This paper describes a study of the local and global effect of an isolated group of cylinders on an incident uniform flow. Using high resolution two-dimensional computations, we analysed the flow through and around a localised circular array of cylinders, where the ratio of array diameter (DG) to cylinder diameter (D) is 21. The number of cylinders varied from NC = 7 to 133, and they were arranged in a series of concentric rings to allow even distribution within the array with an average void fraction φ = NC(D/DG)2, which varied from 0.016 to 0.30. The characteristic Reynolds number of the array was ReG = 2100. A range of diagnostic tools were applied, including the lift/drag forces on each cylinder (and the whole array), Eulerian and Lagrangian average velocity within the array, and the decay of maximum vorticity with distance downstream. To interpret the flow field, we used vorticity and the dimensionless form of the second invariant of the velocity gradient tensor. A mathematical model, based on representing the bodies as point forces, sources and dipoles, was applied to interpret the results. Three distinct flow regimes were identified. For low void fractions (φ < 0.05), the cylinders have uncoupled individual wake patterns, where the vorticity is rapidly annihilated by wake intermingling downstream and the forces are similar to that of an isolated cylinder. At intermediate void fractions (0.05 < φ < 0.15), a shear layer is generated at the shoulders of the array and the force acting on the cylinders is steady. For high void fractions (φ > 0.15), the array generates a wake in a similar way to a solid body of the same scale. For low void fraction arrays, the mathematical model provides a reasonable assessment of the forces on individual bodies within the array, the Eulerian mean velocity and the upstream velocity field. While it broadly captures the change in the rate of decay of the maximum vorticity magnitude Ωmax downstream, the magnitude is underpredicted.

Fluid particles can have a mean motion in time, even when the Eulerian mean flow disappears everywhere in space. In the present article, we demonstrate that this phenomenon, known as the Stokes drift, plays an essential role in the problem of magnetic field generation by fluctuation flows (kinematic dynamo) at high Rm. At leading order, the dynamo is generated by the Stokes drift that acts as if it were a mean flow. This result is derived from a mean-field dynamo theory in terms of time averages, which reveals how classical expressions for alpha and beta tensors actually recombine into a single Stokes drift contribution. In a test case, we find fluctuation flows that have a G. O. Roberts flow as Stokes drift and this allows to confront our model to direct integration of the induction equation. We find an excellent quantitative agreement between the prediction of our model and the results of our simulations. We finally apply our Stokes drift model to prove that a broad class of inertial waves in rapidly rotating flows cannot drive a dynamo.

We investigate the mixing of a warm enclosed space by a series of discrete gusts of cold air from a high-level opening. Initially we examine the case of a series of gusts of identical size each modelled as a turbulent buoyant thermal. We develop a model of the filling box-like flow which develops in the space and identify the key parameter in the system as the ratio between the initial gust size and the product of the height of the room and the entrainment coefficient. We find an approximate analytic solution for the evolution of the density profile within the space which is in good agreement with a full numerical solution of the governing equations. We successfully test the predictions of the model with a series of new laboratory experiments. The experiments combined with the model also provide a new independent estimate for the entrainment coefficient of a thermal, ε = 0.37 ± 0.02, based on the propagation speed of a filling box front. We then examine the mixing produced by a series of thermals of non-identical size which we characterize in terms of a mean size and coefficient of variation. We find that as the coefficient of variation increases, the density profile becomes progressively more stratified owing to the asymmetry of dilution through entrainment of large and small thermals. We discuss the implications of these results for the ventilation of a building subject to gusts of wind.

The finite-Reynolds-number three-dimensional flow in a channel bounded by one and two parallel porous walls is studied numerically. The porous medium is modelled by spheres in a simple cubic arrangement. Detailed results on the flow structure and the hydrodynamic forces and couple acting on the sphere layer bounding the porous medium are reported and their dependence on the Reynolds number illustrated. It is shown that, at finite Reynolds numbers, a lift force acts on the spheres, which may be expected to contribute to the mobilization of bottom sediments. The results for the slip velocity at the surface of the porous layers are compared with the phenomenological Beavers–Joseph model. It is found that the values of the slip coefficient for pressure-driven and shear-driven flow are somewhat different, and also depend on the Reynolds number. A modification of the relation is suggested to deal with these features. The Appendix provides an alternative derivation of this modified relation.

Lattice Boltzmann and immersed boundary methods are used to conduct direct numerical simulations of suspensions of massless, spherical gas bubbles driven by buoyancy in a three-dimensional periodic domain. The drag coefficient CD is computed as a function of the gas volume fraction φ and the Reynolds number Re = 2RUslip/ν for 0.03 φ 0.5 and 5 Re 2000. Here R, Uslip and ν denote the bubble radius, the slip velocity between the liquid and the gas phases and the kinematic viscosity of the liquid phase, respectively. The results are rationalized by assuming a similarity between the CD(Reeff)-relation of the suspension and the CD(Re)-relation of an individual bubble, where the effective Reynolds number Reeff = 2RUslip/νeff is based on the effective viscosity νeff which depends on the properties of the suspension. For Re ≲ 100, we find νeff ≈ ν/(1−0.6φ1/3), which is in qualitative agreement with previous proposed correlations for CD in bubble suspensions. For Re ≳ 100, on the other hand, we find νeff ≈ RUslipφ, which is explained by considering the turbulent kinetic energy levels in the liquid phase. Based on these findings, a correlation is constructed for CD(Re, φ). A modification of the drag correlation is proposed to account for effects of bubble deformation, by the inclusion of a correction factor based on the theory of Moore (J. Fluid Mech., vol. 23, 1995, p. 749).

We develop an asymptotic theory for marine ice sheets from a first-principles Stokes flow contact problem, in which different boundary conditions apply to areas where ice is in contact with bedrock and inviscid sea water, along with suitable inequalities on normal stress and boundary location constraining contact and non-contact zones. Under suitable assumptions about basal slip in the contact areas, the boundary-layer structure for this problem replicates the boundary layers previously identified for marine ice sheets from depth-integrated models and confirms the results of these previous models: the interior of the grounded ice sheet can be modelled as a standard free-surface lubrication flow, while coupling with the membrane-like floating ice shelf leads to two boundary conditions on this lubrication flow model at the contact line. These boundary conditions determine ice thickness and ice flux at the contact line and allow the lubrication flow model with a contact line to be solved as a moving boundary problem. In addition, we find that the continuous transition of vertical velocity from grounded to floating ice requires the presence of two previously unidentified boundary layers. One of these takes the form of a viscous beam, in which a wave-like surface feature leads to a continuous transition in surface slope from grounded to floating ice, while the other provides boundary conditions on this viscous beam at the contact line.

For flows at supercritical pressure, p, the large-eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid-scale (SGS) fluxes but also new SGS terms, each denoted as a ‘correction’. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations and represent differences, other than contributed by the convection terms, between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) which is the difference between the filtered divergence of the molecular heat flux and the divergence of the molecular heat flux computed as a function of the filtered flow field. We revisit here a previous a priori study where we only had partial success in modelling the q-correction term and show that success can be achieved using a different modelling approach. This a priori analysis, based on a temporal mixing-layer direct numerical simulation database, shows that the focus in modelling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES molecular heat-flux calculation. Furthermore, an a posteriori study is conducted for temporal mixing layers initially containing oxygen (O) in the lower stream and hydrogen (H) or helium (He) in the upper stream to examine the benefit of the new model. Results show that for any LES including SGS-flux models (constant-coefficient gradient or scale-similarity models; dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/gradient models), the inclusion of the q-correction in LES leads to the theoretical maximum reduction of the SGS molecular heat-flux difference; the remaining error in modelling this new subgrid term is thus irreducible. The impact of the q-correction model first on the molecular heat flux and then on the mean, fluctuations, second-order correlations and spatial distribution of dependent variables is also demonstrated. Discussions on the utilization of the models in general LES are presented.

This paper presents a numerical and theoretical investigation of the sound generated by premixed flame annihilation. Planar, axisymmetric and spherically symmetric flame annihilation events are considered. The compressible Navier–Stokes, energy and progress variable equations are first solved using simple chemistry simulations, resolving both the flame dynamics and the acoustics. These simulations show that the amplitude of the far-field sound produced by the annihilation events depends on the flame thickness, particularly for the axisymmetric and spherically symmetric flame annihilation events. The flame propagation velocity is also always observed to increase significantly prior to flame annihilation, which is in keeping with other reported experimental and numerical studies. A theory is then presented that relates the far-field sound to the flame annihilation event by using a previously reported and extended form of Lighthill's acoustic analogy. A comparison with the numerical results shows that this theory accurately represents the far-field sound produced by considering only the temporal heat release source term in Lighthill's acoustic analogy, as reported by others. Additional assumptions of an infinitely thin flame and constant flame speed are then invoked in an attempt to simplify the problem. In the planar annihilation, this theory results in good predictions of the overall pressure change. However, these assumptions lead to significant under-prediction of the amplitude of far-field sound produced for the axisymmetric and spherically symmetric annihilation events. Finally, dimensional reasoning supported by the simulations and theory is used to develop scalings of the far-field sound in terms of the flame parameters.

We consider theoretically, computationally and experimentally spontaneous evaporation of water and isopropanol drops on smooth silicon wafers. In contrast to a number of previous works, the solid surface we consider is smooth and therefore the droplets' evolution proceeds without contact line pinning. We develop a theoretical model for evaporation of pure liquid drops that includes Marangoni forces due to the thermal gradients produced by non-uniform evaporation, and heat conduction effects in both liquid and solid phases. The key ingredient in this model is the evaporative flux. We consider two commonly used models: one based on the assumption that the evaporation is limited by the processes originating in the gas (vapour diffusion-limited evaporation), and the other one which assumes that the processes in the liquid are limiting. Our theoretical model allows for implementing evaporative fluxes resulting from both approaches. The required parameters are obtained from physical experiments. We then carry out fully nonlinear time-dependent simulations and compare the results with the experimental ones. Finally, we discuss how the simulation results can be used to predict which of the two theoretical models is appropriate for a particular physical experiment.

An investigation into parameters affecting separation in normal shock wave/boundary layer interactions (SBLIs) has been conducted. It has been shown that the effective aspect ratio of an experimental facility (defined as δ*/tunnel width) is a critical factor in determining when shock-induced separation will occur. Experiments examining M∞ = 1.4 and 1.5 normal shock waves in a wind tunnel with a small rectangular cross-section have been performed and show that a link exists between the extent of shock-induced separation on the tunnel centre-line and the size of corner-flow separations. In tests where the corner-flows were modified ahead of the shock (through suction and vortex generators), the extent of separation around the tunnel centre-line was seen to vary significantly. These observations are attributed to the way corner flows modify the three-dimensional shock-structure and the impact this has on the magnitude of the adverse pressure gradient experienced by the tunnel wall boundary layers.

The direct numerical simulation of the flow over a sphere is performed. The computations are carried out in the sub-critical regime at Re = 3700 (based on the free-stream velocity and the sphere diameter). A parallel unstructured symmetry-preserving formulation is used for simulating the flow. At this Reynolds number, flow separates laminarly near the equator of the sphere and transition to turbulence occurs in the separated shear layer. The vortices formed are shed at a large-scale frequency, St = 0.215, and at random azimuthal locations in the shear layer, giving a helical-like appearance to the wake. The main features of the flow including the power spectra of a set of selected monitoring probes at different positions in the wake of the sphere are described and discussed in detail. In addition, a large number of turbulence statistics are computed and compared with previous experimental and numerical data at comparable Reynolds numbers. Particular attention is devoted to assessing the prediction of the mean flow parameters, such as wall-pressure distribution, skin friction, drag coefficient, among others, in order to provide reliable data for testing and developing statistical turbulence models. In addition to the presented results, the capability of the methodology used on unstructured grids for accurately solving flows in complex geometries is also pointed out.

Many flows especially in geophysics involve turbulent boundary layers forming over rough surfaces with multiscale height distribution. Such surfaces pose special challenges for large-eddy simulation (LES) when the filter scale is such that only part of the roughness elements of the surface can be resolved. Here we consider LES of flows over rough surfaces with power-law height spectra Eh(k) ~ kβs (−3 ≤ βs < −1), as often encountered in natural terrains. The surface is decomposed into resolved and subgrid-scale height contributions. The effects of the unresolved small-scale height fluctuations are modelled using a local equilibrium wall model (log-law or Monin–Obukhov similarity), but the required hydrodynamic roughness length must be specified. It is expressed as the product of the subgrid-scale root-mean-square of the height distribution and an unknown dimensionless quantity, α, the roughness parameter. Instead of specifying this parameter in an ad hoc empirical fashion, a dynamic methodology is proposed based on test-filtering the surface forces and requiring that the total drag force be independent of filter scale or resolution. This dynamic surface roughness (DSR) model is inspired by the Germano identity traditionally used to determine model parameters for closing subgrid-scale stresses in the bulk of a turbulent flow. A series of LES of fully developed flow over rough surfaces are performed, with surfaces built using random-phase Fourier modes with prescribed power-law spectra. Results show that the DSR model yields well-defined, rapidly converging, values of α. Effects of spatial resolution and spectral slopes are investigated. The accuracy of the DSR model is tested by showing that predicted mean velocity profiles are approximately independent of resolution for the dynamically computed values of α, whereas resolution-dependent results are obtained when using other, incorrect, α values. Also, strong dependence of α on βs is found, where α ranges from α ~ 0.1 for βs = −1.2 to α ~ 10−5 for βs = −3.

This paper investigates the non-normal nature of premixed flame–acoustic interaction. The thermoacoustic system is modelled using the acoustic equations for momentum and energy, together with the equation for the evolution of the flame front obtained from the kinematic G-equation. As the unsteady heat addition acts as a volumetric source, the flame front is modelled as a distribution of monopole sources. Evolutions of the system are characterized with a measure of energy due to fluctuations. In addition to the acoustic energy, the energy due to fluctuations considered in the present paper accounts for the energy of the monopole sources. The linearized operator for this thermoacoustic system is non-normal, leading to non-orthogonality of its eigenvectors. Non-orthogonal eigenvectors can cause transient growth even when all the eigenvectors are decaying. Therefore, classical linear stability theory cannot predict the finite-time transient growth observed in non-normal systems. In the present model, the state space variables include the monopole source strengths in addition to the acoustic variables. Inclusion of these variables in the state space is essential to account for the transient growth due to non-normality. A parametric study of the variation in transient growth due to change in parameters such as flame location and flame angle is performed. In addition to projections along the acoustic variables of velocity and pressure, the optimal initial condition for the self-evolving system has significant projections along the strength of the monopole distribution. Comparison of linear and corresponding nonlinear evolutions highlights the role of transient growth in subcritical transition to instability. The notion of phase between acoustic pressure and heat release rate as an indicator of stability is examined.

The flow over a pair of counter-rotating cylinders is investigated numerically and experimentally. It is demonstrated that it is possible to suppress unsteady vortex shedding for gap sizes from one to five cylinder diameters, at Reynolds numbers from 100 to 200, expanding on the more limited work by Chan & Jameson (Intl J. Numer. Meth. Fluids, vol. 63, 2010, p. 22). The degree of unsteady wake suppression is proportional to the speed and the direction of rotation, and there is a critical rotation rate where a complete suppression of flow unsteadiness can be achieved. In the doublet-like configuration at higher rotational speeds, a virtual elliptic body that resembles a potential doublet is formed, and the drag is reduced to zero. The shape of the elliptic body primarily depends on the gap between the two cylinders and the speed of rotation. Prior to the formation of the elliptic body, a second instability region is observed, similar to that seen in studies of single rotating cylinders. It is also shown that the unsteady wake suppression can be achieved by rotating each cylinder in the opposite direction, that is, in a reverse doublet-like configuration. This tends to minimize the wake interaction of the cylinder pair and the second instability does not make an appearance over the range of speeds investigated here.

The spatio-temporal evolution of a turbulent swirling jet undergoing vortex breakdown has been investigated. Experiments suggest the existence of a self-excited global mode having a single dominant frequency. This oscillatory mode is shown to be absolutely unstable and leads to a rotating counter-winding helical structure that is located at the periphery of the recirculation zone. The resulting time-periodic 3D velocity field is predicted theoretically as being the most unstable mode determined by parabolized stability analysis employing the mean flow data from experiments. The 3D oscillatory flow is constructed from uncorrelated 2D snapshots of particle image velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and an azimuthal symmetry associated with helical structures. Stability-derived modes and empirically derived modes correspond remarkably well, yielding prototypical coherent structures that dominate the investigated flow region. The proposed method of constructing 3D time-periodic velocity fields from uncorrelated 2D data is applicable to a large class of turbulent shear flows.

We present a study of polygons forming on the free surface of a water flow confined to a stationary cylinder and driven by a rotating bottom plate as described by Jansson et al. (Phys. Rev. Lett., vol. 96, 2006, 174502). In particular, we study the case of a triangular structure, either completely ‘wet’ or with a ‘dry’ centre. For the dry structures, we present measurements of the surface shapes and the process of formation. We show experimental evidence that the formation can take place as a two-stage process: first the system approaches an almost stable rotationally symmetric state and from there the symmetry breaking proceeds like a low-dimensional linear instability. We show that the circular state and the unstable manifold connecting it with the polygon solution are universal in the sense that very different initial conditions lead to the same circular state and unstable manifold. For a wet triangle, we measure the surface flows by particle image velocimetry (PIV) and show that there are three vortices present, but that the strength of these vortices is far too weak to account for the rotation velocity of the polygon. We show that partial blocking of the surface flow destroys the polygons and re-establishes the rotational symmetry. For the rotationally symmetric state our theoretical analysis of the surface flow shows that it consists of two distinct regions: an inner, rigidly rotating centre and an outer annulus, where the surface flow is that of a point vortex with a weak secondary flow. This prediction is consistent with the experimentally determined surface flow.

The velocity and shape of Taylor bubbles moving in a vertical channel in a Poiseuille liquid flow were studied for the inertial regime, characterized by large Reynolds numbers. Numerical experiments were carried out for positive (upward) and negative (downward) liquid mean velocity. Previous investigations in tube have reported that for upward flow the bubble is symmetric and its velocity follows the law of Nicklin, whereas for certain downward flow conditions the symmetry is broken and the bubble rises appreciably faster. To study the bubble motion and to identify the existence of a transition, a two-dimensional numerical code that solves the Navier–Stokes equations (through a volume of fluid implementation) was used to obtain the bubble shape and the rise velocity for different liquid mean velocities. A reference frame located at the bubble tip and an irregular grid were implemented to allow long simulation times without an excessively large numerical domain. It was observed that whenever the mean liquid velocity exceeded some critical value, bubbles adopted a symmetric final shape even though their initial shape was asymmetric. Conversely, if the mean liquid velocity was smaller than the critical value, a transition to a non-symmetric shape occurred, along with a correspondingly faster velocity. It was also found that surface tension has a stabilizing effect on the transition.

We present an analytical, numerical and experimental study of advective dispersion in isotachophoresis (ITP). We analyse the dynamics of the concentration field of a focused analyte in peak mode ITP. The analyte distribution is subject to electromigration, diffusion and advective dispersion. Advective dispersion results from strong internal pressure gradients caused by non-uniform electro-osmotic flow (EOF). Analyte dispersion strongly affects the sensitivity and resolution of ITP-based assays. We perform axisymmetric time-dependent numerical simulations of fluid flow, diffusion and electromigration. We find that analyte properties contribute greatly to dispersion in ITP. Analytes with mobility values near those of the trailing (TE) or leading electrolyte (LE) show greater penetration into the TE or LE, respectively. Local pressure gradients in the TE and LE then locally disperse these zones of analyte penetration. Based on these observations, we develop a one-dimensional analytical model of the focused sample zone. We treat the LE, TE and LE–TE interface regions separately and, in each, assume a local Taylor–Aris-type effective dispersion coefficient. We also performed well-controlled experiments in circular capillaries, which we use to validate our simulations and analytical model. Our model allows for fast and accurate prediction of the area-averaged sample distribution based on known parameters including species mobilities, EO mobility, applied current density and channel dimensions. This model elucidates the fundamental mechanisms underlying analyte advective dispersion in ITP and can be used to optimize detector placement in detection-based assays.

In natural convection, driven by an unstable density difference due to a heavier fluid (brine) above a lighter fluid (water) across a horizontal permeable membrane, we discover a new regime of convection, where the Sherwood number (Sh) scales approximately as the Rayleigh number (Ra). Inferring from the planforms of plume structure on the membrane and the estimates of velocity through the membrane, we show that such a regime occurs when advection balances diffusion in the membrane, i.e. the Péclet number based on the membrane thickness (Pe) is of order one. The advection is inferred to be caused by the impingement of the large-scale flow on the membrane. Utilizing mass balance and symmetry assumptions in the top and the bottom fluids, we derive an expression for the concentration profile in the membrane pore in the new regime by solving the convection–diffusion equation in the membrane pore; this helps us to obtain the concentration drops above and below the membrane that drive the convection. We find that the net flux, normalised by the diffusive flux corresponding to the concentration drop on the side opposite to the impingement of the large-scale flow remains constant throughout the new regime. On the basis of this finding, we then obtain an expression for the flux scaling in the new regime which matches with the experiments; the expression has the correct asymptotes of flux scaling in the advection and the diffusion regimes. The plume spacings in the new regime are distributed lognormally, and their mean follows the trend in the advection regime.

The rate of change of the perturbation's kinetic energy E of a perturbed inviscid, incompressible, axisymmetric, columnar and near-critical swirling flow in a finite-length, straight, circular pipe with periodic and non-periodic inlet–outlet conditions is studied using the Reynolds–Orr equation. The perturbation's mode shape and growth rate are computed from the linear-stability eigenvalue problem using a novel asymptotic solution in the case of a flow in a long pipe. This solution technique is general and can be applied to any vortex flow profile, in a range of swirl levels around the critical level, and for various boundary conditions. The solutions are used to analytically estimate the production (or loss) of E at the pipe boundaries and inside the domain and to shed new light on the Wang–Rusak mechanism of exchange of global stability around the critical swirl, that is leading to the vortex breakdown process. It is shown that the production of E inside the domain is modulated by the base flow strain-rate tensor. For the special case of a solid-body rotating flow, this term vanishes and the stability is determined only by the asymmetric transfer of E at the boundaries. For a general base flow, the dominant perturbation's mode shape develops deviations in response to the non-periodic inlet–outlet conditions. These deviations couple with the base flow strain-rate tensor to generate production or loss of E in the bulk. Together with the asymmetric transfer of E at the boundaries, they form a critical balance of production of E and determine the flow stability around the critical state. This behaviour is demonstrated for the Lamb–Oseen and Q vortex models. This analysis reveals a more complicated, as well more realistic, interaction between the perturbed flow in the domain and at the boundaries that dominates vortex flow dynamics.