trailing wave which largely cancels the trailing wave that would exist in the absence of breaking. The ‘wave’ resistance of the hydrofoil then manifests itself in the momentum flux of the residual trailing wave, plus the momentum flux in the breaker wake, i.e. the breaker resistance.

For a fixed hydrofoil speed the total momentum flux, or resistance, in the presence of breaking is shown to have a minimum corresponding to a particular value of the trailing-wave steepness. It is thus concluded that the wave resistance must exceed this value for breaking to ensue. For hydrofoil resistance in excess of this minimum, both a weak and strong breaker would seem to exist. It is shown, however, that the weak breaker is unstable. It is also shown that a maximum steady breaking resistance exists, limited by the size of the breaker and dependent on the extent of its aeration.

Good quantitative comparisons between theory and experiments are shown.
The effect of phase variations and cross-shear on vortical structures in a plane mixing layer
Authors: Nygaard Kris J. , Glezer Ari
Published: April 2006

The evolution of spanwise phase variations of nominally two-dimensional instability modes in a plane shear layer is studied in a closed-return water facility using time-harmonic excitation having spanwise-non-uniform phase or frequency distributions. The excitation waveform is synthesized by a linear array of 32 surface film heaters flush-mounted on the flow partition. A span wise-linear phase distribution leads to the excitation of oblique waves and to the rollup of oblique primary vortices. When the prescribed phase distribution is piecewise-constant and spanwise-periodic, the flow is excited with a linear combination of a two-dimensional wavetrain and pairs of equal and opposite oblique waves, the amplitudes of which depend on the magnitude of the phase variation ΔΦ. As a result of the excitation, the primary vortices undergo spanwise-non-uniform rollup and develop spanwise-periodic deformations that induce cross-shear and secondary vortices in the braid region. The amplitude of the deformations of the primary vortices and the shape and strength of the secondary vortices depend on the magnitude of ΔΦ. When ΔΦ is small, the secondary vortices are counter-rotating vortex pairs. As ΔΦ increases, cross-shear induced by oblique segments of the primary vortices in the braid region results in the formation of single secondary vortex strands. The flow is not receptive to spanwise phase variations with wavelengths shorter than the streamwise wavelength of the Kelvin–Helmholtz instability. When the phase variation is ΔΦ = ϕ, the flow is excited with pairs of oblique waves only and undergoes a double rollup, resulting in the formation of spanwise-deformed vortices at twice the excitation frequency. Measurements of the streamwise velocity component show that the excitation leads to a substantial increase in the cross-stream spreading of the shear layer and that distortions of transverse velocity profiles are accompanied by an increase in the high-frequency content of velocity power spectra. Detailed schlieren visualizations shed light on the nature of ‘vortex dislocations’ previously observed by other investigators. Complex spanwise-non-uniform pairing interactions between the spanwise vortices are forced farther downstream by spanwise-amplitude or phase variations of subharmonic excitation wavetrains.
The offshore vortex train
Authors: Matsunaga N. , Takehara K. , Awaya Y.
Published: April 2006

A row of two-dimensional vortices forms in an offshore zone when regular surface waves run up a sloping flat bed. This vortex row is called the offshore vortex train. The vortices begin to appear near the breaking point. Moving in the offshore direction, they develop and increase their horizontal lengthscale through vortex merging. After reaching a particular offshore location, however, they decay rapidly. The formation region of the vortex train has been investigated on the basis of visual experiments for three bed slopes. Its formation does not depend on the type of wave breaking but is observed when the steepness of deep-water waves is smaller than 4.2 × 10−2. The horizontal lengthscale of the vortices and the velocities of the vortex movement have also been evaluated empirically.
Convective instability in ammonium chloride solution directionally solidified from below
Authors: Chen Falin , Lu Jay W. , Yang Tsung L.
Published: April 2006

The stabilities of salt-finger and plume convection, two major flows characterizing the fluid dynamics of NH4Cl solutions cooling from below, are investigated by theoretical and experimental approaches. A linear stability analysis is implemented to study theoretically the onset of salt-finger convection. Special emphasis is placed on the competition between different instability modes. It is found that in most of the cases considered, the neutral curve consists of two separated monotonic branches with a Hopf bifurcation branch in between; the right-hand monotonic branch corresponding to the boundary-layer-mode convection is more unstable than the left-hand monotonic branch corresponding to the mushy-layer mode. We also conducted a series of experiments covering wide ranges of bulk fluid concentration C∞ and bottom temperature TB to study the stability characteristics of plume convection. From the measurement of both temperature and concentration of the interstitial fluid in the mushy layer, we verify that during the progress of solidification the melt in the mush is in a thermodynamic equilibrium state except at the melt/mush interface where most of the solidification occurs. The critical Rayleigh number of the onset of plume convection is found to be Rccm = 1.1 × 107Π* (see (22)), where Π* is the permeability of the mush. This relation is believed to be valid up to supereutectic NH4Cl solutions.
Flows in a rotating spherical shell: the equatorial case
Authors: de Verdière A. Colin , Schopp R.
Published: April 2006

It is well known that the widely used powerful geostrophic equations that single out the vertical component of the Earth's rotation cease to be valid near the equator. Through a vorticity and an angular momentum analysis on the sphere, we show that if the flow varies on a horizontal scale L smaller than (Ha)1/2 (where H is a vertical scale of motion and a the Earth's radius), then equatorial dynamics must include the effect of the horizontal component of the Earth's rotation. In equatorial regions, where the horizontal plane aligns with the Earth's rotation axis, latitudinal variations of planetary angular momentum over such scales become small and approach the magnitude of its radial variations proscribing, therefore, vertical displacements to be freed from rotational constraints. When the zonal flow is strong compared to the meridional one, we show that the zonal component of the vorticity equation becomes (2Ω.Δ)u1 = g/ρ0)(∂ρ/a∂θ). This equation, where θ is latitude, expresses a balance between the buoyancy torque and the twisting of the full Earth's vorticity by the zonal flow u1. This generalization of the mid-latitude thermal wind relation to the equatorial case shows that u1 may be obtained up to a constant by integrating the ‘observed’ density field along the Earth's rotation axis and not along gravity as in common mid-latitude practice. The simplicity of this result valid in the finite-amplitude regime is not shared however by the other velocity components.

Vorticity and momentum equations appropriate to low frequency and predominantly zonal flows are given on the equatorial β-plane. These equatorial results and the mid-latitude geostrophic approximation are shown to stem from an exact generalized relation that relates the variation of dynamic pressure along absolute vortex lines to the buoyancy field. The usual hydrostatic equation follows when the aspect ratio δ = H/L is such that tan θ/δ is much larger than one. Within a boundary-layer region of width (Ha)1/2 and centred at the equator, the analysis shows that the usually neglected Coriolis terms associated with the horizontal component of the Earth's rotation must be kept.

Finally, some solutions of zonally homogeneous steady equatorial inertial jets are presented in which the Earth's vorticity is easily turned upside down by the shear flow and the correct angular momentum ‘Ωr2cos2(θ)+u1rCos(θ)’ contour lines close in the vertical–meridional plane.
On conical swirling flows in an infinite fluid
Authors: Sozou C. , Wilkinson L. C. , Shtern V. N.
Published: April 2006

The steady axisymmetric flow generated in an unbounded incompressible viscous fluid, of density ρ and kinematic viscosity v, by torque-producing singularities with constant line density c along the semi-infinite line θ = 0 of a spherical polar coordinate system (r, θ, ϕ) that was investigated by Paull & Pillow (1985b), is reconsidered. The numerical solution constructed revealed the following features. (i) For values of c up to about 46.9 there is only one solution where the axial component of the meridional flow is directed from θ = 0 to θ = π. This solution can be continued to all values of c. (ii) For c > 46.9 the system of equations allows bifurcation and two more solutions with a single separatrix are possible. (iii) For c = ∞ one of the two branches of the separatrix asymptotes to θ = ½π and the other to θ = π. The asymptotic solution for large c constructed by Paull & Pillow (1985b), where the meridional flow consists of two colliding flows, relates to the bifurcation solution where the separatrix asymptotes to ½π as c → ∞.
Global stability of two-dimensional and axisymmetric Euler flows
Authors: Davidson P. A.
Published: April 2006

This paper is concerned with the stability of steady inviscid flows with closed streamlines. In increasing order of complexity we look at two-dimensional planar flows, poloidal (r, z) flows, and swirling recirculating flows. In each case we examine the relationship between Arnol’d's variational approach to stability, Moffatt's magnetic relaxation technique, and a more recent relaxation procedure developed by Valliset al.We start with two-dimensional (x, y) flows. Here we show that Moffatt's relaxation procedure will, under a wide range of circumstances, produce Euler flows which are stable. The physical reasons for this are discussed in the context of the well-known membrane analogy. We also show that there is a close relationship between Hamilton's principle and magnetic relaxation. Next, we examine poloidal flows. Here we find that, by and large, our planar results also hold true for axisymmetric flows. In particular, magnetic relaxation once again provides stable Euler flows. Finally, we consider swirling recirculating flows. It transpires that the introduction of swirl has a profound effect on stability. In particular, the flows produced by magnetic relaxation are no longer stable. Indeed, we show that all swirling recirculating Euler flows are potentially unstable to the extent that they fail to satisfy Arnol’d's stability criterion. This is, perhaps, not surprising, as all swirling recirculating flows include regions where the angular momentum decreases with radius and we would intuitively expect such flows to be prone to a centrifugal instability. The paper concludes with a discussion of marginally unstable modes in swirling flows. In particular, we examine the extent to which Rayleigh's original ideas on stability may be generalized, through the use of the Routhian, to include flows with a non-zero recirculation.
Structure of turbulent boundary layers on smooth and rough walls
Authors: Krogstad P.-Å. , Antonia R. A.
Published: April 2006

The structure of turbulent boundary layers which develop with zero pressure gradient on a smooth wall and ak-type rough wall was examined using arrays of X-wires. Although the data were obtained only on two orthogonal planes, the technique provides some information on the three-dimensionality of the large-scale structures. The major effect of the roughness is to tilt the inclination of the structures towards the wall-normal direction. This is caused by the reduced damping of the wall-normal velocity fluctuations close to the rough surface and the break-up of structures whose scales are comparable to the size of the roughness elements. Both effects cause a reduction in the streamwise lengthscales, as suggested by all the measured two-point correlations. The correlations also show that the roughness tends to reduce the overall anisotropy of the large-scale motion. There is evidence to suggest that the magnitude of the vorticity field is larger over the rough wall.
Particle response and turbulence modification in fully developed channel flow
Authors: Kulick J. D. , Fessler J. R. , Eaton J. K.
Published: April 2006

The interactions between small dense particles and fluid turbulence have been investigated in a downflow fully developed channel in air. Particle velocities of, and fluid velocities in the presence of, 50 μm glass, 90 μm glass and 70 μm copper spherical beads were measured by laser Doppler anemometry, at particle mass loadings up to 80%. These particles were smaller than the Kolmogorov lengthscale of the flow and could respond to some but not all of the scales of turbulent motion. Streamwise mean particle velocity profiles were flatter than the mean fluid velocity profile, which was unmodified by particle loading. Particle velocity fluctuation intensities were larger than the unladen-fluid turbulence intensity in the streamwise direction but were smaller in the transverse direction. Fluid turbulence was attenuated by the addition of particles; the degree of attenuation increased with particle Stokes number, particle mass loading and distance from the wall. Turbulence was more strongly attenuated in the transverse than in the streamwise direction, because the turbulence energy is at higher frequencies in the transverse direction. Streamwise turbulence attenuation displayed a range of preferred frequencies where attenuation was strongest.
An experimental study of reflected liquefaction shock waves with near-critical downstream states in a test fluid of large molar heat capacity
Authors: Gülen Seyfettin C. , Thompson Philip A. , Cho Hung-Jai
Published: April 2006

Near-critical states have been achieved downstream of a liquefaction shock wave, which is a shock reflected from the endwall of a shock tube. Photographs of the shocked test fluid (iso-octane) reveal a rich variety of phase-change phenomena. In addition to the existence of two-phase toroidal rings which have been previously reported, two-phase structures with a striking resemblance to dandelions and orange slices have been frequently observed. A model coupling the flow and nucleation dynamics is introduced to study the two-wave system of shock-induced condensation and the liquefaction shock wave in fluids of large molar heat capacity. In analogy to the one-dimensional Zeldovich–von Neumann–Döring (ZND) model of detonation waves, the leading part of the liquefaction shock wave is a gasdynamic pressure discontinuity (Δ ≈ 0.1 μm, τ ≈ 1 ns) which supersaturates the test fluid, and the phase transition takes place in the condensation relaxation zone (Δ ≈ 1–103 μm, τ ≈ 0.1–100 μs) via dropwise condensation. At weak to moderate shock strengths, the average lifetime of the metastable state, τ ∞ 1/J, is long such that the reaction zone is spatially decoupled from the forerunner shock wave, and J is the homogeneous nucleation rate. With increasing shock strength, a transition in the phase-change mechanism from nucleation and growth to spinodal decomposition is anticipated based on statistical mechanical arguments. In particular, within a complete liquefaction shock the metastable region is entirely bypassed, and the vapour decomposes inside the unstable region. This mechanism of unmixing in which nucleation and growth become one continuous process provides a consistent framework within which the observed irregularities can be explained.
Optimal energy density growth in Hagen–Poiseuille flow
Authors: Schmid Peter J. , Henningson Dan S.
Published: April 2006

Linear stability of incompressible flow in a circular pipe is considered. Use is made of a vector function formulation involving the radial velocity and radial vorticity only. Asymptotic as well as transient stability are investigated using eigenvalues and ε-pseudoeigenvalues, respectively. Energy stability is probed by establishing a link to the numerical range of the linear stability operator. Substantial transient growth followed by exponential decay has been found and parameter studies revealed that the maximum amplification of initial energy density is experienced by disturbances with no streamwise dependence and azimuthal wavenumber n = 1. It has also been found that the maximum in energy scales with the Reynolds number squared, as for other shear flows. The flow field of the optimal disturbance, exploiting the transient growth mechanism maximally, has been determined and followed in time. Optimal disturbances are in general characterized by a strong shear layer in the centre of the pipe and their overall structure has been found not to change significantly as time evolves. The presented linear transient growth mechanism which has its origin in the non-normality of the linearized Navier–Stokes operator, may provide a viable process for triggering finite-amplitude effects.
On the direct initiation of gaseous detonations by an energy source
Authors: He Longting , Clavin Paul
Published: April 2006

A new criterion for the direct initiation of cylindrical or spherical detonations by a localized energy source is presented. The analysis is based on nonlinear curvature effects on the detonation structure. These effects are first studied in a quasi-steady-state approximation valid for a characteristic timescale of evolution much larger than the reaction timescale. Analytical results for the square-wave model and numerical results for an Arrhenius law of the quasi-steady equations exhibit two branches of solutions with a C-shaped curve and a critical radius below which generalized Chapman–Jouguet (CJ) solutions cannot exist. For a sufficiently large activation energy this critical radius is much larger than the thickness of the planar CJ detonation front (typically 300 times larger at ordinary conditions) which is the only intrinsic lengthscale in the problem. Then, the initiation of gaseous detonations by an ideal point energy source is investigated in cylindrical and spherical geometries for a one-step irreversible reaction. Direct numerical simulations show that the upper branch of quasi-steady solutions acts as an attractor of the unsteady blast waves originating from the energy source. The critical source energy, which is associated with the critical point of the quasi-steady solutions, corresponds approximately to the boundary of the basin of attraction. For initiation energy smaller than the critical value, the detonation initiation fails, the strong detonation which is initially formed decays to a weak shock wave. A successful initiation of the detonation requires a larger energy source. Transient phenomena which are associated with the intrinsic instability of the quasi-steady detonations branch develop in the induction timescale and may induce additional mechanisms close to the critical condition. In conditions of stable or weakly unstable planar detonations, these unsteady phenomena are important only in the vicinity of the critical conditions. The criterion of initiation derived in this paper works to a good approximation and exhibits the huge numerical factor, 106–108, which has been experimentally observed in the critical value of the initiation energy.
Thermocapillary convection and existence of continuous liquid layers in the absence of gravity
Authors: Floryan J. M. , Chen C.
Published: April 2006

Thermocapillary convection in an infinite liquid layer driven by a temperature gradient parallel to the interface in the absence of gravity is considered. It is demonstrated that the temperature field has to satisfy restrictive conditions in order for a continuous layer to exist. It is further shown that the same conditions apply to long finite layers. Such layers, when subject to heating that does not satisfy the existence conditions, undergo large deformations and possible break up if the layer is sufficiently long.
Characterization of disturbance propagation in weak shock-wave reflections
Authors: Sasoh Akihiro , Takayama Kazuyoshi
Published: April 2006

Reflections of weak shock waves over wedges are investigated mainly by considering disturbance propagation which leads to a flow non-uniformity immediately behind a Mach stem. The flow non-uniformity is estimated by the local curvature of a smoothly curved Mach stem, and is characterized not only by a pressure increase immediately behind the Mach stem on the wedge but also by a propagation speed. In the case of a smoothly curved Mach stem as is observed in a von Neumann Mach reflection, the pressure increase behind the Mach stem is approximately determined by Whitham's ray-shock theory. The propagation speed of the flow non-uniformity is approximated by Whitham's shock-shock relation. If the shock-shock does not catch up with a point where a curvature of the Mach stem vanishes, a von Neumann Mach reflection appears. The boundary on which the above-mentioned condition breaks results in the transition from a von Neumann Mach reflection to a simple Mach reflection. This idea leads to a transition criterion for a von Neumann Mach reflection, which is algebraically expressed by χ1 = χs where χ1 is the trajectory angle of the point on the Mach stem where the local curvature vanishes and is approximately replaced by χg—θw (χg is the angle of glancing incidence, and θw is the apex angle of the wedge) and χs is the trajectory angle of Whitham's shock-shock, measured from the surface of the wedge. For shock Mach numbers of 1.02 to 2.2 and a wedge angle from 0° to 30°, the domains of a von Neumann Mach reflection, simple Mach reflection and regular reflection are determined by experiment, numerical simulation and theory. The present transition criterion agrees well with experiments and numerical simulations.
Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion
Authors: Chang Eugene J. , Maxey Martin R.
Published: April 2006

A direct numerical simulation, based on spectral methods, has been used to compute the time-dependent, axisymmetric viscous flow past a rigid sphere. An investigation has been made for oscillatory flow about a zero mean for different Reynolds numbers and frequencies. The simulation has been verified for steady flow conditions, and for unsteady flow there is excellent agreement with Stokes flow theory at very low Reynolds numbers. At moderate Reynolds numbers, around 20, there is good general agreement with available experimental data for oscillatory motion. Under steady flow conditions no separation occurs at Reynolds number below 20; however in an oscillatory flow a separation bubble forms on the decelerating portion of each cycle at Reynolds numbers well below this. As the flow accelerates again the bubble detaches and decays, while the formation of a new bubble is inhibited till the flow again decelerates. Steady streaming, observed for high frequencies, is also observed at low frequencies due to the flow separation. The contribution of the pressure to the resultant force on the sphere includes a component that is well described by the usual added-mass term even when there is separation. In a companion paper the flow characteristics for constant acceleration or deceleration are reported.
Large-eddy simulation of homogeneous turbulence and diffusion in stably stratified shear flow
Authors: Kaltenbach H.-J. , Gerz T. , Schumann U.
Published: April 2006

By means of large-eddy simulation, homogeneous turbulence is simulated for neutrally and stably stratified shear flow at gradient-Richardson numbers between zero and one. We investigate the turbulent transport of three passive species which have uniform gradients in either the vertical, downstream or cross-stream direction. The results are compared with previous measurements in the laboratory and in the stable atmospheric boundary layer, as well as with results from direct numerical simulations. The computed and measured flow properties agree with each other generally within the scatter of the measurements. At strong stratification, the Froude number becomes the relevant flow-controlling parameter. Stable stratification suppresses vertical overturning and mixing when the inverse Froude number based on a turn-over timescale exceeds a critical value of about 3. The turbulent diffusivity tensor is strongly anisotropic and asymmetric. However, only the vertical and the cross-stream diagonal components are of practical importance in shear flows. The vertical diffusion coefficient is much smaller than the cross-stream one at strong stratification. This anisotropy is stronger than predicted by second-order closure models. Turbulence fluxes in downstream and cross-stream directions follow classical mixing-length models.
Numerical and experimental investigations of low-density supersonic jets of hydrogen
Authors: Boyd I. D. , Beattie D. R. , Cappelli M. A.
Published: April 2006

Low-density flow of molecular hydrogen from a small nozzle is studied using numerical and experimental techniques. The conditions in the nozzle indicate that non-equilibrium effects will significantly influence the flow. Therefore, the numerical analysis is undertaken using a Monte Carlo approach. The experimental studies employ spontaneous Raman scattering. Comparisons of the measured data and computed results are made for total number density, rotational temperature, and for the number density of the first rotational level. The numerical results are found to be quite sensitive to the rotational relaxation rate, and a strong degree of thermal non-equilibrium is observed at the exit plane of the nozzle. Comparisons between experiment and analysis permit estimation of the rotational relaxation rate for hydrogen. Investigations are also conducted for expansion of the supersonic jet into a finite back pressure. The interaction of the plume with the chamber background gas is found to form shock waves in both the simulations and experiments. This phenomenon is investigated further by increasing the background pressure. Direct comparison of the simulation results and experimental measurements is very favourable.
Shear dispersion and anomalous diffusion by chaotic advection
Authors: Jones S. W. , Young W. R.
Published: April 2006

The dispersion of passive scalars by the steady viscous flow through a twisted pipe is both a simple example of chaotic advection and an elaboration of Taylor's classic shear dispersion problem. In this article we study the statistics of the axial dispersion of both diffusive and perfect (non-diffusive) tracer in this system.

For diffusive tracer chaotic advection assists molecular diffusion in transverse mixing and so diminishes the axial dispersion below that of integrable advection. As in many other studies of shear dispersion the axial distribution ultimately becomes Gaussian as t → ∞. Thus there is a diffusive regime, but with an effective diffusivity that is enhanced above molecular values. In contrast to the classic case, the effective diffusivity is not necessarily inversely proportional to the molecular diffusivity. For instance, in the irregular regime the effective diffusivity is proportional to the logarithm of the molecular diffusivity.

For perfect tracer chaotic advection does not result in a diffusive process, even in the irregular regime in which streamlines wander throughout the cross-section of the pipe. Instead the variance of the axial position is proportional to t in t so that the measured diffusion coefficent diverges like In t. This faster than linear growth of variance is attributed to the trapping of tracer for long times near the solid boundary, where the no-slip condition ensures that the fluid moves slowly. Analogous logarithmic effects associated with the no-slip condition are well known in the context of porous media.

A simple argument, based on Lagrangian statistics and a local analysis of the trajectories near the pipe wall, is used to calculate the constants of proportionality before the logarithmic terms in both the large- and infinite-Péclet-number limits.
The linear stability of boundary-layer flow over compliant walls: effects of boundary-layer growth
Authors: Yeo K. S. , Khoo B. C. , Chong W. K.
Published: April 2006

The linear stability of boundary-layer flow over compliant or flexible surfaces has been studied by Carpenter & Garrad (1985), Yeo (1988) and others on the assumption of local flow parallelism. This assumption is valid at large Reynolds numbers. Non-parallel effects due to growth of the boundary layer gain in significance and importance as one gets to lower Reynolds number. This is especially so for a compliant surface, which can sustain a variety of wall-related instabilities in addition to the Tollmien—Schlichting instabilities (TSI) that are found over rigid surfaces. The present paper investigates the influence of boundary-layer non-parallelism on the TSI and wall-related travelling-wave flutter (TWF) on compliant layers. Corrections to the growth rate of locally parallel theory for boundary-layer non-parallelism are obtained through a multiple-scale analysis. The results indicate that flow non-parallelism has an overall destabilizing influence on the TSI and TWF. Flow non-parallelism is also found to have a very strong destabilizing effect on the branch of TWF that stretches to low Reynolds number. The results obtained have important implications for the design and use of compliant layers at low Reynolds numbers.
Nonlinear compressible magnetoconvection Part 2. Streaming instabilities in two dimensions
Authors: Proctor M. R. E. , Weiss N. O. , Brownjohn D. P. , Hurlburt N. E.
Published: April 2006

We have conducted further numerical experiments on two-dimensional fully compressible convection in an imposed vertical magnetic field and interpreted the results by reference to appropriate low-order models. Here we focus on streaming instabilities, involving horizontal shear flows, which form an important mechanism for the breakdown of steady convection in relatively weak fields for boxes of sufficiently small aspect ratio. While these shearing modes can arise even in the absence of a field, they will typically lead only to travelling and modulated waves unless there is a field to provide a restoring force. For magnetoconvection a new and dramatic form of pulsating wave appears after a complex sequence of secondary bifurcations.
Dissolving driven by vigorous compositional convection
Authors: Kerr Ross C.
Published: April 2006

The one-dimensional dissolution that occurs when a binary melt is placed above or below a solid of a different composition is examined both theoretically and experimentally. In the case considered, the dissolution is driven by vigorous compositional convection that results from a Rayleigh-Bénard instability of the compositional boundary layer in the vicinity of the dissolving solid. A scaling analysis is used to derive theoretical expressions for both the dissolving velocity and the interfacial fluid concentration. Laboratory experiments are also described in which ice is dissolved when it is overlain or underlain by aqueous solutions. The measured dissolving velocities are consistent with the theoretical expressions, and yield estimates of the critical Rayleigh number for boundary-layer instability. The results of this study are then applied to predict the rate at which dissolution will occur when undersaturated mixed magmas are generated during the periodic replenishment of large basaltic magma chambers in the Earth's crust.
The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water
Authors: Ford Rupert
Published: April 2006

The stability of an axisymmetric vortex with a single radial discontinuity in potential vorticity is investigated in rotating shallow water. It is shown analytically that the vortex is always unstable, using the WKBJ method for instabilities with large azimuthal mode number. The analysis reveals that the instability is of mixed type, involving the interaction of a Rossby wave on the boundary of the vortex and a gravity wave beyond the sonic radius. Numerically, it is demonstrated that the growth rate of the instability is generally small, except when the potential vorticity in the vortex is the opposite sign to the background value, in which case it is shown that inertial instability is likely to be stronger than the present instability.
Topographic Hadley cells
Authors: Condie S. A. , Rhines P. B.
Published: April 2006

When a rotating fluid over sloping topography is heated from below and/or cooled from above, horizontal temperature gradients develop which drive convection cells aligned with isobaths. We refer to these cells as topographic Hadley cells. Laboratory experiments reveal that sinking occurs in small cyclonic vortices situated in relatively shallow regions. This is balanced by slower upwelling in adjacent deeper regions. The cross-isobath motions which connect the upwelling and downwelling are accelerated by Coriolis forces, resulting in strong jets which follow isobathic contours. For anticlockwise rotation, the surface jets keep the shallows to their left when looking in the direction of flow, which is opposite to both Kelvin and Rossby wave propagation. The width of the jets scales with the Rossby deformation radius and if this is much less than the width of the slope region then a number of parallel jets form. Motions on the deeper side of the jets where the flow is accelerating are adequately described by linear inviscid theory. However, the strong shears generated by this acceleration lead to baroclinic instability. The resulting cross-stream momentum fluxes broaden and flatten the velocity profile, allowing the flow on the shallow side of the jet to decelerate smoothly before sinking. Topographic Hadley cells are dynamically similar to terrestrial atmospheric Hadley cells and may also be relevant to the zonal jet motions observed on Jupiter and Saturn. It is also suggested that in coastal seas they may represent an important mode of heat (or salt) transfer where surface cooling (or evaporation) drives convection.
Equilibrium dynamics in a forced-dissipative f-plane shallow-water system
Authors: Yuan Li , Hamilton Kevin
Published: April 2006

The equilibrium dynamics in a homogeneous forced-dissipative f-plane shallow-water system is investigated through numerical simulations. In addition to classical two-dimensional turbulence, inertio-gravity waves also exist in this system. The dynamics is examined by decomposing the full flow field into a dynamically balanced potential-vortical component and a residual ‘free’ component. Here the potential-vortical component is defined as part of the flow that satisfies the gradient-wind balance equation and that contains all the linear potential vorticity of the system. The residual component is found to behave very nearly as linear inertio-gravity waves. The forcing employed is a mass and momentum source balanced so that only the large-scale potential-vortical component modes are directly excited. The dissipation is provided by a linear relaxation applied to the large scales and by an eighth-order linear hyperdiffusion. The statistical properties of the potential-vortical component in the fully developed flow were found to be very similar to those of classical two-dimensional turbulence. In particular, the energy spectrum of the potential-vortical component at scales smaller than the forcing is close to the ∼ k−3 expected for a purely two-dimensional system. Detailed analysis shows that the downscale enstrophy cascade into any wavenumber is dominated by very elongated triads involving interactions with large scales. Although not directly forced, a substantial amount of energy is found in the inertio-gravity modes and interactions among inertio-gravity modes are principally responsible for transferring energy to the small scales. The contribution of the inertio-gravity modes to the flow leads to a shallow tail at the high-wavenumber end of the total energy spectrum. For parameters roughly appropriate for the midlatitude atmosphere (notably Rossby number ∼ 0.5), the break between the roughly ∼ k−3 regime and this shallower regime occurs at scales of a few hundred km. This is similar to the observed mesoscale regime in the atmosphere. The nonlinear interactions among the inertio-gravity modes are extremely broadband in spectral space. The implications of this result for the subgrid-scale closure in the shallow-water model are discussed.
Realizability of second-moment closure via stochastic analysis
Authors: Durbin P. A. , Speziale C. G.
Published: April 2006

It is shown that realizability of second-moment turbulence closure models can be established by finding a Langevin equation for which they are exact. All closure models currently in use can be derived formally from the type of Langevin equation described herein. Under certain circumstances a coefficient in that formalism becomes imaginary. The regime in which models are realizable is, at least, that for which the coefficient is real. The present method does not imply unrealizable solutions when the coefficient is imaginary, but it does guarantee realizability when the coefficient is real; hence, this method provides sufficient, but not necessary, conditions for realizability. Illustrative computations of homogeneous shear flow are presented. It is explained how models can be modified to guarantee realizability in extreme non-equilibrium situations without altering their behaviour in the near-equilibrium regime for which they were formulated.
Direct numerical simulation of H2/O2/N2 flames with complex chemistry in two-dimensional turbulent flows
Authors: Baum M. , Poinsot T. J. , Haworth D. C. , Darabiha N.
Published: April 2006

Premixed H2/O2/N2 flames propagating in two-dimensional turbulence have been studied using direct numerical simulations (DNS: simulations in which all fluid and thermochemical scales are fully resolved). Simulations include realistic chemical kinetics and molecular transport over a range of equivalence ratios Φ (Φ = 0.35, 0.5, 0.7, 1.0, 1.3). The validity of the flamelet assumption for premixed turbulent flames is checked by comparing DNS data and results obtained for steady strained premixed flames with the same chemistry (flamelet ‘library’). This comparison shows that flamelet libraries overestimate the influence of stretch on flame structure. Results are also compared with earlier zero-chemistry (flame sheet) and one-step chemistry simulations. Consistent with the simpler models, the turbulent flame with realistic chemistry aligns preferentially with extensive strain rates in the tangent plane and flame curvature probability density functions are close to symmetric with near-zero means. For very lean flames it is also found that the local flame structure correlates with curvature as predicted by DNS based on simple chemistry. However, for richer flames, by contrast to simple-chemistry results with non-unity Lewis numbers (ratio of thermal to species diffusivity), local flame structure does not correlate with curvature but rather with tangential strain rate. Turbulent straining results in substantial thinning of the flame relative to the steady unstrained laminar case. Heat-release and H2O2 contours remain thin and connected (‘flamelet-like’) while species including H-atom and OH are more diffuse. Peak OH concentration occurs well behind the peak heat-release zone when the flame temperature is high (of the order of 2800 K). For cooler and leaner flames (about 1600 K and for an equivalence ratio below 0.5) the OH radical is concentrated near the reaction zone and the maximum OH level provides an estimate of the local flamelet speed as assumed by Becker et al. (1990).
The effects of thermal conditions on the cell sizes of two-dimensional convection
Authors: Ishiwatari Masaki , Takehiro Shin-Ichi , Hayashi Yoshi-Yuki
Published: April 2006

The effects of thermal conditions on the patterns of two-dimensional Boussinesq convection are studied by numerical integration. The adopted thermal conditions are (i) the heat fluxes through both upper and lower boundaries are fixed, (ii) the same as (i) but with internal cooling, (iii) the temperature on the lower boundary and the heat flux through the upper boundary are fixed, (iv) the same as (iii) but with internal cooling, and (v) the temperatures on both upper and lower boundaries are fixed. The numerical integrations are performed with Ra = 104 and Pr = 1 over the region whose horizontal and vertical lengths are 8 and 1, respectively.

The results confirm that convective cells with the larger horizontal sizes tend to form under the conditions where the temperature is not fixed on any boundaries. Regardless of the existence of internal cooling, one pair of cells spreading all over the region forms in the equilibrium states. On the other hand, three pairs of cells form and remain when the temperature on at least one boundary is fixed. The formation of single pairs of cells appearing under the fixed heat flux conditions shows different features with and without internal cooling. The difference emerges as the appearance of a phase change, whose existence can be suggested by the weak nonlinear equation derived by Chapman & Proctor (1980).
Self-diffusion of bimodal suspensions of hydrodynamically interacting spherical particles in shearing flow
Authors: Chang Chingyi , Powell Robert L.
Published: April 2006

We study the average mobilities and long-time self-diffusion coefficients of a suspension of bimodally distributed spherical particles. Stokesian dynamics is used to calculate the particle trajectories for a monolayer of bimodal-sized spheres. Hydrodynamic forces only are considered and they are calculated using the inverse of the grand mobility matrix for far-field many-body interactions and lubrication formulae for near-field effects. We determine both the detailed microstructure (e.g. the pair-connectedness function and cluster formation) and the macroscopic properties (e.g. viscosity and self-diffusion coefficients). The flow of an ‘infinite’ suspension is simulated by considering 25, 49, 64 and 100 particles to be one ‘cell’ of a periodic array. Effects of both the size ratio and the relative fractions of the different-sized particles are examined. For the microstructures, the pair-connectedness function shows that the particles form clusters in simple shearing flow due to lubrication forces. The nearly symmetric angular structures imply the absence of normal stress differences for a suspension with purely hydrodynamic interactions between spheres. For average mobilities at infinite Péclet number, Ds0, our simulation results suggest that the reduction of Ds0 as concentration increases is directly linked to the influence of particle size distribution on the average cluster size. For long-time self-diffusion coefficients, Ds∞, we found good agreement between simulation and experiment (Leighton & Acrovos 1987 a; Phan and Leighton 1993) for monodispersed suspensions. For bimodal suspensions, the magnitude of Ds∞, and the time to reach the asymptotic diffusive behaviour depend on the cluster size formed in the system, or the viscosity of the suspension. We also consider the effect of the initial configuration by letting the spheres be both organized (size segregated) and randomly placed. We find that it takes a longer time for a suspension with an initially organized structure to achieve steady state than one with a random structure.