bluuebunny/crossref_metadata_2025 huggingface dataset:
The linear stability of channel flow of fluid with temperature-dependent viscosity
Authors: Wall D. P. , Wilson S. K.
Published: April 2006

The classical fourth-order Orr-Sommerfeld problem which arises from the study of the linear stability of channel flow of a viscous fluid is generalized to include the effects of a temperature-dependent fluid viscosity and heating of the channel walls. The resulting sixth-order eigenvalue problem is solved numerically using high-order finite-difference methods for four different viscosity models. It is found that temperature effects can have a significant influence on the stability of the flow. For all the viscosity models considered a non-uniform increase of the viscosity in the channel always stabilizes the flow whereas a non-uniform decrease of the viscosity in the channel may either destabilize or, more unexpectedly, stabilize the flow. In all the cases investigated the stability of the flow is found to be only weakly dependent on the value of the Péclet number. We discuss our results in terms of three physical effects, namely bulk effects, velocity-profile shape effects and thin-layer effects.
Rossby wave interaction in a shear flow with critical levels
Authors: Vanneste Jacques
Published: April 2006

An approach is presented for studying Rossby wave interaction in a shear flow with both regular and singular modes (i.e. those possessing a critical level). The approach relies on a truncated normal mode expansion of the equations of motion. Such an expansion remains valid in the presence of singular modes, provided that these modes are not considered individually, but that complete packets are taken into account in the truncated system. Mathematically, this means that the interaction equations need to be integrated with respect to the phase velocity (or, equivalently, the critical level position) of the singular modes.

The action of two regular modes on a packet of singular modes is treated in detail; in particular, asymptotic results are deduced for the long-term behaviour of the packet. The case of a linear shear is considered as an illustration: analytical expressions are derived for the normal modes and their pseudomomentum, and they are used to present explicit results for the evolution of the packet of singular modes.
Numerical simulations of uniformly stratified fluid flow over topography
Authors: Rottman James W. , Broutman Dave , Grimshaw Roger
Published: April 2006

We use a high-resolution spectral numerical scheme to solve the two-dimensional equations of motion for the flow of a uniformly stratified Boussinesq fluid over isolated bottom topography in a channel of finite depth. The focus is on topography of small to moderate amplitude and slope and for conditions such that the flow is near linear resonance of either of the first two internal wave modes. The results are compared with existing inviscid theories: the steady hydrostatic analysis of Long (1955), time-dependent linear long-wave theory, and the fully nonlinear, weakly dispersive resonant theory of Grimshaw & Yi (1991). For the latter, we use a spectral numerical technique, with improved accuracy over previously used methods, to solve the approximate evolution equation for the amplitude of the resonant mode. Also, we present some new results on the modal similarity of the solutions of Long and of Grimshaw & Yi. For flow conditions close to linear resonance, solutions of Grimshaw & Yi's evolution equation compare very well with our fully nonlinear numerical solutions, except for very steep topography. For flow conditions between the first two resonances, Long's steady solution is approached asymptotically in time when the slope of the topography is sufficiently small. For steeper topography, the flow remains unsteady. This unsteadiness is manifested very clearly as periodic oscillations in the drag, which have been observed in previous numerical simulations and tow-tank experiments. We explain these oscillations as mainly due to the internal waves that according to linear theory persist longest in the neighbourhood of the topography.
The effect of centreline particle concentration in a wave tube
Authors: Vainshtein P. , Fichman M. , Shuster K. , Gutfinger C.
Published: April 2006

The interaction of sound waves with an aqueous suspension of solid particles was analysed experimentally and theoretically. A heretofore unreported effect of particle concentration in the vicinity of a wave-tube centreline was observed. The phenomenon is related to the combined effect of Rayleigh-type acoustic streaming, jet-like streaming (quartz wind) and drift forces occurring in the presence of a sonic wave in the suspension-filled tube.
Interaction of oblique shock waves and planar mixing regions
Authors: Buttsworth D. R.
Published: April 2006

An analysis for predicting the interaction of a steady oblique shock wave and a planar mixing region is presented. Specifically, an equation for the shock curvature was obtained from the shock wave and isentropic wave difference equations which govern the shock transmission within a region of varying Mach number. The effects of nonuniform gas composition within the mixing region were assessed using a similar treatment; however, the wave equations were expanded in terms of a varying ratio of specific heats instead of a varying Mach number. An expression for the shock-induced vorticity due to velocity and density gradients within the mixing region was also obtained. This expression provides a means of estimating the possible mixing augmentation induced in various shock wave-mixing region interactions. When the velocity and density gradients within the mixing region oppose each other, it is demonstrated that the pre-shock vorticity may be attenuated by the shock. Applications of the analysis are discussed with reference to specific examples involving mixing augmentation and shock oscillation.
Penetration of a blade into a vortex core: vorticity response and unsteady blade forces
Authors: Marshall J. S. , Grant J. R.
Published: April 2006

Numerical calculations are performed for the problem of penetration into a vortex core of a blade travelling normal to the vortex axis, where the plane formed by the blade span and the direction of blade motion coincides with the normal plane of the vortex axis at the point of penetration. The calculations are based on a computational method, applicable for unsteady three-dimensional flow past immersed bodies, in which a collocation solution of the vorticity transport equation is obtained on a set of Lagrangian control points. Differences between this method and other Lagrangian vorticity-based methods in the literature are discussed. Lagrangian methods of this type are particularly attractive for problems of unsteady vortex-body interaction, since control points need only be placed on the surface of the body and in regions of the flow with non-negligible vorticity magnitude. The computations for normal blade-vortex interaction (BVI) are performed for an inviscid fluid and focus on the relationship between the vortex core deformation due to penetration of the blade into the vortex ambient position and the resulting unsteady pressure field and unsteady force acting on the blade. Computations for cases with different vortex circulations are performed, and the accuracy of an approximate formulation using rapid distortion theory is assessed by comparison with the full computational results for unsteady blade force. The force generated from blade penetration into the vortex ambient position is found to be of a comparable magnitude to various other types of unsteady BVI forces, such as that due to cutting of the vortex axial flow.
An experimental study of round jets in cross-flow
Authors: Kelso R. M. , Lim T. T. , Perry A. E.
Published: April 2006

The structure of round jets in cross-flow was studied using flow visualization techniques and flying-hot-wire measurements. The study was restricted to jet to freestream velocity ratios ranging from 2.0 to 6.0 and Reynolds numbers based on the jet diameter and free-stream velocity in the range of 440 to 6200.

Flow visualization studies, together with time-averaged flying-hot-wire measurements in both vertical and horizontal sectional planes, have allowed the mean topological features of the jet in cross-flow to be identified using critical point theory. These features include the horseshoe (or necklace) vortex system originating just upstream of the jet, a separation region inside the pipe upstream of the pipe exit, the roll-up of the jet shear layer which initiates the counter-rotating vortex pair and the separation of the flat-wall boundary layer leading to the formation of the wake vortex system beneath the downstream side of the jet.

The topology of the vortex ring roll-up of the jet shear layer was studied in detail using phase-averaged flying-hot-wire measurements of the velocity field when the roll-up was forced. From these data it is possible to examine the evolution of the shear layer topology. These results are supported by the flow visualization studies which also aid in their interpretation.

The study also shows that, for velocity ratios ranging from 4.0 to 6.0, the unsteady upright vortices in the wake may form by different mechanisms, depending on the Reynolds number. It is found that at high Reynolds numbers, the upright vortex orientation in the wake may change intermittently from one configuration of vortex street to another. Three mechanisms are proposed to explain these observations.
The transitional regime between coalescing and splashing drops
Authors: Rein Martin
Published: April 2006

A drop that falls into a deep liquid can either coalesce with the receiving liquid and form a vortex ring or splash. Which phenomenon actually occurs depends on the impact conditions. When the impact conditions are gradually changed the transition between coalescence and splashing proceeds via a number of intermediate steps. These are studied by means of high-speed photography of the normal impact of water drops on a plane water surface. The characteristics of different flows that appear in the transitional regime and possible mechanisms causing these flows are discussed in detail. The phenomena considered include the rise of thick jets and the ejection of high-rising thin jets out of the impact crater, the entrainment of gas bubbles, crater dynamics, crown formation and the generation of splash droplets. Finally, a classification of the phenomena characteristic of the transitional regime is given.
On inertial-range scaling laws
Authors: Bowman John C.
Published: April 2006

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's k−5/3 scaling is derived for the energy inertial range. A related modification is found to Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at the injection wavenumber. The significance of these corrections is illustrated with steady-state energy spectra from recent high-resolution closure computations. Implications for conventional numerical simulations are discussed. These results underscore the asymptotic nature of inertial-range scaling laws.
One- and two-dimensional travelling wave solutions in gas-fluidized beds
Authors: Glasser B. J. , Kevrekidis I. G. , Sundaresan S.
Published: April 2006

Making use of numerical continuation techniques as well as bifurcation theory, both one- and two-dimensional travelling wave solutions of the ensemble-averaged equations of motion for gas and particles in fluidized beds have been computed. One-dimensional travelling wave solutions having only vertical structure emerge through a Hopf bifurcation of the uniform state and two-dimensional travelling wave solutions are born out of these one-dimensional waves. Fully developed two-dimensional solutions of high amplitude are reminiscent of bubbles. It is found that the qualitative features of the bifurcation diagram are not affected by changes in model parameters or the closures. An examination of the stability of one-dimensional travelling wave solutions to two-dimensional perturbations suggests that two-dimensional solutions emerge through a mechanism which is similar to the overturning instability analysed by Batchelor & Nitsche (1991).
Three-dimensional kinematic dynamos dominated by strong differential rotation
Authors: Sarson Graeme R. , Gubbins David
Published: April 2006

In the kinematic dynamo problem a fluid motion is specified arbitrarily and the induction equation is solved for non-decaying magnetic fields; it forms part of the larger magnetohydrodynamic (MHD) dynamo problem in which the fluid flow is buoyancy-driven. Although somewhat restrictive, the kinematic problem is important for two reasons: first, it suffers from numerical difficulties that are holding up progress on the MHD problem; secondly, for the geodynamo, it is capable of reproducing details of the observable magnetic field. It is more efficient to study these two aspects for the kinematic dynamo than for the full MHD dynamo. We explore solutions for a family of fluid flows in a sphere, first studied by Kumar & Roberts (1975), that is heuristically representative of convection in a rotating sphere such as the Earth's core. We guard against numerical difficulties by comparing our results with well-understood solutions from the axisymmetric (αω) limit of Braginskii (1964a) and with solutions of the adjoint problem, which must yield identical eigenvalues in an adequate numerical treatment. Previous work has found a range of steady dipolar solutions; here we extend these results and find solutions of other symmetries, notably oscillatory and quadrupolar fields. The surface magnetic fields, important for comparison with observations, have magnetic flux concentrated by downwelling flow. Roberts (1972) found that meridional circulation promoted stationary solutions of the αω-equations, preferred solutions being oscillatory when no such circulation was present. We find analogous results for the full three-dimensional problem, but note that in the latter case the ‘effective’ meridional circulation arising from the non-axisymmetric convection (a concept made precise in the asymptotic limit of Braginskii 1964a) must be considered. Thus stationary solutions are obtained even in the absence of ‘true’ meridional circulation, and the time-dependence can be controlled by the strength of the convection as well as by the meridional circulation. The preference for fields of dipole or quadrupole parity is largely controlled by the sign of the velocity: a reversal of velocity from a case favouring a dipole will favour quadrupole parity, and vice versa. For the comparison problem of Proctor (1977b) this symmetry is exact; for the physical problem the boundary conditions make a difference. The boundary effect is first removed by surrounding the dynamo region with a thick layer of quiescent conducting fluid, and then studied numerically by progressively reducing the thickness of this layer to zero. The insulating boundary contributes to the difficulty of obtaining dynamo action, and to the numerical difficulties encountered. The effect of an inner boundary on dynamo action is also considered, but found to be slight.
The effect of free-stream turbulence on sectional lift forces on a circular cylinder
Authors: Blackburn H. M. , Melbourne W. H.
Published: April 2006

Wind-tunnel experiments were conducted to examine the effect of grid-generated turbulence on lift forces at sections of a circular cylinder. Turbulence of longitudinal intensity between 0.6% and 18% was employed, with cylinder Reynolds numbers in the range 1 × 105to 5 × 105. Addition of low-intensity turbulence had the primary effect of inducing the critical transition at Reynolds numbers below that for smooth flow; above transition there was little difference between the forces experienced by the cylinder in smooth or turbulent flow, with no sign of organized vortex shedding.

At higher turbulence intensities effects consistent with a return to organized vortex shedding were observed, particularly for the highest intensity and at the upper end of the Reynolds number range; lift coefficients were greater than in smooth supercritical flow, with a broad spectral peak centred near a Strouhal number of 0.23 accompanied by an increase in spanwise correlation lengths of lift force.
Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers
Authors: Borue Vadim , Orszag Steven A.
Published: April 2006

High-resolution numerical simulations (with up to 2563 modes) are performed for three-dimensional flow driven by the large-scale constant force fy = F cos(x) in a periodic box of size L = 2π (Kolmogorov flow). High Reynolds number is attained by solving the Navier-Stokes equations with hyperviscosity (-1)h+1Δh (h = 8). It is shown that the mean velocity profile of Kolmogorov flow is nearly independent of Reynolds number and has the ‘laminar’ form vy = V cos(x) with a nearly constant eddy viscosity. Nevertheless, the flow is highly turbulent and intermittent even at large scales. The turbulent intensities, energy dissipation rate and various terms in the energy balance equation have the simple coordinate dependence a + b cos(2x) (with a, b constants). This makes Kolmogorov flow a good model to explore the applicability of turbulence transport approximations in open time-dependent flows. It turns out that the standard expression for effective (eddy) viscosity used in K-[Escr ] transport models overpredicts the effective viscosity in regions of high shear rate and should be modified to account for the non-equilibrium character of the flow. Also at large scales the flow is anisotropic but for large Reynolds number the flow is isotropic at small scales. The important problem of local isotropy is systematically studied by measuring longitudinal and transverse components of the energy spectra and crosscorrelation spectra of velocities and velocity-pressure-gradient spectra. Cross-spectra which should vanish in the case of isotropic turbulence decay only algebraically but somewhat faster than corresponding isotropic correlations. It is verified that the pressure plays a crucial role in making the flow locally isotropic. It is demonstrated that anisotropic large-scale flow may be considered locally isotropic at scales which are approximately ten times smaller than the scale of the flow.
Surface manifestations of turbulent flow
Authors: Longuet-Higgins Michael S.
Published: April 2006

The surface of a turbulent, open-channel flow is often characterized by smooth areas of upwelling, each surrounded by a zone of downwelling marked by short steep waves. The dynamics of short waves on such a downwelling region are investigated and some laboratory experiments are proposed. Assuming that the horizontal strain rate Ω is locally constant, a simple expression is derived for the amplitude a of the short capillary–gravity waves, and hence also for the spectrum of the surface slopes.
The effect of counterflow on the development of compressible shear layers
Authors: Strykowski P. J. , Krothapalli A. , Jendoubi S.
Published: April 2006

A compressible countercurrent shear layer was investigated experimentally by establishing reverse flow around the perimeter of a supersonic jet. Measurements demonstrate that spatial growth rates of the countercurrent shear layer significantly exceed those of the classical coflowing layer at comparable density ratios and levels of compressibility. Experiments also reveal the presence of coherent three-dimensional structures in the countercurrent shear layer at convective Mach numbers where similar structures are not present in coflowing layers. It is argued that these kinematic differences are responsible for the enhanced diffusion of the shear layer with counterflow. The spatio-temporal theory is used to examine the connection between the experimental observations and the existence of a transition from convective to absolute instability in high-speed shear layers.
Symmetrical flow past an accelerated circular cylinder
Authors: Badr H. M. , Dennis S. C. R. , Kocabiyik S.
Published: April 2006

The development of the two-dimensional flow of a viscous incompressible fluid around a circular cylinder which suddenly starts to move with the velocity U = U0 + U1t + U2t2 is studied. Equations for the flow in terms of the stream function and vorticity in boundary-layer coordinates are presented. A perturbation series solution for small times is developed. The flow for longer times is computed numerically using an accurate implicit time-integration procedure. The numerical method is checked for small times by comparison with the results of the analytical solution. Reynolds numbers R in the range 200 to 104 (based on the diameter of the cylinder) are considered. One particularly interesting result is that for certain values of U1 and U2 at R = 500 and R = 103 it is found that two co-rotating vortices and three co-rotating vortices develop with time in each half of the wake in the two respective cases.
Measurements of scalar power spectra in high Schmidt number turbulent jets
Authors: Miller Paul L. , Dimotakis Paul E.
Published: April 2006

We report on an experimental investigation of temporal, scalar power spectra of round, high Schmidt number (Sc ≃ 1.9 × 103), momentum-dominated turbulent jets, for jet Reynolds numbers in the range of 1.25 × 104 ≤ Re ≤ 7.2 × 104. At intermediate scales, we find a spectrum with a slope (logarithmic derivative) that increases in absolute value with Reynolds number, but remains less than 5/3 at the highest Reynolds number in our experiments. At the smallest scales, our spectra exhibit no k−1 power-law behaviour, but, rather, seem to be approximated by a log-normal function, over a range of scales exceeding a factor of 40, in some cases.
Finite-amplitude effects on steady lee-wave patterns in subcritical stratified flow over topography
Authors: Yang T.-S. , Akylas T. R.
Published: April 2006

The flow of a continuously stratified fluid over a smooth bottom bump in a channel of finite depth is considered. In the weakly nonlinear-weakly dispersive régime ε = a/h [Lt ] 1, μ = h/l [Lt ] 1 (where h is the channel depth and a, l are the peak amplitude and the width of the obstacle respectively), the parameter A = ε/μp (where p < 0 depends on the obstacle shape) controls the effect of nonlinearity on the steady lee wavetrain that forms downstream of the obstacle for subcritical flow speeds. For A = O(1), when nonlinear and dispersive effects are equally important, the interaction of the long-wave disturbance over the obstacle with the lee wave is fully nonlinear, and techniques of asymptotics ‘beyond all orders’ are used to determine the (exponentially small as μ → 0) lee-wave amplitude. Comparison with numerical results indicates that the asymptotic theory often remains reasonably accurate even for moderately small values of μ and ε, in which case the (formally exponentially small) lee-wave amplitude is greatly enhanced by nonlinearity and can be quite substantial. Moreover, these findings reveal that the range of validity of the classical linear lee-wave theory (A [Lt ] 1) is rather limited.
Permeability of three-dimensional models of fibrous porous media
Authors: Higdon J. J. L. , Ford G. D.
Published: April 2006

Viscous flow through three-dimensional models of fibrous porous media is analysed. The periodic models are based on ordered networks of cylindrical fibres on regular cubic lattices. Numerical solutions are obtained using the spectral boundary element method introduced by Muldowney & Higdon (1995). Results are presented for solid volume fractions ranging from extreme dilution to near the maximum volume fraction for permeable media. Theoretical estimates are derived using slender-body theory and lubrication approximations in the appropriate asymptotic regimes. Comparisons are made with model predictions based on properties of two-dimensional media (Jackson & James 1986), and with results for disordered dispersions of prolate spheroids (Claeys & Brady 1993b).
Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 1. Velocity field
Authors: Wang Lian-Ping , Chen Shiyi , Brasseur James G. , Wyngaard John C.
Published: April 2006

The fundamental hypotheses underlying Kolmogorov-Oboukhov (1962) turbulence theory (K62) are examined directly and quantitutivezy by using high-resolution numerical turbulence fields. With the use of massively parallel Connection Machine-5, we have performed direct Navier-Stokes simulations (DNS) at 5123 resolution with Taylor microscale Reynolds number up to 195. Three very different types of flow are considered: free-decaying turbulence, stationary turbulence forced at a few large scales, and a 2563 large-eddy simulation (LES) flow field. Both the forced DNS and LES flow fields show realistic inertial-subrange dynamics. The Kolmogorov constant for the k−5/3 energy spectrum obtained from the 5123 DNS flow is 1.68 ±.15. The probability distribution of the locally averaged disspation rate εr, over a length scale r is nearly log-normal in the inertial subrange, but significant departures are observed for high-order moments. The intermittency parameter p, appearing in Kolmogorov's third hypothesis for the variance of the logarithmic dissipation, is found to be in the range of 0.20 to 0.28. The scaling exponents over both εr, and r for the conditionally averaged velocity increments $\overline{\delta_ru|\epsilon_r}$ are quantified, and the direction of their variations conforms with the refined similarity theory. The dimensionless averaged velocity increments $(\overline{\delta_ru^n|\epsilon_r})/(\epsilon_rr)^{n/3}$ are found to depend on the local Reynolds number Reεr = ε1/3rr4/3/ν in a manner consistent with the refined similarity hypotheses. In the inertial subrange, the probability distribution of δru/(εrr)1/3 is found to be universal. Because the local Reynolds number of K62, Rεr = ε1/3rr4/3/ν, spans a finite range at a given scale r as compared to a single value for the local Reynolds number Rr = ε−1/3r4/3/ν in Kolmogorov's (1941a,b) original theory (K41), the inertial range in the K62 context can be better realized than that in K41 for a given turbulence field at moderate Taylor microscale (global) Reynolds number Rλ. Consequently universal constants in the second refined similarity hypothesis can be determined quite accurately, showing a faster-than-exponential growth of the constants with order n. Finally, some consideration is given to the use of pseudo-dissipation in the context of the K62 theory where it is found that the probability distribution of locally averaged pseudo-dissipation ε′r deviates more from a log-normal model than the full dissipation εr. The velocity increments conditioned on ε′r do not follow the refined similarity hypotheses to the same degree as those conditioned on εr.
An experimental and theoretical study of the turbulent coflowing jet
Authors: Nickels T. B. , Perry A. E.
Published: April 2006

Experiments carried out recently on a family of axisymmetric coflowing turbulent jets with different nozzle to free-stream velocity ratios are described. Special care was taken to ensure top-hat velocity profiles at the nozzle exit so as to reduce the number of parameters associated with the initial conditions. This results in a collapse of the data without the need to introduce different effective origins for the streamwise coordinate. The mean flow behaviour is compared to self-preserving asymptotic forms and stresses are also examined to investigate the possibility of self-preservation. Comparisons are made with measurements of other workers in coflowing jets and axisymmetric wakes. Further information on the structure of the coflowing jet is found by examining the spectral Reynolds shear stress correlation coefficient, the premultiplied spectra and the high-wavenumber forms of the spectra. An analysis was carried out to see if the mean flow, Reynolds stress distributions and spectra are consistent with an inviscid ‘double-roller’ vortex structure for the representative large-scale energy-containing motions. Results show support for such a model.
The behaviour of a gas cavity impacted by a weak or strong shock wave
Authors: Ding Zhong , Gracewski S. M.
Published: April 2006

Two-dimensional simulations of gas cavity responses to both weak shocks (p≤ 30 MPa) and strong shocks (pranging from 500 to 2000 MPa) are performed using a finite volume method. An artificial viscosity to capture the shock and a simple, stable, and adaptive mesh generation technique have been developed for the computations. The details of the shock propagation, rarefaction, transmission and bubble wall motions are obtained from the numerical computations. A weak shock is defined in the present context as one that does not cause liquid jet formation upon impact with the bubble. For this case, a large pressure is created within the gas upon collapse due to rapid compression of the gas, ultimately causing the re-expansion of the bubble. The bubble collapse and re-expansion time predicted by this model agree well with spherically symmetric computations. When impacted by strong shock waves, the bubble will collapse and a liquid jet is formed that propagates through the bubble to the opposite bubble wall. Jet speeds as high as 2000 m s−1are predicted by this model.
Shear-induced dispersion in a dilute suspension of rough spheres
Authors: Da Cunha F. R. , Hinch E. J.
Published: April 2006

In the absence of Brownian motion, inertia and inter-particle forces, two smooth spheres collide in a simple shear flow in a reversible way returning to their initial streamlines. Because the minimum separation during the collision can be less than 10−4 of the radius, quite a small surface roughness can have a significant irreversible effect on the collision. We calculate the change between the initial and final streamlines caused by roughness. Repeated random collisions in a dilute suspension lead to a diffusion of the particles across the streamlines. We calculate the shear-induced diffusivity for both self-diffusion and down-gradient diffusion.
On the dynamics of multi-dimensional detonation
Authors: Yao Jin , Stewart D. Scott
Published: April 2006

We present an asymptotic theory for the dynamics of detonation when the radius of curvature of the detonation shock is large compared to the one-dimensional, steady, Chapman-Jouguet (CJ) detonation reaction-zone thickness. The analysis considers additional time-dependence in the slowly varying reaction zone to that considered ill previous works. The detonation is assumed to have a sonic point in the reaction- zone structure behind the shock, and is referred to as an eigenvalue detonation. A new, iterative method is used to calculate the eigenvalue relation, which ultimately is expressed as an intrinsic, partial differential equation (PDE) for the motion of the shock surface. Two cases are considered for an ideal equation of state. The first corresponds to a model of a condensed-phase explosive, with modest reaction rate sensitivity, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity, Dn, the first normal time derivative of the normal shock velocity, Dn, and the shock curvature, K. The second case corresponds to a gaseous explosive mixture, with the large reaction rate sensitivity of Arrhenius kinetics, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity, Dn, its first and second normal time derivatives of the normal shock velocity, Dn, Dn, and the shock curvature, K, and its first normal time derivative of the curvature, k. For the second case, one obtains a one-dimensional theory of pulsations of plane CJ detonation and a theory that predicts the evolution of self-sustained cellular detonation. Versions of the theory include the limits of near-CJ detonation, and when the normal detonation velocity is significantly below its CJ value. The curvature of the detonation can also be of either sign, corresponding to both diverging and converging geometries.
A laboratory simulation of mixing across tidal fronts
Authors: Thomas P. J. , Linden P. F.
Published: April 2006

A laboratory study which simulates the dynamics of shallow sea fronts and the mixing across a tidal front is described. The experiments show, for the first time, that it is possible to simulate a stationary tidal front with the inclusion of buoyancy effects, Coriolis effects and turbulence in the laboratory. Experimental data obtained for the cross-front mixing rate are presented. The data analysis shows that the mixing rate increases with stratification and decreases with rotation. A theoretical model of the flow which collapses the experimental data is developed which shows that the cross-front mixing is controlled by baroclinic processes. The model enables an extrapolation of the laboratory results to oceanographic conditions. Estimates of the cross-front mixing velocity for oceanographic conditions give values consistent with estimates obtained from North Sea data.
Averaging of unsteady flows in heterogeneous media of stationary conductivity
Authors: Indelman Peter
Published: April 2006

A procedure for deriving equations of average unsteady flows in random media of stationary conductivity is developed. The approach is based on applying perturbation methods in the Fourier-Laplace domain. The main result of the paper is the formulation of an effective Darcy's Law relating the mean velocity to the mean head gradient. In the Fourier-Laplace domain the averaged Darcy's Law is given by a linear local relation. The coefficient of proportionality depends only on the heterogeneity structure and is called the effective conductivity tensor. In the physical domain this relation has a non-local structure and it defines the effective conductivity as an integral operator of convolution type in time and space. The mean head satisfies an unsteady integral-differential equation. The kernel of the integral operator is the inverse Fourier-Laplace transform (FLT) of the effective conductivity tensor. The FLT of the mean head is obtained as a product of two functions: the first describes the FLT of the mean head distribution in a homogeneous medium; the second corrects the solution in a homogeneous medium for the given spatial distribution of heterogeneities. This function is simply related to the effective conductivity tensor and determines the fundamental solution of the governing equation for the mean head. These general results are applied to derive the effective conductivity tensor for small variances of the conductivity. The properties of unsteady average flows in isotropic media are studied by analysing a general structure of the effective Darcy's Law. It is shown that the transverse component of the effective conductivity tensor does not affect the mean flow characteristics. The effective Darcy's Law is obtained as a convolution integral operator whose kernel is the inverse FLT of the effective conductivity longitudinal component. The results of the analysis are illustrated by calculating the effective conductivity for one-, two- and three-dimensional flows. An asymptotic model of the effective Darcy's Law, applicable for distances from the sources of mean flow non-uniformity much larger than the characteristic scale of heterogeneity, is developed. New bounds for the effective conductivity tensor, namely the effective conductivity tensor for steady non-uniform average flow and the arithmetic mean, are proved for weakly heterogeneous media.
Unsteady tube flow over an expansion
Authors: Pedrizzetti Gianni
Published: April 2006

Unsteady flow in a circular conduit with a smooth expansion is studied in detail by numerical integration of the equation of motion in the axisymmetric approximation. The values of governing parameters are chosen to be relevant to medical problems, and the geometry corresponds to a scenario of post-surgical conditions. The flow determined by an oscillatory volume is characterized by a sequence of vortex rings moving in the expanded part of the tube. The development of wall shear stress is governed by the separated translating vorticity which induces an evolving band of large intensity for about a complete oscillation cycle. This influences the dynamics of unsteady separation whose space-time development has revealed features of some generality which have been classified. The time variation of the pressure jump is dominated by inertial effects. The dependence of the details of the flow on the dimensionless parameters has been investigated systematically. The results obtained here have been compared with experimental and numerical studies of similar problems, similarities have been pointed out and differences discussed. Finally, the relevance of these results to physiological applications has been quantified by simulating the flow induced by a pulsatile flow rate.
Unsteady transonic nozzle flow of dense gases
Authors: Kluwick A. , Scheichl St.
Published: April 2006

Vapours of retrograde fluids, i.e. media with large values of the specific heats, may have the remarkable property that sonic conditions are reached three times rather than once during isentropic expansion or compression. As a result, the acceleration of such a fluid through a converging-diverging Laval nozzle under steady flow conditions may lead to the occurrence of an expansion shock discontinuity. Theoretical considerations then suggest that nozzles with two throats should be designed to achieve a full shock-free subsonic-supersonic expansion.

In this study the unsteady flow of a dense, retrograde gas through slender nozzles (with one and two throats) is considered. The combination of the Navier-Stokes equations supplemented with a non-classical equation of state for the fluid yields a generalized wave equation, with its validity restricted to flow conditions near the critical value M = 1. This equation is used to study the transition process which sets in if a steady subsonic solution is perturbed by lowering the pressure at the end of the nozzle.
Rayleigh number scaling in numerical convection
Authors: Kerr Robert M.
Published: April 2006

Using direct simulations of the incompressible Navier-Stokes equations with rigid upper and lower boundaries at fixed temperature and periodic sidewalls, scaling with respect to Rayleigh number is determined. At large aspect ratio (6:6:1) on meshes up to 288 × 288 × 96, a single scaling regime consistent with the properties of ‘hard’ convective turbulence is found for Pr = 0.7 between Ra = 5 × 104 and Ra = 2 × 107. The properties of this regime include Nu ∼ RaβT with βT = 0.28 ≈ 2/7, exponential temperature distributions in the centre of the cell, and velocity and temperature scales consistent with experimental measurements. Two velocity boundary-layer thicknesses are identified, one outside the thermal boundary layer that scales as Ra−1/7 and the other within it that scales as Ra−3/7. Large-scale shears are not observed; instead, strong local boundary-layer shears are observed in regions between incoming plumes and an outgoing network of buoyant sheets. At the highest Rayleigh number, there is a decade where the energy spectra are close to k−5/3 and temperature variance spectra are noticeably less steep. It is argued that taken together this is good evidence for ‘hard’ turbulence, even if individually each of these properties might have alternative explanations.
Entrainment in a shear-free turbulent mixing layer
Authors: Briggs D. A. , Ferziger J. H. , Koseff J. R. , Monismith S. G.
Published: April 2006

Results from a direct numerical simulation of a shear-free turbulent mixing layer are presented. The mixing mechanisms associated with the turbulence are isolated. In the first set of simulations, the turbulent mixing layer decays as energy is exchanged between the layers. Energy spectra with E(k) ∼ k2 and E(k) ∼ k4 dependence at low wavenumber are used to initialize the flow to investigate the effect of initial conditions. The intermittency of the mixing layer is quantified by the skewness and kurtosis of the velocity fields: results compare well with the shearless mixing layer experiments of Veeravalli & Warhaft (1989). Eddies of size of the integral scale (k3/2/∈) penetrate the mixing layer intermittently, transporting energy and causing the layer to grow. The turbulence in the mixing layer can be characterized by eddies with relatively large vertical kinetic energy and vertical length scale. In the second set of simulations, a forced mixing layer is created by continuously supplying energy in a local region to maintain a stationary kinetic energy profile. Assuming the spatial decay of r.m.s. velocity is of the form u &∞ yn, predictions of common two-equation turbulence models yield values of n ranging from -1.25 to -2.5. An exponent of -1.35 is calculated from the forced mixing layer simulation. In comparison, oscillating grid experiments yield decay exponents between n = -1 (Hannoun et al. 1989) and n = -1.5 (Nokes 1988). Reynolds numbers of 40 and 58, based on Taylor microscale, are obtained in the decaying and forced simulations, respectively. Components of the turbulence models proposed by Mellor & Yamada (1986) and Hanjalić & Launder (1972) are analysed. Although the isotropic models underpredict the turbulence transport, more complicated anisotropic models do not represent a significant improvement. Models for the pressure-strain tensor, based on the anisotropy tensor, performed adequately.
Boundary-layer receptivity for a parabolic leading edge
Authors: Hammerton P. W. , Kerschen E. J.
Published: April 2006

The effect of the nose radius of a body on boundary-layer receptivity is analysed for the case of a symmetric mean flow past a body with a parabolic leading edge. Asymptotic methods based on large Reynolds number are used, supplemented by numerical results. The Mach number is assumed small, and acoustic free-stream disturbances are considered. The case of free-stream acoustic waves, propagating obliquely to the symmetric mean flow is considered. The body nose radius,rn, enters the theory through a Strouhal number,S= ωrn/U, where ω is the frequency of the acoustic wave andUis the mean flow speed. The finite nose radius dramatically reduces the receptivity level compared to that for a flat plate, the amplitude of the instability waves in the boundary layer being decreased by an order of magnitude whenS= 0.3. Oblique acoustic waves produce much higher receptivity levels than acoustic waves propagating parallel to the body chord.
Symmetry-breaking bifurcations in spherical Couette flow
Authors: Zikanov Oleg Yu.
Published: April 2006

The solutions of the nonlinear and linearized Navier-Stokes equations are computed to investigate the instabilities and the secondary two- and three-dimensional regimes in the flow of an incompressible viscous fluid in a thin gap between two concentric differentially rotating spheres. The numerical technique is finite difference in the radial direction, spectral in the azimuthal direction, and pseudo-spectral in the meridional direction. The study follows the experiments by Yavorskaya, Belyaev and co-workers in which a variety of steady axisymmetric and three-dimensional travelling wave secondary regimes was observed in the case of a thin layer and both boundary spheres rotating. In agreement with the experimental results three different types of symmetry-breaking primary bifurcations of the basic equilibrium are detected in the parameter range under consideration.
Hydrodynamic diffusion of suspended particles: a symposium
Authors: Davis Robert H.
Published: April 2006

Hydrodynamic diffusion refers to the fluctuating motion of non-Brownian particles (or droplets or bubbles) in a dispersion, which occurs due to multiparticle interactions. For example, in a concentrated sheared suspension, particles do not move along streamlines but instead exhibit fluctuating motions as they tumble around each other (figure 1a). This leads to a net migration of particles down gradients in particle concentration and in shear rate, due to the higher frequency of encounters of a test particle with other particles on the side of the test particle which has higher concentration or shear rate. As another example, suspended particles subject to sedimentation or fluidization do not generally move relative to the fluid with a constant velocity, but instead experience diffusion-like fluctuations in velocity due to interactions with neighbouring particles and the resulting variation in the microstructure or configuration of the suspended particles (figure 1b). In flowing granular materials, the particles interact through direct collisions or contacts; these collisions also cause the particles to undergo fluctuating motions characteristic of diffusion processes. Although the existence and importance of hydrodynamic diffusion of particles have been embraced only in the past several years, the subject has already captured the attention of a growing number of researchers in several diverse fields (e.g. suspension mechanics, fluidization, materials processing, and granular flows).
The mechanics of the Tollmien-Schlichting wave
Authors: Baines Peter G. , Majumdar Sharan J. , Mitsudera Humio
Published: April 2006

We describe a mechanistic picture of the essential dynamical processes in the growing Tollmien-Schlichting wave in a Blasius boundary layer and similar flows. This picture depends on the interaction between two component parts of a disturbance (denoted ‘partial modes’), each of which is a complete linear solution in some idealization of the system. The first component is an inviscid mode propagating on the vorticity gradient of the velocity profile with the free-slip boundary condition, and the second, damped free viscous modes in infinite uniform shear with the no-slip condition. There are two families of these viscous modes, delineated by whether the phase lines of the vorticity at the wall are oriented with or against the shear, and they are manifested as resonances in a forced system. The interaction occurs because an initial ‘inviscid’ disturbance forces a viscous response via the no-slip condition at the wall. This viscous response is large near the resonance associated with the most weakly damped viscous mode, and in the unstable parameter range it has suitable phase at the outer part of the boundary layer to increase the amplitude of the inviscid partial mode by advection.
Instabilities of the upstream meniscus in directional viscous fingering
Authors: Michalland Sylvain , Rabaud Marc , Couder Yves
Published: April 2006

New instabilities affecting the meniscus of a viscous fluid are presented. They occur in an experimental set-up introduced previously by Rabaud et al. (1990) in which a small quantity of a viscous fluid is placed in the narrow gap between two rotating cylinders. In this geometry the downstream meniscus located in the region where the two solid surfaces move away from each other is known to be unstable and to exhibit directional viscous fingering. In the present article it is shown that the upstream meniscus can also be unstable. Two types of instabilities are observed. In the first supercritical transition the front becomes time-dependent with either standing or propagating waves. In a second transition, which is subcritical, parallel fingers of finite amplitude are formed. The various types of spatio-temporal dynamical behaviour are discussed.
Modelling of chemical reactions in hypersonic rarefied flow with the direct simulation Monte Carlo method
Authors: Gallis Michael A. , Harvey John K.
Published: April 2006

In this paper the phenomenon of chemical reactivity in hypersonic rarefied flows is examined. A new model is developed to describe the reactions and post-collision energy exchange processes that take place under conditions of molecular non-equilibrium. The new scheme, which is applied within the framework of the direct simulation Monte Carlo (DSMC) method, draws its inspiration from the principles of maximum entropy which were developed by Levine & Bernstein. Sample hypersonic flow fields, typical of spacecraft re-entry conditions in which reactions play an important role, are presented and compared with results from experiments and other DSMC calculations. The latter use traditional methods for the modelling of chemical reactions and energy exchange. The differences are discussed and evaluated.