bluuebunny/crossref_metadata_2025 huggingface dataset:
Convection in a rotating cylinder. Part 1 Linear theory for moderate Prandtl numbers
Authors: Goldstein H. F. , Knobloch E. , Mercader I. , Net M.
Published: April 2006

The onset of convection in a uniformly rotating vertical cylinder of height h and radius d heated from below is studied. For non-zero azimuthal wavenumber the instability is a Hopf bifurcation regardless of the Prandtl number of the fluid, and leads to precessing spiral patterns. The patterns typically precess counter to the rotation direction. Two types of modes are distinguished: the fast modes with relatively high precession velocity whose amplitude peaks near the sidewall, and the slow modes whose amplitude peaks near the centre. For aspect ratios τ ≡ d/h of order one or less the fast modes always set in first as the Rayleigh number increases; for larger aspect ratios the slow modes are preferred provided that the rotation rate is sufficiently slow. The precession velocity of the slow modes vanishes as τ → ∞. Thus it is these modes which provide the connection between the results for a finite-aspect-ratio System and the unbounded layer in which the instability is a steady-state one, except in low Prandtl number fluids.

The linear stability problem is solved for several different sets of boundary conditions, and the results compared with recent experiments. Results are presented for Prandtl numbers σ in the range 6.7 ≤ σ ≤ 7.0 as a function of both the rotation rate and the aspect ratio. The results for rigid walls, thermally conducting top and bottom and an insulating sidewall agree well with the measured critical Rayleigh numbers and precession frequencies for water in a τ = 1 cylinder. A conducting sidewall raises the critical Rayleigh number, while free-slip boundary conditions lower it. The difference between the critical Rayleigh numbers with no-slip and free-slip boundaries becomes small for dimensionless rotation rates Ωh2/v ≥ 200, where v is the kinematic viscosity.
Strange interface deformation pulses in the flow of layered liquids
Authors: Chatterjee B. K. , Engineer M. H. , Roy B. , Roy Pradip
Published: April 2006

The interface in acoustically driven layered liquids, in an enclosed geometry, was found to be unstable to the production of spatially localized, quasi-periodic pulses of deformation. The most interesting property of these pulses is that they propagate in a direction opposite to that of the axial streaming velocity of both liquids. Experimental data are presented describing aspects of the phenomenon which occur only when both the interfacial tension and the density difference are small.
A direct numerical simulation of laminar and turbulent flow over riblet-mounted surfaces
Authors: Chu Douglas C. , Karniadakis George Em
Published: April 2006

The flow in a channel with its lower wall mounted with streamwise riblets is simulated using a highly efficient spectral element-Fourier method. The range of Reynolds numbers investigated is 500 to 3500, which corresponds to laminar, transitional, and turbulent flow states. A complete study is presented for V-groove riblets; the effect of rounded riblets is also investigated. Our results suggest that in the laminar regime there is no drag reduction, while in the transitional and turbulent regimes drag reduction exists (approximately 6 % at Reynolds number 3500) for the riblet-mounted wall in comparison with the smooth wall of the channel. For the first time, we present detailed turbulent statistics (turbulence intensities, Reynolds shear stresses, skewness and flatness) as well as a temporal analysis using a numerical analog of the VITA technique. The flow structure over the riblet-mounted wall is also analysed in some detail and compared with the corresponding flow over the smooth wall in an attempt to identify the physical mechanisms that cause drag reduction. The accuracy of the computation is established by comparing flow quantities corresponding to the smooth wall with previous direct numerical simulation results as well as with experimental results; on the riblet-mounted wall comparison is made with available experimental results. The agreement is very good for both cases. The current computation is the first direct numerical simulation of turbulence in a complex geometry domain.
Buoyancy effects in stably stratified horizontal boundary-layer flow
Authors: Daniels P. G. , Gargaro R. J.
Published: April 2006

This paper describes numerical and asymptotic solutions of the steady two-dimensional boundary-layer equations governing buoyant flow on a horizontal, thermally insulated surface. The class of flows considered is one for which there is a uniform external stream at constant temperature but for which conditions upstream lead to a statically stable temperature field within the boundary layer. This has the effect of generating an adverse pressure gradient which, if sufficiently strong, causes the boundary-layer solution to terminate in a singularity. Results are obtained for a range of Prandtl numbers.
Oscillatory instabilities produced by heat from a temperature-controlled hot wire below an interface
Authors: Rozé C. , Gouesbet G. , Darrigo R.
Published: April 2006

New experimental results are reported for the motion of a liquid surface caused by the heat released from a hot wire below the surface. Starting from a base state with steady convection and steady deformation of the free surface caused by variations in surface tension and heat transport to the surface, the system loses its stability through a supercritical Hopf bifurcation occurring on a curve f(ΔT*, d) = 0 in which d is the distance between hot wire and surface and ΔT* a critical temperature difference. These experiments are a model for more complex laser heating experiments in which chaotic motions may occur. Some emphasis is placed on the characterization of propagating waves produced on the surface after the occurrence of the bifurcation.
Surface motion induced by the interaction of pulsed laser radiation with highly absorbing dielectric fluids
Authors: Naugol'nykh Konstantin A. , Puchenkov Oleg V. , Zosimov Victor V. , Pashin Alexander E.
Published: April 2006

The disturbances on the free surface of dielectric fluids resulting from intense laser heating of their boundary layer are studied theoretically and experimentally. The heating is accompanied by pronounced evaporation from the surface and thereby leads to a recoil pressure momentum applied to the surface. For small values of total momentum transferred to the fluid, the low-amplitude initially hollow-like displacement of the surface in the impact zone decays to produce linear gravity–capillary waves (GCW) spreading out on the surface. This regime is treated analytically and the results obtained are compared with experiments involving weakly viscous (water, ethanol) and highly viscous (glycerol) liquids. An experimental arrangement for remote generation and subsequent detection of probe GCW-packets is given. The evolution of broadband GCW-disturbances on clean and surfactant-contaminated water surfaces are described. Results of GCW-attenuation spectrum measurements on clean water surfaces and on film-covered surfaces are presented.

High total recoil momentum values give rise to substantially nonlinear surface motion: after a short transient stage the surface takes the shape of a hemisphere expanding into the liquid, and later the liquid above the hemisphere closes up to form a cavity and slow down the expansion. For this regime the dynamics of the hemisphere expansion are determined and satisfactory agreement with experimental data obtained with the shadowgraph technique is established. Consistency of theory and experiment allowed the determination of the total recoil pressure momentum and its surface distribution.

In the intermediate case of moderate values of recoil momentum, the nonlinear evolution of broadband GCW-packets on clean and surfactant-contaminated water surfaces is investigated experimentally.
Stratified Sadovskii flow in a channel
Authors: Chernyshenko S.
Published: April 2006

Stably stratified and non-stratified flows past a touching pair of vortices with continuous velocity are considered. An asymptotic solution for the very long eddies is determined. Numerical results cover the whole range of subcritical stratification and eddy length.
Vortex-induced vibrations of a long flexible circular cylinder
Authors: Brika D. , Laneville A.
Published: April 2006

In an experimental study of the vortex-induced oscillations of a long flexible circular cylinder, the observed stationary amplitudes describe an hysteresis loop partially different from earlier studies. Each branch of the loop is associated with a vortex shedding mode and, as a jump from one branch to the other occurs, the phase difference between the cylinder displacement and the vortex shedding undergoes an abrupt change. The critical flow velocities at which the jump occurs concur with the flow visualization observations of Williamson & Roshko (1988) on the vortex shedding modes near the fundamental synchronization region. Impulsive regimes, obtained at a given flow velocity with the cylinder initially at rest or pre-excited, and progressive regimes resulting from a variation of the flow velocity, are examined. The occurrence of bifurcations is detected for a flow velocity range in the case of the impulsive regimes. The coordinates of the bifurcations define a boundary between two vortex shedding modes, a boundary that verifies the critical curve obtained by Williamson & Roshko (1988). The experimental set-up of this study simulates half the wavelength of a vibrating cable, eliminates the end effects present in oscillating rigid cylinder set-up and has one of the lowest damping ratios reported for the study of this phenomenon.
Low Reynolds numberk—ε modelling with the aid of direct simulation data
Authors: Rodi W. , Mansour N. N.
Published: April 2006

The constantCμand the near-wall damping functionfμin the eddy-viscosity relation of thek–ε model are evaluated from direct numerical simulation (DNS) data for developed channel and boundary-layer flow, each at two Reynolds numbers. Various existingfμmodel functions are compared with the DNS data, and a new function is fitted to the high-Reynolds-number channel flow data. The ε-budget is computed for the fully developed channel flow. The relative magnitude of the terms in the ε-equation is analysed with the aid of scaling arguments, and the parameter governing this magnitude is established. Models for the sum of all source and sink terms in the ε-equation are tested against the DNS data, and an improved model is proposed.
Temperature dissipation in a turbulent round jet
Authors: Antonia R. A. , Mi J.
Published: April 2006

Parallel cold wires were used to measure the temperature derivative, in each of the three spatial directions, in the self-preserving region of a turbulent round jet. The temperature derivative variances were inferred from the correlation method and from the temperature derivative spectra after correcting these for the effect of wire separation. Both methods yielded fully consistent results for the components of the average temperature dissipation: the radial and azimuthal values are nearly equal and only slightly larger than the axial component. The resulting departure from isotropy of the temperature dissipation is small, especially when compared with results in other free shear flows. The high-wavenumber behaviour of the corrected temperature derivative spectra conforms closely with isotropy on the jet axis but small departures occur away from the axis. Conditional averages, based on spatially coherent temperature jumps, indicate that, while the organized motion makes a significant contribution to the temperature variance, its contribution to the temperature-derivative variances is small.
Barotropic flow over finite isolated topography: steady solutions on the beta-plane and the initial value problem
Authors: Thompson Luanne , Flierl Glenn R.
Published: April 2006

Solutions for inviscid rotating flow over a right circular cylinder of finite height are studied, and comparisons are made to quasi-geostrophic solutions. To study the combined effects of finite topography and the variation of the Coriolis parameter with latitude a steady inviscid model is used. The analytical solution consists of one part which is similar to the quasi-geostrophic solution that is driven by the potential vorticity anomaly over the topography, and another, similar to the solution of potential flow around a cylinder, that is driven by the matching conditions on the edge of the topography. When the characteristic Rossby wave speed is much larger than the background flow velocity, the transport over the topography is enhanced as the streamlines follow lines of constant background potential vorticity. For eastward flow, the Rossby wave drag can be very much larger than that predicted by quasi-geostrophic theory. The combined effects of finite height topography and time-dependence are studied in the inviscid initial value problem on the f-plane using the method of contour dynamics. The method is modified to handle finite topography. When the topography takes up most of the layer depth, a stable oscillation exists with all of the fluid which originates over the topography rotating around the topography. When the Rossby number is order one, a steady trapped vortex solution similar to the one described by Johnson (1978) may be reached.
Experimental studies of the deformation of a synthetic capsule in extensional flow
Authors: Chang K. S. , Olbricht W. L.
Published: April 2006

Experiments are described to study the motion and deformation of a synthetic, liquid-filled capsule that is freely suspended in hyperbolic extensional flow. The capsule is a composite particle consisting of a viscous liquid drop surrounded by a thin polymeric membrane. The method used to fabricate capsules suitable for macroscopic flow experiments is described. The deformation of the capsule is measured as a function of strain rate for an extensional flow generated in a four-roll mill. The data agree well with results from small-deformation theory developed by Barthes-Biesel and co-workers, provided the deformation of the capsule is not too large. Using the theory to correlate the experimental data produces an estimate for the elastic modulus of the membrane that agrees reasonably well with the elastic modulus obtained by an independent technique. However, for sufficiently large strain rates, the membrane exhibits strain hardening and a permanent change in its structure, both of which are reflected in the shape of the capsule.
The propagation of intrusion fronts of high density ratios
Authors: Gröbelbauer H. P. , Fanneløp T. K. , Britter R. E.
Published: April 2006

The propagation of gravity fronts of high density ratios has been studied experimentally (exchange flow) and by computer simulation. Non-Boussinesq fronts are known to occur in certain safety problems (chemical spills and fires), and we have investigated seven gas combinations giving density ratios from near unity to well over 20. The results are presented in terms of a density parameter ρ* which remains finite both in the weak (ρ* = 0) and the strong (ρ* = 1) limit. The front velocities, measured by means of hot wires, are found to fall on two distinct curves, one for the slower lightgas fronts and one for the faster heavy-gas fronts. Two fractional depths, Φ = ½ (lock exchange) and Φ = ⅙, have been investigated in detail and results for the interesting case Φ → 0 have been obtained by extrapolation. To aid in the extrapolation and for comparison, all experimental (and some intermediate) cases have been simulated by means of a general purpose CFD-code (PHOENICS). Good agreement is found for cases without convergence problems, i.e. for heavy-gas fronts of density ratio less than 5. Further information on frontal shape etc. has been obtained from visualization. The extrapolations to infinite depth indicate a limiting speed for both the heavy- and light-gas fronts close to the values predicted from shallow-layer theory for the analogous dam-break problem.
The structure of the near wake of a sphere moving horizontally in a stratified fluid
Authors: Chomaz J. M. , Bonneton P. , Hopfinger E. J.
Published: April 2006

We present experimental results for the wake structure of spheres moving in homogeneous and stratified fluid. In homogeneous fluid, the results of Kim & Durbin (1988) are confirmed and it is shown that the two characteristic frequencies of the wake correspond to two instability modes, the Kelvin–Helmholtz instability and a spiral instability. For the stratified wake four general regimes have been identified, depending principally on the Froude number F. For F > 4.5 the near wake is similar to the homogeneous case, and for F < 0.8 it corresponds to a triple-layer flow with two lee waves, of amplitude linear in F, surrounding a layer dominated by quasi-two-dimensional motion. Froude numbers close to one (F∈]0.8, 1.5[) give rise to a saturated lee wave of amplitude equal to half the sphere radius, which suppresses the separation region or splits it into two. Between F = 1.5 and 4.5 a more complex regime exists where the wake recovers progressively its behaviour in homogeneous fluid: the axisymmetry of the recirculating zone, the Kelvin–Helmholtz instability and, finally, the spiral instability.
Internal waves produced by the turbulent wake of a sphere moving horizontally in a stratified fluid
Authors: Bonneton P. , Chomaz J. M. , Hopfinger E. J.
Published: April 2006

The internal gravity wave field generated by a sphere towed in a stratified fluid was studied in the Froude number range 1.5 ≤ F ≤ 12.7, where F is defined with the radius of the sphere. The Reynolds number was sufficiently large for the wake to be turbulent (Re∈[380, 30000]). A fluorescent dye technique was used to differentiate waves generated by the sphere, called lee waves, from the internal waves, called random waves, emitted by the turbulent wake. We demonstrate that the lee waves are well predicted by linear theory and that the random waves due to the turbulence are related to the coherent structures of the wake. The Strouhal number of these structures depends on F when F [lsim ] 4.5. Locally, these waves behave like transient internal waves emitted by impulsively moving bodies.
On explicit algebraic stress models for complex turbulent flows
Authors: Gatski T. B. , Speziale C. G.
Published: April 2006

Explicit algebraic stress models that are valid for three-dimensional turbulent flows in non-inertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope (1975) who based his analysis on the Launder, Reece & Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models – as well as anisotropic eddy viscosity models – is theoretically established. A need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.
On the stability of rapid granular flows
Authors: Babić Marijan
Published: April 2006

Numerical simulations of rapid granular flows in large periodic domains have demonstrated the existence of an ‘inelastic microstructure’ characterized by agglomerations of particles into clusters. In the present work the phenomenon of particle clustering is considered to be a manifestation of hydrodynamic instability of the equations governing the dynamics of rapid granular flows. A linear stability analysis of the simple shear flow of smooth, slightly, inelastic disks and spheres is carried out utilizing the governing equations formulated by the kinetic theory. The results indicate that disturbances of large wavelengths initially grow at an exponential rate for any value of the restitution coefficient. The results also demonstrate that this phenomenon will not be exposed in numerical simulations within small periodic domains, because the range of possible disturbance wavelengths is limited by the size of the periodic domain.
Interactions between a solid surface and a viscous compressible flow field
Authors: Wu Jie-Zhi , Wu Jain-Ming
Published: April 2006

This paper presents a general theory and physical interpretation of the interaction between a solid body and a Newtonian fluid flow in terms of the vorticity ω and the compression/expansion variable Π instead of primitive variables, i.e. velocity and pressure. Previous results are included as special simplified cases of the theory. The first part of this paper shows that the action of a solid wall on a fluid can be exclusively attributed to the creation of a vorticity-compressing ω–Π field directly from the wall, a process represented by respective boundary fluxes. The general formulae for these fluxes, applicable to any Newtonian flow over an arbitrarily curved surface, are derived from the force balance on the wall. This part of the study reconfirms and extends Lighthil's (1963) assertion on vorticity-creation physics, clarifies some currently controversial issues, and provides a sound basis for the formulation of initial boundary conditions for the ω-Π variables.

The second part of this paper shows that the reaction of a Newtonian flow to a solid body can also be exclusively attributed to that of the ω-Π field created. In particular, the integrated force and moment formulae can be expressed solely in terms of the boundary vorticity flux. This implies an inherent unity of the action and reaction between a solid body and a ω-Π field.

In both action and reaction phases the ω-Π coupling on the wall plays an essential role. Thus, once a solid wall is introduced into a flow, any theory that treats ω and Π separately will be physically incomplete.
On the second-order solution to the Sears problem for compressible flow
Authors: Amiet R. K.
Published: April 2006

Significant simplifications and minor corrections are made to a previous second-order solution of Graham & Kullar for the lift on a flat-plate airfoil encountering a sinusoidal gust in compressible flow. The related cases of a skewed gust in incompressible flow, a parallel gust in compressible flow and the generalized case of a skewed gust in compressible flow are considered. In addition to the simplifications, the solutions are combined into a composite solution that is more accurate than the solutions from which it is composed, making it useful for numerical calculations.
A note on the nonlinear development of the Batchelor–Nitsche instability
Authors: Proctor M. R. E.
Published: April 2006

The nonlinear development of the Batchelor–Nitsche instability (of a periodically stratified fluid) is considered, utilizing the disparity between vertical and horizontal scales of motion. The resulting evolution equation is used to show that the preferred pattern of convection takes the form of rolls, and that the motion evolves to larger and larger horizontal scales as time increases.
The evolution of thermocline waves from an oscillatory disturbance
Authors: Nicolaou D. , Liu R. , Stevenson T. N.
Published: April 2006

The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier–Stokes equations.
Global density effects on the self-preservation behaviour of turbulent free jets
Authors: Richards C. D. , Pitts W. M.
Published: April 2006

An experimental investigation was designed to test the hypothesis that all axisymmetric turbulent free jets become asymptotically independent of the source conditions and may be described by classical similarity analysis. Effects of initial conditions were studied by varying jet exit boundary conditions and the global density ratio. The exit velocity profile and turbulence level was changed by using both pipe and nozzle flow hardware. Initial density differences were imposed by using three gases: helium, methane, and propane. The scalar field (concentration) in the momentum-dominated regime of the far field (10 to 60 jet exit diameters downstream) of turbulent free jets was characterized using Rayleigh light scattering as the diagnostic. The results show that regardless of the initial conditions axisymmetric turbulent free jets decay at the same rate, spread at the same angle, and both the mean and r.m.s. values collapse in a form consistent with full self-preservation. The means and fluctuations follow a law of full self-preservation in which two virtual origins must be specified. The two displacements are required to account for the effects of a finite source of momentum and different development of the velocity and mass distributions in the near fields of the jets. The memory of the jet is embodied in these two virtual origins.
On internal waves generated by travelling wind
Authors: Kundu Pijush K.
Published: April 2006

Oceanic internal waves forced by a latitude-independent wind field travelling eastward at speed U is investigated, extending the hydrostatic f-plane model of Kundu & Thomson (1985). The ocean has a well-mixed surface layer overlying a stratified interior with a depth-dependent buoyancy frequency N(z), and f can vary with latitude. Solutions are found by decomposition into vertical normal modes. Problems discussed are (i) the response to a slowly moving line front, and (ii) the response in a variable f ocean.

For the slowly moving line front assuming a depth-independent N, the trailing waves are found to have large frequencies, and the vertical acceleration ∂w/∂t is important (that is the dynamics are non-hydrostatic) if the frequency ω is larger than a few times (Nf)½. The wake contains waves associated with all vertical modes, in contrast to hydrostatic dynamics in which slowly moving line fronts do not generate trailing waves of low-order modes. It is argued that slowly moving wind fields can provide an explanation for the frequently observed broad peak in the spectrum of vertical motion at a frequency somewhat smaller than N, and of the vertical coherence of the associated waves in the upper ocean.

To study lower-frequency internal waves, the hydrostatic constant-f model of Kundu & Thomson is extended to variable f. Various sections through such a flow clearly illustrate the development of a meridional wavelength λy = 2π/βt as predicted by D'Asaro (1989), in addition to the zonal wavelength λx due to translation of the wind. The two effects combine to cause a greater horizontal inhomogeneity, so that energy from the surface layer descends quickly, travelling equatorward and downward. Since waves at any point arrive from different latitudes, spectra no longer consist of discrete peaks but are more continuous and broader than those in the constant-f model. The waves are more intermittent because of the larger spectral width, and vertically less correlated in the thermocline because of a larger bandwidth of vertical modes. The vertical correlation in the deep ocean, however, is still high because the response is dominated by one or two low-order modes after 30 days of integration. As U decreases, the larger bandwidth of frequency increases the intermittency, and the larger bandwidth of vertical wavenumber decreases the vertical correlation. A superposition of travelling wind events intensifies the high-frequency end of the spectrum; a month-long travelling series of realistic strength can generate waves with amplitudes of order 4 cm/s in the deep ocean.

It is suggested that propagating winds and linear dynamics are responsible for the generation of a large fraction of internal waves in the ocean at all depths. The main effect of nonlinearity and mean flow may be to shape the internal wave spectra to a ω-2 form.
The difference between monopole vortices in planetary flows and laboratory experiments
Authors: Nycander J.
Published: April 2006

This work is an attempt to explain observations of vortices in experiments with shallow water in rotating paraboloidal vessels. The most long-lived vortices are invariably anticyclones, while cyclones quickly disperse, and they are larger than the Rossby radius. These experiments are designed to simulate geophysical flows, where large, long-lived, anticyclonic vortices are common.

The general condition for vortices to be steady is that they propagate faster than linear Rossby waves, so that the vortex energy is not dispersed by coupling to linear waves. The propagation velocity is determined by a general integral relation that gives the velocity of the centre of mass. In geophysical flows, to lowest order in the Rossby number, the difference between the centre-of-mass velocity and the maximum phase velocity of the Rossby waves is proportional to the relative perturbation of the fluid depth. Since for anticyclones the difference is positive they may be steady, whereas cyclones cannot be.

In the laboratory experiments this velocity difference is absent because of the latitudinal dependence of the effective gravity caused by the centrifugal force. However, to the next order in the Rossby number, there is another nonlinear contribution, so that anticyclones (but not cyclones) still propagate faster than the linear Rossby waves, and may thus be steady. The velocity difference is smaller than for geophysical flows, and vanishes in the limit of small Rossby number. The existence conditions also show that we can expect the experimental vortices to be smaller (as measured by the Rossby radius) than the planetary vortices. The theory does not apply to vortices that are much smaller than the Rossby radius.
On Marangoni drying: nonlinear kinematic waves in a thin film
Authors: O'Brien S. B. G. M.
Published: April 2006

In the field of industrial drying, a recent innovation has exploited the occurrence of Marangoni effects in such a way that the resultant free-surface flow enhances the drying process. To this end, alcohol vapour, soluble in water, is introduced above a drying film and as a result of diffusion through the air and water phases a favourable concentration gradient gives rise to the required shear flow. We consider here a simple process driven by this mechanism, and by means of asymptotic simplification and the concepts of singular perturbation theory a leading-order approximation is obtained in which the alcohol concentration in the water is a specified function of space and time. The evolution of the free surface thus reduces to a single nonlinear partial differential equation of a similar form to the Korteweg–de Vries and Burgers equations, higher-derivative terms corresponding to surface tension and gravity effects. Numerical solutions of this equation are obtained and are compared to the application of first order nonlinear kinematic wave theory with corresponding shock solutions.
On the dynamics of buoyant and heavy particles in a periodic Stuart vortex flow
Authors: Tio Kek-Kiong , Liñán Amable , Lasheras Juan C. , Gañán-Calvo Alfonso M.
Published: April 2006

In this paper, we study the dynamics of small, spherical, rigid particles in a spatially periodic array of Stuart vortices given by a steady-state solution to the two-dimensional incompressible Euler equation. In the limiting case of dominant viscous drag forces, the motion of the particles is studied analytically by using a perturbation scheme. This approach consists of the analysis of the leading-order term in the expansion of the ‘particle path function’ Φ, which is equal to the stream function evaluated at the instantaneous particle position. It is shown that heavy particles which remain suspended against gravity all move in a periodic asymptotic trajectory located above the vortices, while buoyant particles may be trapped by the stable equilibrium points located within the vortices. In addition, a linear map for Φ is derived to describe the short-term evolution of particles moving near the boundary of a vortex. Next, the assumption of dominant viscous drag forces is relaxed, and linear stability analyses are carried out to investigate the equilibrium points of the five-parameter dynamical system governing the motion of the particles. The five parameters are the free-stream Reynolds number, the Stokes number, the fluid-to-particle mass density ratio, the distribution of vorticity in the flow, and a gravitational parameter. For heavy particles, the equilibrium points, when they exist, are found to be unstable. In the case of buoyant particles, a pair of stable and unstable equilibrium points exist simultaneously, and undergo a saddle-node bifurcation when a certain parameter of the dynamical system is varied. Finally, a computational study is also carried out by integrating the dynamical system numerically. It is found that the analytical and computational results are in agreement, provided the viscous drag forces are large. The computational study covers a more general regime in which the viscous drag forces are not necessarily dominant, and the effects of the various parametric inputs on the dynamics of buoyant particles are investigated.
Turbulence-driven secondary flows and formation of sand ridges
Authors: Colombini Marco
Published: April 2006

The mechanism of generation of sand ridges, longitudinal stripes observed both in natural rivers and in the laboratory, is investigated with the aim of showing that the initiation mechanism is intrinsically associated with an instability of the erodible bottom rather than with the effect of the secondary vortices induced by the sidewalls as suggested by previous works. A linear stability analysis of flow in infinitely wide channels with an erodible bed is then presented. In order to model the generation of turbulence-driven cellular secondary motions a nonlinear turbulence closure scheme is used. Comparison with published experimental data for the case of air duct flow over a fixed ‘ridge-shaped’ bed is performed in order to check the performance of the turbulence model and proves satisfactory. It turns out that under suitable conditions the uniform unidirectional flow is unstable with respect to spanwise disturbances with a characteristic wavelength of the order of the flow depth. This theoretical finding is supported by experimental observations on wide open-channel flows. The secondary vortices are directed in such a way as to amplify bed perturbations, eventually leading to the formation of sand ridges irrespective of the presence of the sidewalls.
Experimental investigation of periodic flow in curved pipes
Authors: Swanson Chris J. , Stalp Steven R. , Donnelly Russell J.
Published: April 2006

We have studied oscillatory flow through a 180° curved tube with the ratio of tube radius to radius of curvature equal to 1/7. The flow rate is constrained to vary sinusoidally about a non-zero mean at a specified period T, and mean flow rate Q. At a certain parameter range of interest Hamakiotes & Berger (1990) predict that fully developed flow undergoes a period-tripling bifurcation. Our measurements using laser-Doppler velocimetry found no bifurcation. An additional experiment was done to ensure that the flow was fully developed.
A critical-layer analysis of the resonant triad in boundary-layer transition: nonlinear interactions
Authors: Mankbadi Reda R. , Wu Xuesong , Lee Sang Soo
Published: April 2006

A systematic theory is developed to study the nonlinear spatial evolution of the resonant triad in Blasius boundary layers. This triad consists of a plane wave at the fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low-frequency asymptotic scaling leads to a distinct critical layer wherein nonlinearity first becomes important, and the critical layer's nonlinear, viscous dynamics determine the development of the triad.

The plane wave initially causes double-exponential growth of the oblique waves. The plane wave, however, continues to follow the linear theory, even when the oblique waves’ amplitude attains the same order of magnitude as that of the plane wave. However, when the amplitude of the oblique waves exceeds that of the plane wave by a certain level, a nonlinear stage comes into effect in which the self-interaction of the oblique waves becomes important. The self-interaction causes rapid growth of the phase of the oblique waves, which causes a change of the sign of the parametric-resonance term in the oblique-waves amplitude equation. Ultimately this effect causes the growth rate of the oblique waves to oscillate around their linear growth rate. Since the latter is usually small in the nonlinear regime, the net outcome is that the self-interaction of oblique waves causes the parametric resonance stage to be followed by an ‘oscillatory’ saturation stage.
Unsteady natural convection in a cavity with non-uniform absorption of radiation
Authors: Coates Michael J. , Patterson John C.
Published: April 2006

A study of the unsteady natural convection in a cavity which was heated by the absorption of radiation entering through part of the surface is reported. While a general scaling analysis is quite complex, involving five separate timescales, most naturally occurring problems fall into just one regime, and it is only this regime which is discussed. To test the scaling, a series of laboratory experiments were performed in which the radiation parameters (surface flux and attenuation coefficient) were varied. The method by which these parameters were determined is also discussed. Numerical experiments were used to extend the parameter range, and the results of all these experiments confirmed the validity of the scaling over a range of parameters.
Monte Carlo simulation of the Taylor–Couette flow of a rarefied gas
Authors: Stefanov Stefan , Cercignani Carlo
Published: April 2006

We report and discuss the results of a direct Monte Carlo simulation of the flow of a rarefied gas flowing between two cylinders when the inner one rotates. The formation of Taylor vortices is clearly exhibited.
The one-dimensional adiabatic flow of equilibrium gas–particle mixtures in variable-area ducts with friction
Authors: Buresti Guido , Casarosa Claudio
Published: April 2006

A general one-dimensional model for the steady adiabatic motion of gas-particle mixtures in arbitrarily oriented ducts with gradually varying cross-section and wall friction is presented. The particles are assumed to be incompressible and in thermomechanical equilibrium with a perfect gas phase, and the effects of their finite volume and of gravity are also taken into account.

The equations of motion are written in a form that allows a theoretical analysis of the behaviour of the solutions to be carried out. In particular, the results of the application to the model of a procedure that permits the identification and the topological classification of the singular points of the trajectories representing, in a suitable phase space, the solutions of the set of equations defining the problem are described. This characterization of the singular points is useful in order to overcome difficulties in the numerical integration of the equations.

Subsequently, a geometrical analysis is carried out which allows a study of the signs of the local variations of the flow quantities, and shows that some unusual behaviour may occur if certain geometrical and fluid dynamic conditions are fulfilled. For instance, in an upward motion it is possible to have a simultaneous decrease of velocity, pressure and temperature, while in a downward flow an increase of all these quantities may be found. It is also shown that conditions exist in which expansion and heating of the mixture may take place simultaneously, both in accelerating and decelerating flows.

The model is applied to the study of upward motion in particular ducts, having converging-diverging and constant-diverging cross-sections; to this end the equations are integrated numerically by using the Mach number as the independent variable. The results show that even limited variations of the duct diameter may give rise to significant qualitative and quantitative variations in the flow conditions inside the duct and in the mass flow rate. Finally, an example is given of a subsonic downward flow in which a simultaneous increase of pressure, temperature and velocity occurs even in the case of a pure perfect gas.
A new mechanism for oblique wave resonance in the ‘natural’ far wake
Authors: Williamson C. H. K. , Prasad A.
Published: April 2006

There has been some debate recently on whether the far-wake structure downstream of a cylinder is dependent on, or ‘connected’ with, the precise details of the near-wake structure. Indeed, it has previously been suggested that the far-wake scale and frequency are unconnected with those of the near wake. In the present paper, we demonstrate that both the far-wake scale and frequency are dependent on the near wake. Surprisingly, the characteristic that actually forges a ‘connection’ between the near and far wakes is the sensitivity to free-stream disturbances. It is these disturbances that are also responsible for the regular three-dimensional patterns that may be visualized. Observations of a regular ‘honeycomb’-like three-dimensional pattern in the far wake is found to be caused by an interaction between oblique shedding waves from upstream and large-scale two-dimensional waves, amplified from the free-stream disturbances. The symmetry and spanwise wavelength of Cimbala, Nagib & Roshko's (1988) three-dimensional pattern are precisely consistent with such wave interactions. In the presence of parallel shedding, the lack of a honeycomb pattern shows that such a three-dimensional pattern is clearly dependent on upstream oblique vortex shedding.

With the deductions above as a starting point, we describe a new mechanism for the resonance of oblique waves, as follows. In the case of two-dimensional waves, corresponding to a very small spectral peak in the free stream (fT) interacting (quadratically) with the oblique shedding waves frequency (fK), it appears that the most amplified or resonant frequency in the far wake is a combination frequency fFW = (fK–fT), which corresponds physically with ‘oblique resonance waves’ at a large oblique angle. The large scatter in (fFW/fK) from previous studies is principally caused by the broad response of the far wake to a range of free-stream spectral peaks (fT). We present clear visualization of the oblique wave phenomenon, coupled with velocity measurements which demonstrate that the secondary oblique wave energy can far exceed the secondary two-dimensional wave energy by up to two orders of magnitude. Further experiments show that, in the absence of an influential free-stream spectral peak, the far wake does not resonate, but instead has a low-amplitude broad spectral response. The present phenomena are due to nonlinear instabilities in the far wake, and are not related to vortex pairing. There would appear to be distinct differences between this oblique wave resonance and the subharmonic resonances that have been previously studied in channel flow, boundary layers, mixing layers and airfoil wakes.
Nonlinear drift interactions between fluctuating colloidal particles: oscillatory and stochastic motions
Authors: Hinch E. J. , Nitsche Ludwig C.
Published: April 2006

In this work we consider how nonlinear hydrodynamic effects can lead to a mean force of interaction between two spheres of equal radiusaundergoing translational fluctuations parallel or perpendicular to their line of centres. Motivated by amplitudes and Reynolds numbers characteristic of Brownian motion in colloidal systems, nonlinearities due to motion of the boundaries and to inertia throughout the fluid are treated as regular perturbations of the time-dependent Stokes equations. This formulation ultimately leads to a prescription for computing, at leading order, the time-average nonlinear force for the case of pure oscillatory modes – which represents the Fourier decomposition of more general motions. The associated hydrodynamic problems are solved numerically using a least-squares boundary singularity method. Frequency-dependent results over the whole spectrum are presented for a sphere-sphere gap equal to one radius; illustrative calculations are also carried out at other separations. Subsequently we extend the analysis of nonlinear drift to a Langevin equation formulation of the more complex problem of stochastic motion due to thermal fluctuations in the suspending fluid, i.e. Brownian motion. By integrating (numerically) over the spectrum of frequencies, we quantify how the mutual interactions of all translational disturbance modes give rise, on ensemble average, to a stochastic nonlinear force of interaction between the particles. It is particularly interesting that this net interaction – arising from a zero-mean random force – is ofO(1) on the Brownian scalekT/a, even though it represents a smallO(Re) correction at each frequency of pure oscillations. Finally, we discuss how the presence of stochastic nonlinear drift would lead to non-uniform equilibrium distributions of dilute colloidal suspensions, unless one adds to the random force in the Langevin equation a cancelling non-zero mean component.
Fundamental–subharmonic interaction: effect of phase relation
Authors: Hajj M. R. , Miksad R. W. , Powers E. J.
Published: April 2006

The effect of the phase relation (i.e. phase difference and coupling) between the fundamental and subharmonic modes on the transition to turbulence of a mixing layer is investigated. Experiments are conducted to study the development of the subharmonic and fundamental modes under different phase-controlled excitations. Higher-order spectral moments are used to measure phase differences, levels of phase coupling, and energy transfer rates between the two modes at different downstream locations. Local measurements of the wavenumber–frequency spectra are used to examine the phase-speed matching conditions required for efficient energy transfer. The results show that when the phase coupling between the fundamental and the subharmonic is high, maximum subharmonic growth is found to occur at a critical phase difference close to zero. The subharmonic growth is found to result from a resonant parametric interaction between the fundamental and the subharmonic in which phase-speed matching conditions are satisfied. In contrast, when the phase coupling level is low, the phase difference is irregular and varying, the efficiency of parametric interactions is low, phase-speed matching conditions are not met and subharmonic growth is suppressed.