Showing papers in "Journal of Fluid Mechanics in 2005"

On the relationships between local vortex identification schemes

Abstract: We analyse the currently popular vortex identification criteria that are based on point-wise analysis of the velocity gradient tensor. A new measure of spiralling compactness of material orbits in vortices is introduced and using this measure a new local vortex identification criterion and requirements for a vortex core are proposed. The inter-relationships between the different criteria are explored analytically and in a few flow examples, using both zero and non-zero thresholds for the identification parameter. These inter-relationships provide a new interpretation of the various criteria in terms of the local flow kinematics. A canonical turbulent flow example is studied, and it is observed that all the criteria, given the proposed usage of threshold, result in remarkably similar looking vortical structures. A unified interpretation based on local flow kinematics is offered for when similarity or differences can be expected in the vortical structures educed using the different criteria.

An objective definition of a vortex

Abstract: The most widely used definitions of a vortex are not objective: they identify different structures as vortices in frames that rotate relative to each other. Yet a frame-independent vortex definition is essential for rotating flows and for flows with interacting vortices. Here we define a vortex as a set of fluid trajectories along which the strain acceleration tensor is indefinite over directions of zero strain. Physically, this objective criterion identifies vortices as material tubes in which material elements do not align with directions suggested by the strain eigenvectors. We show using examples how this vortex criterion outperforms earlier frame-dependent criteria. As a side result, we also obtain an objective criterion for hyperbolic Lagrangian structures.

Numerical and experimental investigation of flow and scour around a circular pile

Abstract: The flow around a vertical circular pile exposed to a steady current is studied numerically and experimentally. The numerical model is a three-dimensional model. The model validation was achieved against new experimental data (which include two-component laser-Doppler anemometry (LDA) flow measurements and the hot-film bed shear stress measurements, and reported in the present paper) and the data of others, and a k-w turbulence model was used for closure. The model does not have a free-surface facility and therefore is applicable only to cases where the Froude number is small (Fr < 0(0.2)). The flow model was used to study the horseshoe vortex and lee-wake vortex flow processes around the pile. The influence on the horseshoe vortex of three parameters, namely the boundary-layer thickness, the Reynolds number and the bed roughness, was investigated. In the latter investigation, the steady solution of the model was chosen. A study of the influence of the unsteady solution on the previously mentioned flow processes was also carried out. The ranges of the parameters covered in the numerical simulations are: The boundary-layer-thickness-to-pile-diameter ratio is varied from 2 x 10 -2 to 10 2 , the pile Reynolds number from 10 2 to 2 × 10 6 , and the pile diameter-to-roughness ratio from 2 to about 10 3 . The amplification of the bed shear stress around the pile (including the areas under the horseshoe vortex and the lee-wake region) was obtained for various values of the previously mentioned parameters. The steady-state flow model was coupled with a morphologic model to calculate scour around a vertical circular pile exposed to a steady current in the case of non-cohesive sediment. The morphologic model includes (i) a two-dimensional bed load sediment-transport description, and (ii) a description of surface-layer sand slides for bed slopes exceeding the angle of repose. The results show that the present numerical simulation captures all the main features of the scour process. The equilibrium scour depth obtained from the simulation agrees well with the experiments for the upstream scour hole. Some discrepancy (up to 30 %) was observed, however, for the downstream scour hole. The calculations show that the amplification of the bed shear stress around the pile in the equilibrium state of the scour process is reduced considerably with respect to that experienced at the initial stage where the bed is plane.

Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force

Abstract: We report on lattice-Boltzmann simulations of slow fluid flow past mono- and bidisperse random arrays of spheres. We have measured the drag force on the spheres for a range of diameter ratios, mass fractions and packing fractions; in total, we studied 58 different parameter sets. Our simulation data for the permeability agrees well with previous simulation results and the experimental findings. On the basis of our data for the individual drag force, we have formulated new drag force relations for both monodisperse and polydisperse systems, based on the Carman?Kozeny equations; the average deviation of our binary simulation data with the new relation is less than 5%. We expect that these new relations will significantly improve the numerical modelling of gas?solid systems with polydisperse particles, in particular with respect to mixing and segregation phenomena. For binary systems with large diameter ratios (1:4), the individual drag force on a particle, as calculated from our relations, can differ by up to a factor of five compared with predictions presently favoured in chemical engineering.

Componentwise energy amplification in channel flows

Abstract: We study the linearized Navier–Stokes (LNS) equations in channel flows from an input–output point of view by analysing their spatio-temporal frequency responses. Spatially distributed and temporally varying body force fields are considered as inputs, and components of the resulting velocity fields are considered as outputs into these equations. We show how the roles of Tollmien–Schlichting (TS) waves, oblique waves, and streamwise vortices and streaks in subcritical transition can be explained as input–output resonances of the spatio-temporal frequency responses. On the one hand, we demonstrate the effectiveness of input field components, and on the other, the energy content of velocity perturbation components. We establish that wall-normal and spanwise forces have much stronger influence on the velocity field than streamwise force, and that the impact of these forces is most powerful on the streamwise velocity component. We show this using the relative scaling of the different input–output system components with the Reynolds number. We further demonstrate that for the streamwise constant perturbations, the spanwise force localized near the lower wall has, by far, the strongest effect on the evolution of the velocity field. In this paper, we analyse the dynamical properties of the Navier–Stokes (NS) equations with spatially distributed and temporally varying body force fields. These fields are considered as inputs, and different combinations of the resulting velocity fields are considered as outputs. This input–output analysis can in principle be done in any geometry and for the full nonlinear NS equations. In such generality, however, it is difficult to obtain useful results. We therefore concentrate on the geometry of channel flows, and the input–output dynamics of the linearized Navier–Stokes (LNS)

The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows

Abstract: Low-dimensional empirical Galerkin models are developed for spatially evolving laminar and transitional shear layers, based on a Karhunen–Loeve decomposition of incompressible two- and three-dimensional Navier–Stokes simulations. It is shown that the key to an accurate Galerkin model is a novel analytical pressure-term representation. The effect of the pressure term is elucidated by a modal energy-flow analysis in a mixing layer, which generalizes the framework developed by Rempfer (1991). In convectively unstable shear layers, it is shown in particular that neglecting small energy terms leads to large amplitude errors in the Galerkin model. The effect of the pressure term and small neglected energy flows is very important for a two-dimensional mixing layer, is less pronounced for the three-dimensional analogue, and can be considered as small in an absolutely unstable wake flow.

Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions

Abstract: High-resolution large-eddy simulation is used to investigate the mean and turbulence properties of a separated flow in a channel constricted by periodically distributed hill-shaped protrusions on one wall that obstruct the channel by 33% of its height and are arranged 9 hill heights apart. The geometry is a modification of an experimental configuration, the adaptation providing an extended region of post-reattachment recovery and allowing high-quality simulations to be performed at acceptable computing costs. The Reynolds number, based on the hill height and the bulk velocity above the crest is 10595. The simulated domain is streamwise as well as spanwise periodic, extending from one hill crest to the next in the streamwise direction and over 4.5 hill heights in the spanwise direction. This arrangement minimizes uncertainties associated with boundary conditions and makes the flow an especially attractive generic test case for validating turbulence closures for statistically two-dimensional separation. The emphasis of the study is on elucidating the turbulence mechanisms associated with separation, recirculation reattachment, acceleration and wall proximity. Hence, careful attention has been paid to resolution, and a body-fitted, low-aspect-ratio, nearly orthogonal numerical grid of close to 5 million nodes has been used. Unusually, the results of two entirely independent simulations with different codes for identical flow and numerical conditions are compared and shown to agree closely. Results are included for mean velocity, Reynolds stresses, anisotropy measures, spectra and budgets for the Reynolds stresses. Moreover, an analysis of structural characteristics is undertaken on the basis of instantaneous realizations, and links to features observed in the statistical results are identified and interpreted. Among a number of interesting features, a distinct ‘splatting’ of eddies on the windward hill side following reattachment is observed, which generates strong spanwise fluctuations that are reflected, statistically, by the spanwise normal stress near the wall exceeding that of the streamwise stress by a substantial margin, despite the absence of spanwise strain.

Crucial role of sidewalls in granular surface flows: consequences for the rheology

Abstract: In this paper we study the steady uniform flows that develop when granular material is released from a hopper on top of a static pile in a channel. We more specifically focus on the role of side walls by carrying out experiments in setup of different widths, from narrow channels 20 particle diameters wide to channels 600 particle diameters wide. Results show that steady flows on pile are entirely controlled by side wall effects. A theoretical model, taking into account the wall friction and based on a simple local constitutive law recently proposed for other granular flow configurations (GDR MiDi 2004), gives predictions in quantitative agreement with the measurements. This result gives new insights in our understanding of free surface granular flows and strongly supports the relevance of the constitutive law proposed.

Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations

Abstract: Laboratory experiments on stably stratified grid turbulence have suggested that turbulent diffusivity , suggesting that such Reynolds–Richardson number or Reynolds–Froude number aggregates are more descriptive of stratified turbulent flow conditions than the conventional reliance on Richardson number alone.

Lagrangian measurement of vorticity dynamics in turbulent flow

Abstract: The full set of velocity derivatives, -alignment of vorticity. Lagrangian measurements of enstrophy budget terms suggest that there is no pointwise balancing of production and viscous reduction of enstrophy and that the role played by viscosity is of great importance.

An experimental investigation of swirling jets

Abstract: The 'plug' flow emerging from a long rotating tube into a large stationary reservoir has been used in an experimental investigation of centrifugally unstable swirling jets. A moderate Reynolds number, Re = 1000, was studied extensively, and swirl numbers, S, the ratio of nozzle exit rotating speed to the mean mass axial velocity, were in the range 0-1.1. Four regimes were covered: non-swirling jets with S=0, weakly swirling jets in the range 0 S c2 , where S c1 =0.6 and S c2 = 0.88. Particular attention was paid to the dominant role of the underlying vortical flow structures and their dynamic evolution. Kelvin-Helmholtz (K-H) instability in the axial shear layer, generated by the axial velocity, leading to vortex ring formation, dominated non-swirling and weakly swirling jets

Retraction dynamics of aqueous drops upon impact on non-wetting surfaces

Abstract: We study the impact and subsequent retraction of liquid droplets upon high-speed impact on hydrophobic surfaces. Extensive experiments show that the drop retraction rate is a material constant and does not depend on the impact velocity. We show that on increasing the Ohnesorge number, Oh = η/ √ ρRIγ , the retraction, i.e. dewetting, dynamics crosses from a capillary–inertial regime to a capillary–viscous regime. We rationalize the experimental observations by a simple but robust semi-quantitative model for the solid–liquid contact line dynamics inspired by the standard theories for thin-film dewetting.

Study of trajectories of jets in crossflow using direct numerical simulations

Abstract: This paper studies the trajectories and near field of round jets in crossflow. Incompressible direct numerical simulations are performed at velocity ratios of 1.5 and 5.7 and the effects of jet velocity profile and boundary layer thickness on the jet trajectory are examined. The ‘rd’ scaling used at present (Margason 1993) does not contain any information on these parameters, and trajectories scaled by rd do not collapse. The trajectory is strongly influenced by the near field which depends on both the jet velocity profile and the crossflow boundary layer. A length scale is proposed to describe the near field of the jet. An analytical expression is proposed for this length scale which is a measure of the relative inertia of the jet and the crossflow. Incorporating this length scale significantly improves the scaling of the trajectories.

Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure

Abstract: This paper deals with an experimental and numerical study of the dynamics of an underwater explosion and its associated fluid–structure interaction. Experimental studies of the complex fluid–structure interaction phenomena were carried out in a specially designed test pond. The pond is equipped with a high-speed camera and pressure and displacement sensors. The high-speed camera was used to capture the expansion and collapse of the gas bubble created by the explosion. Several different structures were used in the experiments, including both rigid and resilient plates of circular shape. The deformation of the plate was measured with a non-contact laser telemetry device. The numerical simulations of the explosion bubble interacting with a submerged resilient structure were performed using a three-dimensional bubble dynamics code in conjunction with a structural code. The bubble code is based on the boundary-element method (BEM) and has been coupled to a structural finite-element code (PAM-CRASH. The experimental results were compared against the numerical results for different bubble–structure configurations and orientations. Several physical phenomena that have been observed, such as bubble jetting and bubble migration towards the structure are discussed.

Unsteady aerodynamics of fluttering and tumbling plates

Abstract: We investigate the aerodynamics of freely falling plates in a quasi-two-dimensional flow at Reynolds number of , which is typical for a leaf or business card falling in air. We quantify the trajectories experimentally using high-speed digital video at sufficient resolution to determine the instantaneous plate accelerations and thus to deduce the instantaneous fluid forces. We compare the measurements with direct numerical solutions of the two-dimensional Navier–Stokes equation. Using inviscid theory as a guide, we decompose the fluid forces into contributions due to acceleration, translation, and rotation of the plate. For both fluttering and tumbling we find that the fluid circulation is dominated by a rotational term proportional to the angular velocity of the plate, as opposed to the translational velocity for a glider with fixed angle of attack. We find that the torque on a freely falling plate is small, i.e. the torque is one to two orders of magnitude smaller than the torque on a glider with fixed angle of attack. Based on these results we revise the existing ODE models of freely falling plates. We get access to different kinds of dynamics by exploring the phase diagram spanned by the Reynolds number, the dimensionless moment of inertia, and the thickness-to-width ratio. In agreement with previous experiments, we find fluttering, tumbling, and apparently chaotic motion. We further investigate the dependence on initial conditions and find brief transients followed by periodic fluttering described by simple harmonics and tumbling with a pronounced period-two structure. Near the cusp-like turning points, the plates elevate, a feature which would be absent if the lift depended on the translational velocity alone.

Clustering of aerosol particles in isotropic turbulence

Abstract: It has been recognized that particle inertia throws dense particles out of regions of high vorticity and leads to an accumulation of particles in the straining-flow regions of a turbulent flow field. However, recent direct numerical simulations (DNS) indicate that the tendency to cluster is evident even at particle separations smaller than the size of the smallest eddy. Indeed, the particle radial distribution function (RDF), an important measure of clustering, increases as an inverse power of the interparticle separation for separations much smaller than the Kolmogorov length scale. Motivated by this observation, we have developed an analytical theory to predict the RDF in a turbulent flow for particles with a small, but non-zero Stokes number. Here, the Stokes number (. Predictions of the analytical theory are compared with two types of numerical simulation: (i) particle pairs interacting in a local linear flow whose velocity varies according to a stochastic velocity gradient model; (ii) particles interacting in a flow field obtained from DNS of isotropic turbulence. The agreement with both types of simulation is very good. The theory also predicts the RDF for unlike particle pairs (particle pairs with different Stokes numbers). In this case, a second diffusion process occurs owing to the difference in the response of the pair to local fluid accelerations. The acceleration diffusivity is independent of the pair separation distance; thus, the RDF of particles with even slightly different viscous relaxation times undergoes a transition from the power law behaviour at large separations to a constant value at sufficiently small separations. The radial separation corresponding to the transition between these two behaviours is predicted to be proportional to the difference between the Stokes numbers of the two particles. Once again, the agreement between the theory and simulations is found to be very good. Clustering of particles enhances their rate of coagulation or coalescence. The theory and linear flow simulations are used to obtain predictions for the rate of coagulation of particles in the absence of hydrodynamic and colloidal particle interactions.

Wall-induced forces on a rigid sphere at finite Reynolds number

Abstract: We perform direct numerical simulations of a rigid sphere translating parallel to a flat wall in an otherwise quiescent ambient fluid. A spectral element method is employed to perform the simulations with high accuracy. For above about 100. Detailed analysis of the flow field around the sphere suggests that this increase is due to an imperfect bifurcation resulting in the formation of a double-threaded wake vortical structure. In addition to a non-rotating sphere, we also simulate a freely rotating sphere in order to assess the importance of free rotation on the translational motion of the sphere. We observe the effect of sphere rotation on lift and drag forces to be small. We also explore the effect of the wall on the onset of unsteadiness.

Probability distributions of surface gravity waves during spectral changes

Abstract: Simulations have been performed with a fairly narrow band numerical gravity wave model (higher-order NLS type) and a computational domain of dimensions 128 x 128 typical wavelengths. The simulations are initiated with ∼ 6 x 10 4 Fourier modes corresponding to truncated JONSWAP spectra and different angular distributions giving both short- and long-crested waves. A development of the spectra on the so-called Benjamin-Feir timescale is seen, similar to the one reported by Dysthe et al. (J. Fluid Mech. vol. 478, 2003, p. 1). The probability distributions of surface elevation and crest height are found to fit theoretical distributions found by Tayfun (J. Geophys. Res. vol. 85, 1980, p. 1548) very well for elevations up to four standard deviations (for realistic angular spectral distributions). Moreover, in this range of the distributions, the influence of the spectral evolution seems insignificant. For the extreme parts of the distributions a significant correlation with the spectral change can be seen for very long-crested waves. For this case we find that the density of large waves increases during spectral change, in agreement with a recent experimental study by Onorato et al. (J. Fluid Mech. 2004 submitted).

Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations

Abstract: This is a publisher’s version of an article published in Journal of Fluid Mechanics © 2005 Cambridge University Press. www.cambridge.org/

Runup and rundown generated by three-dimensional sliding masses

Abstract: To study the waves and runup/rundown generated by a sliding mass, a numerical simulation model, based on the large-eddy-simulation (LES) approach, was developed. The Smagorinsky subgrid scale model was employed to provide turbulence dissipation and the volume of fluid (VOF) method was used to track the free surface and shoreline movements. A numerical algorithm for describing the motion of the sliding mass was also implemented. To validate the numerical model, we conducted a set of large-scale experiments in a wave tank of 104m long, 3.7m wide and 4.6m deep with a plane slope (1:2) located at one end of the tank. A freely sliding wedge with two orientations and a hemisphere were used to represent landslides. Their initial positions ranged from totally aerial to fully submerged, and the slide mass was also varied over a wide range. The slides were instrumented to provide position and velocity time histories. The time-histories of water surface and the runup at a number of locations were measured. Comparisons between the numerical results and experimental data are presented only for wedge shape slides. Very good agreement is shown for the time histories of runup and generated waves. The detailed three-dimensional complex flow patterns, free surface and shoreline deformations are further illustrated by the numerical results. The maximum runup heights are presented as a function of the initial elevation and the specific weight of the slide. The effects of the wave tank width on the maximum runup are also discussed.

Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry

Abstract: Particle image velocimetry experiments have been performed in a turbulent boundary-layer wind tunnel in order to study the coherent structures taking part in the generation and preservation of wall turbulence. The particular wind tunnel used is suitable for high-resolution experiments ($delta gt 0.3$ m) at high Reynolds numbers (up to $R_{theta} = 19,000$ in the present results). Eddy structures were identified in instantaneous velocity maps in order to determine their mean characteristics and possible relationships between these structures. In the logarithmic region, the results show that the observed eddy structures appear to organize like elongated vortices, tilted downstream, mainly at an angle of about 45° and having a cane shape. The characteristics of these vortices appear here to be universal in wall units for $R_{theta},{leq},19,000$. They seem to find their origin at a wall distance of about 25 wall units as quasi-streamwise vortices and to migrate away from the wall while tilting to form a head and a leg. Away from the wall, their radius increases and their vorticity decreases very slowly so that their circulation is nearly constant. Near the wall, the picture obtained is in fair agreement with existing models. The analysis of the results indicates a universality of the buffer-layer mechanism, even at low Reynolds number, and a sensitivity of the logarithmic region to low-Reynolds-number effects.

Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution : theoretical formalism and numerical study

Abstract: The velocity distribution of dilute suspensions of heavy particles in gas–solid turbulent flows is investigated. A statistical approach – the mesoscopic Eulerian formalism (MEF) – is developed in which an average conditioned on a realization of the turbulent carrier flow is introduced and enables a decomposition of the instantaneous particle velocity into two contributions. The first is a contribution from an underlying continuous turbulent velocity field shared by all the particles – the mesoscopic Eulerian particle velocity field (MEPVF) – that accounts for all particle–particle and fluid–particle two-point correlations. The second contribution corresponds to a distribution – the quasi-Brownian velocity distribution (QBVD) – that represents a random velocity component satisfying the molecular chaos assumption that is not spatially correlated and identified with each particle of the system. The MEF is used to investigate properties of statistically stationary particle-laden isotropic turbulence. The carrier flow is computed using direct numerical simulation (DNS) or large-eddy simulation (LES) with discrete particle tracking employed for the dispersed phase. Particle material densities are much larger than that of the fluid and the force of the fluid on the particle is assumed to reduce to the drag contribution. Computations are performed in the dilute regime for which the influences of inter-particle collisions and fluid-turbulence modulation are neglected. The simulations show that increases in particle inertia increase the contribution of the quasi-Brownian component to the particle velocity. The particle velocity field is correlated at larger length scales than the fluid, with the integral length scales of the MEPVF also increasing with particle inertia. Consistent with the previous work of Abrahamson (1975), the MEF shows that in the limiting case of large inertia, particle motion becomes stochastically equivalent to a Brownian motion with a random spatial distribution of positions and velocities. For the current system of statistically stationary isotropic turbulence, both the DNS and LES show that the fraction of the kinetic energy residing in the mesoscopic field decreases with particle inertia as the square root of the ratio of the total particulate-phase kinetic energy to that of the fluid.

Turbulent entrainment in jets with arbitrary buoyancy

Abstract: Explosive volcanic jets present an unusual dynamic situation of reversing buoyancy. Their initially negative buoyancy with respect to ambient fluid first opposes the motion, but can change sign to drive a convective plume if a sufficient amount of entrainment occurs. The key unknown is the entrainment behaviour for the initial flow regime in which buoyancy acts against the momentum jet. To describe and constrain this regime, we present an experimental study of entrainment into turbulent jets of negative and reversing buoyancy. Using an original technique based on the influence of the injection radius on the threshold between buoyant convection and partial collapse, we show that entrainment is significantly reduced by negative buoyancy. We develop a new theoretical parameterization of entrainment as a function of the local (negative) Richardson number that (i) predicts the observed reduction of entrainment and (ii) introduces a similarity drift in the velocity and buoyancy profiles as a function of distance from source. This similarity drift allows us to reconcile the different estimates found in the literature for entrainment in plumes.

Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows

Abstract: The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a pre­ dominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular signi­ ficance is attached to the viscous/Reynolds-stress-gradient balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In parti­ cular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds num ber approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds num ber and have the same order of magnitude, there is additional theore­ tical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged momentum balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.

Granular collapse in two dimensions

Abstract: An experimental investigation is conducted into the collapse of granular columns inside rectangular channels. The final shape is documented for slumps inside relatively wide channels, and for collapses inside much narrower slots. In both cases, the collapse is initiated by withdrawing a swinging gate or sliding door, and the flow remains fairly two-dimensional. Four different granular media are used; the properties of the materials vary significantly, notably in their angles of friction for basal sliding and internal deformation. If ). In all cases, the numerical constant of proportionality in these scaling relations shows clear material dependence. In wide slots, there is no obvious universal scaling behaviour of the final profile, but such a behaviour is evident in narrow slots. The experimental results are compared with theoretical results based on a shallow granular-flow model. The qualitative behaviour of the slump in the wide slot is reproduced by the theoretical model. However, there is qualitative disagreement between theory and the experiments in the narrow slot because of the occurrence of secondary surface avalanching.

Secondary instability of crossflow vortices

Abstract: Crossflow-dominated swept-wing boundary layers are known to undergo a highly nonlinear transition process. In low-disturbance environments, the primary instability of these flows consists mainly of stationary streamwise vortices that modify the mean velocity field and hence the stability characteristics of the boundary layer. The result is amplitude saturation of the dominant stationary mode and strong spanwise modulation of the unsteady modes. Breakdown is not caused by the primary instability but instead by a high-frequency secondary instability of the shear layers of the distorted mean flow. The secondary instability has been observed in several previous experiments and several computational models for its behaviour exist. None of the experiments has been sufficiently detailed to allow either model validation or transition correlation. The present experiment conducted using a 45 ◦ swept wing in the low-disturbance Arizona State University Unsteady Wind Tunnel addresses the secondary instability in a detailed fashion under a variety of conditions. The results reveal that this instability is active in the breakdown of all cases investigated, and furthermore, it appears to be well-described by the computational models.

Wave capture and wave-vortex duality

Abstract: New and unexpected results are presented regarding the nonlinear interactions between a wavepacket and a vortical mean flow, with an eye towards internal wave dynamics in the atmosphere and oceans and the problem of ‘missing forces’ in atmospheric gravity-wave parametrizations. The present results centre around a prewave-breaking scenario termed ‘wave capture’, which differs significantly from the standard such scenarios associated with critical layers or mean density decay with altitude. We focus on the peculiar wave–mean interactions that accompany wave capture. Examples of these interactions are presented for layerwise-two-dimensional, layerwise-non-divergent flows in a three-dimensional Boussinesq system, in the strongstratification limit. The nature of the interactions can be summarized in the phrase ‘wave–vortex duality’, whose key points are firstly that wavepackets behave in some respects like vortex pairs, as originally shown in the pioneering work of Bretherton (1969), and secondly that a collection of interacting wavepackets and vortices satisfies a conservation theorem for the sum of wave pseudomomentum and vortex impulse, provided that the impulse is defined appropriately. It must be defined as the rotated dipole moment of the Lagrangian-mean potential vorticity (PV). This PV differs crucially from the PV evaluated from the curl of either the Lagrangian-mean or the Eulerian-mean velocity. The results are established here in the strong-stratification limit for rotating (quasi-geostrophic) as well as for non-rotating systems. The concomitant momentum budgets can be expected to be relatively complicated, and to involve far-field recoil effects in the sense discussed in B¨ & McIntyre (2003). The results underline the three-way distinction between impulse, pseudomomentum, and momentum. While momentum involves the total velocity field, impulse and pseudomomentum involve, in different ways, only the vortical part of the velocity field.

Three-dimensional instabilities and transition of steady and pulsatile axisymmetric stenotic flows

Abstract: A straight tube with a smooth axisymmetric constriction is an idealized representation of a stenosed artery. We examine the three-dimensional instabilities and transition to turbulence of steady flow, steady flow plus an oscillatory component, and an idealized vascular pulsatile flow in a tube with a smooth 75 % stenosis using both linear stability analysis and direct numerical simulation. Steady flow undergoes a weak Coanda-type wall attachment and turbulent transition through a subcritical bifurcation, leading to hysteretic behaviour with respect to changes in Reynolds number. The pulsatile flows become unstable through a subcritical period-doubling bifurcation involving alternating tilting of the vortex rings that are ejected from the throat with each pulse. These tilted vortex rings rapidly break down through a self-induction mechanism within the confines of the tube. While the linear instability modes for pulsatile flow have maximum energy well downstream of the stenosis, we have established using direct numerical simulation that breakdown can gradually propagate upstream until it occurs within a few tube diameters of the constriction, in agreement with previous experimental observations. At the Reynolds numbers employed in the present study, transition is localized, with relaminarization occurring further downstream. A non-exhaustive investigation has also been undertaken into the receptivity of the axisymmetric shear layer in the idealized physiological pulsatile flow, with the results suggesting it has localized convective instability over part of the pulse cycle.

Mode interaction and the bypass route to transition

Abstract: The manner by which external vortical disturbances penetrate the laminar boundary layer and induce transition is explored. Linear theory suggests that the well-known Klebanoff mode precursor to transition can be understood as a superposition of Squire continuous modes. Shear sheltering influences the ability of free-stream disturbances to generate a packet of Squire modes. A coupling coefficient between continuous spectrum spectrum Orr–Sommerfeld and Squire modes is used to characterize the interaction. Full numerical simulations with prescribed modes at the inlet substantiate this approach. With two weakly coupled modes at the inlet, the boundary layer is little perturbed; with two strongly coupled modes, Klebanoff modes are produced; with one strongly coupled and one weakly coupled high-frequency mode, the complete transition process is simulated.

Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers

Abstract: © Cambridge University Press. Hutchins, N., Hambleton, W. T., & Marusic, I. (2005). Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. Journal of Fluid Mechanics, 541, 21-54. http://www.jfm.damtp.cam.ac.uk/