A turbulent boundary layer formed over an external surface is spatially evolving. The flow develops from an initial set of conditions and accordingly the state of the layer at some downstream location owes a debt to its upstream history. Schlatter & Örlü (J. Fluid Mech., this issue, vol. 710, 2012, pp. 5–34) demonstrate succinctly this sensitivity to upstream history, finding that relatively minor modifications to the trip parameters can produce non-canonical development up to surprisingly high Reynolds numbers. This interesting study will serve as a cautionary note to experimentalists and numericists while providing a plausible explanation for some of the disparity noted among previously published results.

A recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter & Örlü, J. Fluid Mech., vol. 659, 2010, pp. 116–126) showed surprisingly large differences not only in the skin friction coefficient or shape factor, but also in their predictions of mean and fluctuation profiles far into the sublayer. While such differences are expected at very low Reynolds numbers and/or the immediate vicinity of the inflow or tripping region, it remains unclear whether inflow and tripping effects explain the differences observed even at moderate Reynolds numbers. This question is systematically addressed by re-simulating the DNS of a zero-pressure-gradient turbulent boundary layer flow by Schlatter et al. (Phys. Fluids, vol. 21, 2009, art. 051702). The previous DNS serves as the baseline simulation, and the new DNS with a range of physically different inflow conditions and tripping effects are carefully compared. The downstream evolution of integral quantities as well as mean and fluctuation profiles is analysed, and the results show that different inflow conditions and tripping effects do indeed explain most of the differences observed when comparing available DNS at low Reynolds number. It is further found that, if transition is initiated inside the boundary layer at a low enough Reynolds number (based on the momentum-loss thickness) , all quantities agree well for both inner and outer layer for . This result gives a lower limit for meaningful comparisons between numerical and/or wind tunnel experiments, assuming that the flow was not severely over- or understimulated. It is further shown that even profiles of the wall-normal velocity fluctuations and Reynolds shear stress collapse for higher irrespective of the upstream conditions. In addition, the overshoot in the total shear stress within the sublayer observed in the DNS of Wu & Moin (Phys. Fluids, vol. 22, 2010, art. 085105) has been identified as a feature of transitional boundary layers.

This paper reports experimental findings on the flow of sand down a steep chute. Nearly all granular flow models have a maximum value for the friction and therefore predict that flows on steep slopes will accelerate at a constant rate until the interaction with the ambient fluid becomes important. This prediction has not been tested by previous work, which has focused on relatively low slope angles where steady, fully developed flows occur after short distances. We test this by investigating flows over a much greater range of slope angles (30–50) and flow depths (4–130 particle diameters). We examine flows with two basal conditions, one flat and frictional, the other bumpy. The latter imposes a no-slip condition for slow, deep flows, but permits some degree of slip for high flow velocities. The data suggests that friction can be much larger than theories such as the rheology proposed by Jop, Forterre & Pouliquen (Nature, vol. 441, 2006) suggest and that there may be constant velocity states above the angle of vanishing . Although these flows do not vary in time, all but the flows on the bumpy base at low inclinations accelerate down the slope. A recirculation mechanism sustains flows with a maximum mass flux of , allowing observations to be made at multiple points for each flow for an indefinite period. Flows with Froude number in the range 0.1–25 and bulk inertial number 0.1–2.7 were observed in the dense regime, with surface velocities in the range 0.2–5.6 . Previous studies have focused on . We show that a numerical implementation of the rheology does not fully capture the accelerating dynamics or the transverse velocity profile on the bumpy base. We also observe the transverse separation of the flow into a dense core flanked by dilute regions and the formation of longitudinal vortices.

Experiments on high-pressure vessel decompression have shown that vaporization occurs in ‘boiling shocks’ moving with a velocity of . To explain this phenomenon, a model accounting for bubble breakup was suggested (Ivashnyov, Ivashneva & Smirnov, J. Fluid. Mech., vol. 413, 2000, pp. 149–180). It was shown that the explosive boiling was caused by chain bubble fragmentation, which led to a sharp increase in the interface area and instantaneous transformation of the mixture into an equilibrium state. In the present study, this model is used to simulate nozzle flows with no change in the free parameters chosen earlier for modelling a tube decompression. It is shown that an advanced model ensures the best correspondence to experiments for flashing flows in comparison with an equilibrium model and with a model of boiling at a constant number of centres. It is also shown that the formation of a boiling shock in a critical nozzle flow leads to autovibrations.

This study examines the influence of angle of attack of a square section cylinder on the cylinder’s flow-induced vibration, where the direction of the vibration is transverse to the oncoming flow. Our experiments, which traversed the velocity–angle of attack parameter space in considerable breadth and depth, show that a low-mass ratio body can undergo combinations of both vortex-induced vibration and galloping. When the body has an angle of attack that makes it symmetric to the flow, such as when it assumes the square or diamond orientation, the two mechanisms remain independent. However, when symmetry is lost we find a mixed mode response with a new branch of vortex-induced oscillations that exceeds the amplitudes resulting from the two phenomena independently. The oscillations of this higher branch have amplitudes larger than the ‘upper branch’ of vortex-induced vibrations and at half the frequency. For velocities above this resonant region, the frequency splits into two diverging branches. Analysis of the amplitude response reveals that the transition between galloping and vortex-induced vibrations occurs over a narrow range of angle of incidence. Despite the rich set of states found in the parameter space the vortex shedding modes remain very similar to those found previously in vortex-induced vibration.

Flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via solution of the pertinent global (BiGlobal) partial differential equation (PDE)-based eigenvalue problem. Subsequently, a simple extension of the extended Görtler–Hämmerlin ordinary differential equation (ODE)-based polynomial model proposed by Theofilis et al. (2003) for orthogonal flow, which includes previous models as special cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the analysis results and unravel the limits of validity of the basic flow model analysed. The effect of the angle of attack, , on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from (orthogonal flow) up to values close to which make the assumptions under which the basic flow is derived questionable, is found to systematically destabilize the flow. The critical conditions of non-orthogonal flows at are shown to be recoverable from those of orthogonal flow, via a simple algebraic transformation involving .

The linear stability of inviscid zonal jet flows on a rotating sphere is re-examined. A semi-circle theorem for inviscid zonal flows on a rotating sphere is proved. It is also shown that numerically obtained eigenvalues of the linear stability problem do not converge well with a spectral method which was adopted in previous studies, due to an emergence of critical layers near the poles. By using a shooting method where the integral path bypasses the critical layers in the complex plane, the eigenvalues are successfully obtained with correction of the critical rotation rates compared to those obtained in Baines (J. Fluid Mech., vol. 73, 1976, pp. 193–213).

We use the weak-curvature, slow-time asymptotics of detonation shock dynamics (DSD) to calculate an intrinsic relation between the normal acceleration, the normal velocity and the curvature of a lead detonation shock for self-sustained detonation waves in condensed phase explosives. The formulation uses the compressible Euler equations for an explosive that is described by a general equation of state with multiple reaction progress variables. The results extend an earlier asymptotic theory for a polytropic equation of state and a single-step reaction rate model discussed by Kasimov (Theory of instability and nonlinear evolution of self-sustained detonation waves. PhD thesis, University of Illinois Urbana-Champaign, Urbana, Illinois) and by Kasimov & Stewart (Phys. Fluids, vol. 16, 2004, pp. 3566–3578). The asymptotic relation is used to study the dynamics of ignition events in solid explosive PBX-9501 and in porous PETN powders. In the case of porous or powdered explosives, two composition variables are used to represent the extent of exothermic chemical reaction and endothermic compaction. Predictions of the asymptotic formulation are compared against those of alternative DSD calculations and against shock-fitted direct numerical simulations of the reactive Euler equations.

The flow around six in-line square cylinders has been studied numerically and experimentally for and , where is the surface-to-surface distance between two cylinders, is the size of the cylinder and is the Reynolds number. The effect of spacing on the flow regimes is initially studied numerically at for which a synchronous flow regime is observed for , while quasi-periodic-I, quasi-periodic-II and chaotic regimes occur between , and , respectively. These regimes have been confirmed via particle-image-velocimetry-based experiments. A flow regime map is proposed as a function of spacing and Reynolds number. The flow is predominantly quasi-periodic-II or chaotic at higher Reynolds numbers. The quasi-periodic and chaotic nature of the flow is due to the wake interference effect of the upstream cylinders which becomes more severe at higher Reynolds numbers. The appearance of flow regimes is opposite to that for a row of cylinders. The Strouhal number for vortex shedding is the same for all the cylinders, especially for synchronous and quasi-periodic-I flow regimes. The mean drag () experienced by the cylinders is less than that for an isolated cylinder, irrespective of the spacing. The first cylinder is relatively insensitive to the presence of downstream cylinders and the is almost constant at 1.2. The for the second and third cylinders may be negative, with the value of increasing monotonically with spacing. The changes in root mean square lift coefficient are consistent with changes in . Interestingly, the instantaneous lift force can be larger than the instantaneous drag force on the cylinders. These results should help improve understanding of flow around multiple bluff bodies.

Near-wall streamwise vortices are closely related to the generation of high skin friction in wall-bounded turbulent flows. A common feature of controlled, friction-reduced turbulent flows is weakened near-wall streamwise vortices. In the present study, the streak transient growth (STG) mechanism for generating near-wall streamwise vortices by Schoppa & Hussain (J. Fluid Mech., vol. 453, 2002, pp. 57–108) is employed, and the opposition control proposed by Choi, Moin & Kim (J. Fluid Mech., vol. 262, 1994, pp. 75–110) is imposed during the transient growth process of perturbations to determine how active control affects the generation of quasi-streamwise vortices. In the transient growth stage, when the detection plane is located near the wall (), the control can suppress the production of streamwise vorticity by weakening the near-wall vertical velocity; when the detection plane moves away from the wall (), the control has the opposite effect. In the vortex generation stage, the control cannot change the dominance of the stretching effect. Controls imposed at different stages reveal the importance of the STG stage in vortex generation. Strengthened out-of-phase control and lessened in-phase control are proposed as an extension of the original opposition-control scheme. Application in a fully developed turbulent channel flow shows that strengthened control can yield an even higher drag reduction rate than the original control. Moreover, lessened control can also achieve drag reduction and turbulence suppression.

We report high-precision measurements of the Nusselt number as a function of the Rayleigh number in water-filled rectangular Rayleigh–Bénard convection cells. The horizontal length and width of the cells are 50.0 and 15.0 cm, respectively, and the heights , 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios , , , , , and . The measurements were carried out over the Rayleigh number range and the Prandtl number range . Our results show that for rectangular geometry turbulent heat transport is independent of the cells’ aspect ratios and hence is insensitive to the nature and structures of the large-scale mean flows of the system. This is slightly different from the observations in cylindrical cells where is found to be in general a decreasing function of , at least for and larger. Such a difference is probably a manifestation of the finite plate conductivity effect. Corrections for the influence of the finite conductivity of the top and bottom plates are made to obtain the estimates of for plates with perfect conductivity. The local scaling exponents of are calculated and found to increase from 0.243 at to 0.327 at .

Oceans that are stratified by density into distinct layers support internal waves. An internal soliton gives rise to characteristic features on the surface, a signature of its presence, in the form of a ‘rip’ region, as reported in Osborne & Burch (Science, vol. 208, 1980, pp. 451–460), which results in a change in reflectance as seen in NASA photographs from the space shuttle. In the present paper, we give a new analysis of this signature of an internal soliton, and the ‘mill pond’ effect of an almost completely calm sea after its passage. Our analysis models the resonant interaction of nonlinear internal waves with the surface modes, where the surface signature is generated by a process analogous to radiative absorption. These theoretical results are illustrated with numerical simulations that take oceanic parameters into account.

The onset of thermoconvective instability in a horizontal porous layer with a basic Hadley flow is studied, under the assumption of weak vertical heterogeneity. Hadley flow is a single-cell convective circulation induced by horizontal linear changes of the layer boundary temperatures. When combined with heating from below, these thermal boundary conditions yield a temperature gradient inclined to the vertical, in the basic state. The linear stability of the basic state is studied by considering small-amplitude disturbances of the velocity field and the temperature field. The linearized governing equations for the disturbances are then solved both by Galerkin’s method of weighted residuals and by a combined use of the Runge–Kutta method and the shooting method. The effect of weak heterogeneity of the permeability and the effective thermal conductivity of the porous medium is studied with respect to neutral stability conditions. It is shown that, among the normal mode disturbances, the most unstable are longitudinal rolls, that is, plane waves with a wave vector perpendicular to the imposed horizontal temperature gradient. The effect of heterogeneity becomes important only for high values of the horizontal Rayleigh number, associated with the horizontal temperature gradient, approximately greater than 60. In this regime, the effect of heterogeneity is destabilizing. It is shown that heterogeneity with respect to thermal conductivity is of major importance in the onset of instability.

The stability with respect to initial condition perturbations of solitary travelling-wave solutions of the Euler equations for continuously, stably stratified, near two-layer fluids is examined numerically and analytically for a set of parameters of relevance for laboratory experiments. Numerical travelling-wave solutions of the Dubreil–Jacotin–Long equation are first obtained with a variant of Turkington, Eyland and Wang’s iterative code by testing convergence on the equation’s residual. In this way, stationary solutions with very thin pycnoclines (and small Richardson numbers) approaching the near two-layer configurations used in experiments can be obtained, allowing for a stability study free of non-stationary effects, introduced by lack of numerical resolution, which develop when these solutions are used as initial conditions in a time-dependent evolution code. The thin pycnoclines in this study permit analytical results to be derived from strongly nonlinear models and their predictions compared with carefully controlled numerical simulations. This brings forth shortcomings of simple criteria for shear instability manifestations based on parallel shear approximations due to subtle higher-order effects. In particular, evidence is provided that the fore–aft asymmetric growth observed in all simulations requires non-parallel shear analysis. Collectively, the results of this study reveal that while the wave-induced shear can locally reach unstable configurations and give rise to local convective instability, the global wave/self-generated shear system is in fact stable, even for extreme cases of thin pycnoclines and near-maximum-amplitude waves.

Particle capture, whereby suspended particles contact and adhere to a solid surface (a ‘collector’), is an important mechanism in a range of environmental processes. In aquatic systems, typically characterized by low collector Reynolds numbers (), the rate of particle capture determines the efficiencies of a range of processes such as seagrass pollination, suspension feeding by corals and larval settlement. In this paper, we use direct numerical simulation (DNS) of a two-dimensional laminar flow to accurately quantify the rate of capture of low-inertia particles by a cylindrical collector for (i.e. a range where there is no vortex shedding). We investigate the dependence of both the capture rate and maximum capture angle on both the collector Reynolds number and the ratio of particle size to collector size. The inner asymptotic expansion of Skinner (Q. J. Mech. Appl. Maths, vol. 28, 1975, pp. 333–340) for flow around a cylinder is extended and shown to provide an excellent framework for the prediction of particle capture and flow close to the leading face of a cylinder up to . Our results fill a gap between theory and experiment by providing, for the first time, predictive capability for particle capture by aquatic collectors in a wide (and relevant) Reynolds number and particle size range.

The steady-state fully resonant wave system, consisting of two progressive primary waves in finite water depth and all components due to nonlinear interaction, is investigated in detail by means of analytically solving the fully nonlinear wave equations as a nonlinear boundary-value problem. It is found that multiple steady-state fully resonant waves exist in some cases which have no exchange of wave energy at all, so that the energy spectrum is time-independent. Further, the steady-state resonant wave component may contain only a small proportion of the wave energy. However, even in these cases, there usually exist time-dependent periodic exchanges of wave energy around the time-independent energy spectrum corresponding to such a steady-state fully resonant wave, since it is hard to be exactly in such a balanced state in practice. This view serves to deepen and enrich our understanding of the resonance of gravity waves.

Direct numerical simulations (DNS) of two time-dependent, axially homogeneous, axisymmetric turbulent wakes having very different initial conditions are presented in order to assess whether they reach a universal self-similar state as classically hypothesized by Townsend. It is shown that an extensive early-time period exists during which the two wakes are individually self-similar with wake widths growing like , as predicted by classical dimensional analysis, but have very different growth rates and are thus not universal. Subsequently, however, the turbulence adjusts to yield, eventually, wakes that are structurally identical and have the same growth rate (also with ) so provide clear evidence of a universal, self-similar state. The former non-universal but self-similar state extends, in terms of a spatially equivalent flow behind a spherical body of diameter , to a distance of whereas the final universal state does not appear before (and exists despite relatively low values of the Reynolds number and no evidence of a spectral inertial subrange). Universal wake evolution is therefore likely to be rare in practice. Despite its low Reynolds number, the flow does not exhibit the sometime-suggested alternative self-similar behaviour with (as for the genuinely laminar case) at large times (or, equivalently, distances), since the eddy viscosity remains large compared to the molecular viscosity and its temporal variations are not negligible.

A strategy to extract turbulence structures from direct numerical simulation (DNS) data is described along with a systematic analysis of geometry and spatial distribution of the educed structures. A DNS dataset of decaying homogeneous isotropic turbulence at Reynolds number is considered. A bandpass filtering procedure is shown to be effective in extracting enstrophy and dissipation structures with their smallest scales matching the filter width, . The geometry of these educed structures is characterized and classified through the use of two non-dimensional quantities, ‘planarity’ and ‘filamentarity’, obtained using the Minkowski functionals. The planarity increases gradually by a small amount as is decreased, and its narrow variation suggests a nearly circular cross-section for the educed structures. The filamentarity increases significantly as decreases demonstrating that the educed structures become progressively more tubular. An analysis of the preferential alignment between the filtered strain and vorticity fields reveals that vortical structures of a given scale are most likely to align with the largest extensional strain at a scale 3–5 times larger than . This is consistent with the classical energy cascade picture, in which vortices of a given scale are stretched by and absorb energy from structures of a somewhat larger scale. The spatial distribution of the educed structures shows that the enstrophy structures at the scale (where is the Kolmogorov scale) are more concentrated near the ones that are 3–5 times larger, which gives further support to the classical picture. Finally, it is shown by analysing the volume fraction of the educed enstrophy structures that there is a tendency for them to cluster around a larger structure or clusters of larger structures.

Direct numerical simulation has been used to study the effects of external turbulence on axisymmetric wakes. In the absence of such turbulence, the time-developing axially homogeneous wake is found to have the self-similar properties expected whereas, in the absence of the wake, the turbulence fields had properties similar to Saffman-type turbulence. Merging of the two flows was undertaken for three different levels of external turbulence (relative to the wake strength) and it is shown that the presence of the external turbulence enhances the decay rate of the wake, with the new decay rates increasing with the relative strength of the initial external turbulence. The external turbulence is found to destroy any possibility of self-similarity within the developing wake, causing a significant transformation in the latter as it gradually evolves towards the former.

The problem of an incompressible flow between two coaxial cylinders with radii and subjected to a sliding motion of the inner cylinder in the axial direction is considered. The energy stability and the non-modal stability have been investigated for both axisymmetric and non-axisymmetric disturbances. For the non-modal stability, we focus on two problems: response to external excitations and response to initial conditions. The former is studied by examining the -pseudospectrum, and the latter by examining the energy growth function . Unlike the results of the modal analysis in which the stability of sliding Couette flow is determined by axisymmetric disturbances, the energy analysis shows that a non-axisymmetric disturbance has a critical energy Reynolds number for all radius ratios . The results for non-modal stability show that rather large transient growth occurs over a wide range of azimuthal wavenumber and streamwise wavenumber , even though the Reynolds number is far below its critical value. For the problem of response to external excitations, the response is sensitive to low-frequency external excitations. For all values of the radius ratio, the maximum response is achieved by non-axisymmetric and streamwise-independent disturbances when the frequency of external forcing . For the problem of response to initial conditions, the optimal disturbance is in the form of helical streaks at low Reynolds numbers. With the increase of , the optimal disturbance becomes very close to straight streaks. For each , the maximum energy growth of streamwise-independent disturbances is of the order of , and the optimal time is of the order of . This relation is qualitatively similar to that for plane Couette flow, plane Poiseuille flow and pipe Poiseuille flow. Direct numerical simulations are applied to investigate the transition of the streamwise vortex (SV) scenario at and 1500 for various . The initial disturbances are the optimal streamwise vortices predicted by the non-modal analysis. We studied the streak breakdown phase of the SV scenarios by examining the instability of streaks. Moreover, we have investigated the sustainment of the energy of disturbances in the SV scenario.