How internal flow states can influence the global transport properties in a turbulent system has always been an intriguing question. Weiss & Ahlers (J. Fluid Mech., this issue, vol. 676, 2011, pp. 5–40) have provided an example by measuring the instantaneous Nusselt number in turbulent Rayleigh-Bénard convection and correlating it to the different modes of large-scale flow.

Measurements of the Nusselt number and properties of the large-scale circulation (LSC) are presented for turbulent Rayleigh–Bénard convection in water-filled cylindrical containers (Prandtl number Pr = 4.38) with aspect ratio Γ = 0.50. They cover the range 2 × 108 ≲ Ra ≲ 1 × 1011 of the Rayleigh number Ra. We confirm the occurrence of a double-roll state (DRS) of the LSC and focus on the statistics of the transitions between the DRS and a single-roll state (SRS). The fraction of the run time when the SRS existed varied continuously from about 0.12 near Ra = 2 × 108 to about 0.8 near Ra = 1011, while the fraction of the run time when the DRS could be detected changed from about 0.4 to about 0.06 over the same range of Ra. We determined separately the Nusselt number of the SRS and the DRS, and found the former to be larger than the latter by about 1.6% (0.9%) at Ra = 1010 (1011). We report a contribution to the dynamics of the SRS from a torsional oscillation similar to that observed for cylindrical samples with Γ = 1.00. Results for a number of statistical properties of the SRS are reported, and some are compared with the cases Γ = 0.50, Pr = 0.67 and Γ = 1.00, Pr = 4.38. We found that genuine cessations of the SRS were extremely rare and occurred only about 0.3 times per day, which is less frequent than for Γ = 1.00; however, the SRS was disrupted frequently by roll-state transitions and other less well-defined events. We show that the time derivative of the LSC plane orientation is a stochastic variable which, at constant LSC amplitude, is Gaussian distributed. Within the context of the LSC model of Brown & Ahlers (Phys. Fluids, vol. 20, 2008b, art. 075101), this demonstrates that the stochastic force due to the small-scale fluctuations that is driving the LSC dynamics has a Gaussian distribution.

A correction for streamwise Reynolds stress data acquired with insufficient spatial resolution is proposed for wall-bounded flows. The method is based on the attached eddy hypothesis to account for spatial filtering effects at all wall-normal positions. This analysis reveals that outside the near-wall region the spatial filtering effect scales inversely with the distance from the wall, in contrast to the commonly assumed scaling with the viscous length scale. The new formulation is shown to work very well for data taken over a wide range of Reynolds numbers and wire lengths.

How to design an artificial inflow condition in simulations of the Navier–Stokes equation that is already fully turbulent? This is the turbulent inflow problem. This first question is followed by: How much of the true turbulence must be reproduced at the inflow? We present a technique able to produce a random field with the exact two-point two-time covariance of a given reference turbulent flow. It is obtained as the output of a linear filter fed with white noise. The method is illustrated on the simulation of a turbulent free shear layer. The filter coefficients are obtained from the solution of the Yule–Walker equation, and the computation can be performed efficiently using a recursive solution procedure. The method should also be useful in the study of flow receptivity, when the processes of transition to turbulence are sensitive to the perturbation environment.

Direct numerical simulations (DNS) are employed to investigate laminar boundary layer separation and its control by pulsed vortex generator jets (VGJs), i.e. by injecting fluid into the flow through a spanwise array of small holes. Particular focus is directed towards identifying the relevant physical mechanisms associated with VGJ control of low-Reynolds-number separation, as encountered in low-pressure turbine applications. Pulsed VGJs are shown to be much more effective than steady VGJs when the same momentum coefficient is used for the actuation. From our investigations we have found that the increased control effectiveness of pulsed VGJs can be explained by the fact that linear hydrodynamic instability mechanisms are exploited. When pulsing with frequencies to which the separated shear layer is naturally unstable, instability modes are shown to develop into large-scale, spanwise coherent structures. These structures provide the necessary entrainment of high-momentum fluid to successfully reattach the flow.

We investigate the stability properties and flow regimes of laminar wakes behind slender cylindrical bodies, of diameter D and length L, with a blunt trailing edge at zero angle of attack, combining experiments, direct numerical simulations and local/global linear stability analyses. It has been found that the flow field is steady and axisymmetric for Reynolds numbers below a critical value, Recs (L/D), which depends on the length-to-diameter ratio of the body, L/D. However, in the range of Reynolds numbers Recs(L/D) < Re < Reco(L/D), although the flow is still steady, it is no longer axisymmetric but exhibits planar symmetry. Finally, for Re > Reco, the flow becomes unsteady due to a second oscillatory bifurcation which preserves the reflectional symmetry. In addition, as the Reynolds number increases, we report a new flow regime, characterized by the presence of a secondary, low frequency oscillation while keeping the reflectional symmetry. The results reported indicate that a global linear stability analysis is adequate to predict the first bifurcation, thereby providing values of Recs nearly identical to those given by the corresponding numerical simulations. On the other hand, experiments and direct numerical simulations give similar values of Reco for the second, oscillatory bifurcation, which are however overestimated by the linear stability analysis due to the use of an axisymmetric base flow. It is also shown that both bifurcations can be stabilized by injecting a certain amount of fluid through the base of the body, quantified here as the bleed-to-free-stream velocity ratio, Cb = Wb/W∞.

In this paper, we study the linear stability of a plane Couette flow of a power-law fluid. The influence of shear-thinning effect on the stability is investigated using the classical eigenvalue analysis, the energy method and the non-modal stability theory. For the plane Couette flow, there is no stratification of viscosity. Thus, for the stability problem the stress tensor is anisotropic aligned with the strain rate perturbation. The results of the eigenvalue analysis and the energy method show that the shear-thinning effect is destabilizing. We focus on the effect of non-Newtonian viscosity on the transition from laminar flow towards turbulence in the framework of non-modal stability theory. Response to external excitations and initial conditions has been studied by examining the ε-pseudospectrum and the transient energy growth. For both Newtonian and non-Newtonian fluids, it is found that there can be a rather large transient growth even though the linear operator of the Couette flow has no unstable eigenvalue. The results show that shear-thinning significantly increases the amplitude of response to external excitations and initial conditions.

Measurements are presented from turbulent boundary layers over periodic two- and three-dimensional roughness. Cases with transverse rows of staggered cubes and cases with solid square transverse bars of two sizes were considered. Previous results by Volino, Schultz & Flack (J. Fluid Mech. vol. 635, 2009, p. 75) showed outer-layer similarity between cases with three-dimensional roughness and smooth walls, and deviations from similarity in cases with large two-dimensional transverse bars. The present results show that differences also occur with small two-dimensional bars and to a lesser extent when the bars are replaced with rows of staggered cubes. Differences are most apparent in correlations of turbulence quantities, which are of larger spatial extent for the rough-wall cases. The results with the staggered cubes indicate that part of the periodic roughness effect is caused by the repeated disturbance and recovery of the boundary layer as it encounters a row of roughness followed by a smooth surface. A larger effect, however, is due to the blockage caused by the two-dimensional transverse bars, which extend across the entire width of the boundary layer. The small two-dimensional bars have a larger effect than the staggered cubes, in spite of the bar height being only 11 viscous units and 1/7 of the cube height. The effect of the small bars extends well into the outer flow, indicating that effects observed previously with larger bars were not due only to a thickening of the roughness sublayer. The observed differences between the rough- and smooth-wall results are believed to be caused by large-scale attached eddies which extend from the roughness elements to the edge of the boundary layer.

We investigate the single-point probability density function of the velocity in three-dimensional stationary and decaying homogeneous isotropic turbulence. To this end, we apply the statistical framework of the Lundgren–Monin–Novikov hierarchy combined with conditional averaging, identifying the quantities that determine the shape of the probability density function. In this framework, the conditional averages of the rate of energy dissipation, the velocity diffusion and the pressure gradient with respect to velocity play a key role. Direct numerical simulations of the Navier–Stokes equation are used to complement the theoretical results and assess deviations from Gaussianity.

This paper considers the stability of liquid metal drops subject to a high-frequency AC magnetic field. An energy variation principle is derived in terms of the surface integral of the scalar magnetic potential. This principle is applied to a thin perfectly conducting liquid disk, which is used to model the drops constrained in a horizontal gap between two parallel insulating plates. Firstly, the stability of a circular disk is analysed with respect to small-amplitude harmonic edge perturbations. Analytical solution shows that the edge deformations with the azimuthal wavenumbers m = 2, 3, 4, . . . start to develop as the magnetic Bond number exceeds the critical threshold Bmc = 3π(m + 1)/2. The most unstable is m = 2 mode, which corresponds to an elliptical deformation. Secondly, strongly deformed equilibrium shapes are modelled numerically by minimising the associated energy in combination with the solution of a surface integral equation for the scalar magnetic potential on an unstructured triangular mesh. The edge instability is found to result in the equilibrium shapes of either two- or threefold rotational symmetry depending on the magnetic field strength and the initial perturbation. The shapes of higher rotational symmetries are unstable and fall back to one of these two basic states. The developed method is both efficient and accurate enough for modelling of strongly deformed drop shapes.

We investigate the run-up of a shock wave from inside to the surface of a perfect fluid star in equilibrium and bounded by vacuum. Near the surface we approximate the fluid motion as plane-symmetric and the gravitational field as constant. We consider the ‘hot’ equation of state P = (Γ − 1)ρe and its ‘cold’ (fixed entropy, barotropic) form P = K0ρΓ (the latter does not allow for shock heating). We numerically find that the evolution of generic initial data approaches universal similarity solutions sufficiently near the surface, and we explicitly construct these similarity solutions. The two equations of state show very different behaviour because shock heating becomes the dominant effect when it is allowed. In the barotropic case, the fluid velocity behind the shock approaches a constant value, while the density behind the shock approaches a power law in space, as the shock approaches the surface. In the hot case with shock heating, the density jumps by a constant factor through the shock, while the sound speed and fluid velocity behind the shock diverge in a whiplash effect. We tabulate the similarity exponents as a function of the equation of state parameter Γ and the stratification index n∗.

We investigate the flow field in an electrokinetic micromixer. The concept of the micromixer is based on the combination of an alternating electrical field applied to a pressure-driven base flow in a meander–channel geometry. The presence of the electrical field leads to an additional electro-osmotic velocity contribution, which results in a complex flow field within the meander bends. The velocity fields within the meander are measured by means of a microparticle-image velocimetry method. Furthermore, we introduce a mathematical model, describing the electrical and fluid-mechanical phenomena present within the device, and perform simulations comparable to the experiments. The comparison of simulations and experiments reveals good agreement, with minor discrepancies in flow topology, obviously caused by small but crucial differences between experimental and numerical geometries. In detail, simulations are performed for sharp corners of the bends, while in the experiments these corners are rounded due to the microfabrication process.

The flow around a finite circular cylinder with a height-to-diameter ratio of 6 was studied using large eddy simulation (LES). The cylinder was mounted on a ground plane where a thin boundary layer with a thickness of only 7% of the cylinder's diameter was formed. The flow resulting from the present LES was used to present a detailed picture of both the instantaneous and the time-averaged flow. Among the results of the present study is the explanation for the formation of two time-averaged tip vortices from two pairs of instantaneous vortices. The main recirculation region on the cylinder's top was found to be one vortex with both legs attached to the top surface, in agreement with some previous investigations. The mean flow in the near wake region was found to contain two horseshoe vortices, one large arch vortex stretching from the cylinder's top and another vortex resulting from the flow moving down below the rear stagnation point on the cylinder. The instantaneous horseshoe vortex near the ground was found to be unsteady and changed shape over time. The time-averaged flow showed three complete horseshoe vortices, in agreement with previous knowledge. The downwash process above the free end into the near wake occurs at a rather constant angle with respect to the plane normal to the streamwise direction. The same angle was preserved in the inclination of the arch vortex in the time-averaged flow.

The large deformations of an initially-ellipsoidal capsule in a simple shear flow are studied by coupling a boundary integral method for the internal and external flows and a finite-element method for the capsule wall motion. Oblate and prolate spheroids are considered (initial aspect ratios: 0.5 and 2) in the case where the internal and external fluids have the same viscosity and the revolution axis of the initial spheroid lies in the shear plane. The influence of the membrane mechanical properties (mechanical law and ratio of shear to area dilatation moduli) on the capsule behaviour is investigated. Two regimes are found depending on the value of a capillary number comparing viscous and elastic forces. At low capillary numbers, the capsule tumbles, behaving mostly like a solid particle. At higher capillary numbers, the capsule has a fluid-like behaviour and oscillates in the shear flow while its membrane continuously rotates around its deformed shape. During the tumbling-to-swinging transition, the capsule transits through an almost circular profile in the shear plane for which a long axis can no longer be defined. The critical transition capillary number is found to depend mainly on the initial shape of the capsule and on its shear modulus, and weakly on the area dilatation modulus. Qualitatively, oblate and prolate capsules are found to behave similarly, particularly at large capillary numbers when the influence of the initial state fades out. However, the capillary number at which the transition occurs is significantly lower for oblate spheroids.

The concentration of platelets near the blood vessel wall is important because platelets survey the condition of the vessel wall and respond to injuries to it. Under arterial flow conditions, platelets are non-uniformly distributed across the vessel lumen and have a high concentration within a few microns of the vessel wall. This is believed to be a consequence of the complex motion of red blood cells which constitute a large fraction of the blood's volume. We use a novel lattice Boltzmann-immersed boundary method to simulate, in two dimensions, the motion of dense red blood cell suspensions and their effect on platelet-sized particles. We track the development of a red blood cell-free layer near the wall and the later development of the platelet near-wall excess. We find that the latter develops more quickly at high wall shear rates and that the magnitude of the excess and its proximity to the wall are dependent on haematocrit. Treating the simulation data as if it were generated by a drift–diffusion process, we find that the effective lateral platelet diffusivity depends strongly on lateral position; it has a magnitude of order of 10−6 cm2 s−1 over much of the lumen but drops to almost zero close to the wall. This large effective diffusivity over the core of the lumen combined with reduced space for platelets in this region because of the inward migration of red blood cells largely but not completely accounts for the observed platelet-concentration profiles. We present evidence for a highly localized red blood cell-induced platelet drift at the edge of the red cell-free layer and suggest a physical mechanism that may generate it.

The analysis of the energy transfer mechanisms in a filtered wall-turbulent flow is traditionally accomplished via the turbulent kinetic energy balance, as in Härtel et al. (Phys. Fluids, vol. 6, 1994, p. 3130) or via the analysis of the energy spectra, as in Domaradzki et al. (Phys. Fluids, vol. 6, 1994, p. 1583). However, a generalized Kolmogorov equation for channel flow has recently been proven successful in accounting for both spatial fluxes and energy transfer across the scales in a single framework by Marati, Casciola & Piva (J. Fluid Mech., vol. 521, 2004, p. 191). In this context, the same machinery is applied for the first time to a filtered velocity field. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter scale compared to the cross-over scale between production-dominated scales and inertial range, lc, and the reverse energy cascade region ΩB. Finally, we will briefly discuss how the filtered Kolmogorov equation can be used as a new tool for the assessment of large eddy simulation (LES) models. Classical purely dissipative eddy viscosity models will be analysed via an a priori procedure.

A phenomenon referred to as ‘shock-wave surfing’, in which a body moves in such a way as to follow the shock wave generated by another upstream body, is investigated numerically and analytically. During the surfing process, the downstream body can accumulate a significantly higher lateral velocity than would otherwise be possible. The surfing effect is first investigated for interactions between a sphere and a planar oblique shock. Numerical simulations are performed and a simple analytical model is developed to determine the forces acting on the sphere. A phase-plane description is employed to elucidate features of the system dynamics. The analytical model is then generalised to the more complex situation of aerodynamic interactions between two spheres, and, through comparisons with further computations, is shown to adequately predict the final separation velocity of the surfing sphere in initially touching configurations. Both numerical simulations and a theoretical analysis indicate a strong influence of the sphere radius ratio on the separation process and predict a critical radius ratio that delineates entrainment of the smaller body within the flow region bounded by the larger body's shock from expulsion. Furthermore, it is shown that an earlier scaling law does not accurately describe the separation behaviour. The surfing effect has important implications for meteoroid fragmentation: in particular, a large fraction of the variation in the separation velocity deduced by previous authors from an analysis of terrestrial crater fields can be explained by a combination of surfing and a modest rotation rate of the parent body.

There have been numerous studies on the steady-state transition criteria between regular and Mach reflection of shock waves generated by a stationary, two-dimensional wedge in a steady supersonic flow, since the original shock-wave reflection research by Ernst Mach in 1878. The steady, two-dimensional transition criteria between regular and Mach reflection are well established. There has been little done to consider the dynamic effect of a rapidly rotating wedge on the transition between regular and Mach reflection. This paper presents the results of an investigation on the effect of rapid wedge rotation on regular to Mach reflection transition in the weak- and strong-reflection ranges with the aid of experiment and computational fluid dynamics. The experimental set-up includes a novel facility to rotate a pair of large aspect ratio wedges in a 450 mm × 450 mm supersonic wind tunnel at wedge rotation speeds up to 11000 deg s−1. High-speed images and measurements are presented. A numerical solution of the inviscid governing flow equations was used to mimic the experimental motion and to extend the investigation beyond the limits of the current facility to explore the influence of variables in the parameter space. There is good agreement between experimental measurements and numerical simulation. This paper includes the first experimental evidence of the regular to Mach reflection transition beyond the steady-state detachment condition in the weak- and strong-reflection ranges. It also presents results of simulations for the dynamic regular to the Mach reflection transition which show a difference between the sonic, length-scale and detachment conditions. This paper includes experimental evidence of the Mach to regular reflection transition below the steady-state von Neumann condition.

Using high-resolution 3-D vortex simulations, this study seeks a mechanistic understanding of vorticity dynamics in transverse jets at a finite Reynolds number. A full no-slip boundary condition, rigorously formulated in terms of vorticity generation along the channel wall, captures unsteady interactions between the wall boundary layer and the jet – in particular, the separation of the wall boundary layer and its transport into the interior. For comparison, we also implement a reduced boundary condition that suppresses the separation of the wall boundary layer away from the jet nozzle. By contrasting results obtained with these two boundary conditions, we characterize near-field vortical structures formed as the wall boundary layer separates on the backside of the jet. Using various Eulerian and Lagrangian diagnostics, it is demonstrated that several near-wall vortical structures are formed as the wall boundary layer separates. The counter-rotating vortex pair, manifested by the presence of vortices aligned with the jet trajectory, is initiated closer to the jet exit. Moreover tornado-like wall-normal vortices originate from the separation of spanwise vorticity in the wall boundary layer at the side of the jet and from the entrainment of streamwise wall vortices in the recirculation zone on the lee side. These tornado-like vortices are absent in the case where separation is suppressed. Tornado-like vortices merge with counter-rotating vorticity originating in the jet shear layer, significantly increasing wall-normal circulation and causing deeper jet penetration into the crossflow stream.

Oceanic observations from western Europe and the south-western Indian ocean have provided evidence of the generation of internal solitary waves due to an internal tidal beam impinging on the pycnocline from below – a process referred to as ‘local generation’ (as opposed to the more direct generation over topography). Here we present the first direct numerical simulations of such a generation process with a fully nonlinear non-hydrostatic model for an idealised configuration. We show that, depending on the parameters, different modes can be excited and we provide examples of internal solitary waves as first, second and third modes, trapped in the pycnocline. A criterion for the selection of a particular mode is put forward, in terms of phase speeds. In addition, another simpler geometrical criterion is presented to explain the selection of modes in a more intuitive way. Finally, results are discussed and compared with the configuration of the Bay of Biscay.