This paper reports an experimental investigation of pressure and force distributions on a sharp-nosed circular cylinder inclined to a uniform low-speed air flow under conditions of laminar separation of the boundary layer. The main concern is with the out-of-plane force (i.e. the side force if the body is at incidence). The experimental model consisted of an extensively pressure-tapped cylinder to which four different noses were fitted. The results show that there is an oscillatory distribution of out-of-plane force along the cylinder for most of the inclination range 0-90°. The amplitude of this distribution is strongly affected by nose shape in conditions where the out-of-plane force extends onto the nose. At very high angles of inclination the oscillatory distribution disappears and is replaced by a vortex pattern like that found on an infinite yawed cylinder. The general nature of the out-of-plane force is found to be consistent with the impulsively started flow analogy. Unsteadiness in the flow was found to cause a serious reduction in many of the time-averaged values. The unsteadiness is ascribed to the switching of the flow pattern due to free-stream turbulence. Measurements of the time histories of certain pressures enabled values of the force in the unswitched state to be calculated. The Reynolds number was found to have an important influence at inclinations above 55°. However, it was also found that the range of Reynolds numbers over which this effect occurs can depend on the scale of the model.

This paper is concerned with the theoretical behaviour of the laminar Ekman layer and the family of related rotating problems that includes both the Bödewadt and the von Kármán boundary-layer flows. Results from inviscid and viscous analyses are presented. In both cases, within specific regions of the parameter space, it is shown that the flows are absolutely unstable in the radial direction, i.e. disturbances grow in time at every radial location within these regions. Outside these regions, the flows are convectively unstable or stable. The absolute or convective nature of the flows is determined by examining the branch-point singularities of the dispersion relation. The onset of absolute instability is consistent with available experimental observations of the onset of laminar–turbulent transition in these flows.

The instability of an initially flat vortex sheet to a sinusoidal perturbation of the vorticity is studied by means of high-order Taylor series in time t. All finite-amplitude corrections are retained at each order in t. Our analysis indicates that the sheet develops a curvature singularity at t = tc < ∞. The variation of tc with the amplitude a of the perturbation vorticity is in good agreement with the asymptotic results of Moore. When a is O(1), the Fourier coefficient of order n decays slightly faster than predicted by Moore. Extensions of the present prototype of Kelvin-Helmholtz instability to other layered flows, such as Rayleigh-Taylor instability, are indicated.

An experimental investigation of flows of a large number of inert and polyatomic gases in various channels, a non-ideal orifice, flat slits with different surface roughnesses and wall materials, capillary packets with molten walls and a capillary sieve, has been made.

The unsteady flow method and a highly sensitive capacitance micromanometer were used (the sensitivity being ∼ 3 × 10−4N/m2Hz). Measurements were made in a range of Knudsen numbers 5 × 104–10−3 at ∼ 293 °K, and some measurements for flow through a non-ideal orifice were carried out at 77.2°K.

It was found that, both in the viscous slip-flow and free-molecule regimes for the channels with molten walls, the experimental conductivities were higher (by ∼ 15%) than theoretical ones calculated assuming diffuse molecular scattering by the walls. We have also observed that the channel conductivity essentially depends on the channel surface roughness and on the kind of gas. The larger the roughness height, the lower the conductivity. From the experimental data the tangential momentum accommodation coefficients were calculated.

A computer simulation is used to make a detailed study of the stress tensor in a simple shear flow of two-dimensional disks. The stresses are shown to arise from two momentum-transfer mechanisms: the 'streaming’ or kinetic mode. By which momentum is carried by particles are they move through the bulk material: and the collisional mode, by which momentum is transferred from one point to another in the material by interparticle collisions. As might be expected, the results show that the streaming mode dominates at disperse packings and the collisional mode dominates at dense packings. The friction coefficient, the ratio of shear to normal forces, is shown to decrease at high particle packing for both the collisional and streaming modes of transport. Normal-stress differences are observed within the shear plane and are evident in both the streaming and collisonal parts.

Direct numerical simulation (DNS) of spatially developing turbulent boundary layer with uniform blowing (UB) or uniform suction (US) is performed aiming at skin friction drag reduction. The Reynolds number based on the free stream velocity and the 99% boundary layer thickness at the inlet is set to be 3000. A constant wall-normal velocity is applied on the wall in the range, −0.01U∞ ≤ Vctr ≤ 0.01U∞. The DNS results show that UB reduces the skin friction drag, while US increases it. The turbulent fluctuations exhibit the opposite trend: UB enhances the turbulence, while US suppresses it. Dynamical decomposition of the local skin friction coefficient cf using the identity equation (FIK identity) (Fukagata, Iwamoto & Kasagi, Phys. Fluids, vol. 14, 2002, pp. L73–L76) reveals that the mean convection term in UB case works as a strong drag reduction factor, while that in US case works as a strong drag augmentation factor: in both cases, the contribution of mean convection on the friction drag overwhelms the turbulent contribution. It is also found that the control efficiency of UB is much higher than that of the advanced active control methods proposed for channel flows.

The separated flow past a zero-thickness flat plate held normal to a free stream at Re=250 has been investigated through numerical experiments. The long-time signatures of the drag and lift coefficients clearly capture a low-frequency unsteadiness with a period of approximately 10 times the primary shedding period. The amplitude and frequency of drag and lift variations during the shedding process are strongly modulated by the low frequency. A physical interpretation of the low-frequency behaviour is that the flow gradually varies between two different regimes: a regime H of high mean drag and a regime L of low mean drag. It is observed that in regime H the shear layer rolls up closer to the plate to form coherent spanwise vortices, while in regime L the shear layer extends farther downstream and the rolled-up Kármán vortices are less coherent. In the high-drag regime three-dimensionality is characterized by coherent Kármán vortices and reasonably well-organized streamwise vortices connecting the Kármán vortices. With a non-dimensional spanwise wavelength of about 1.2, the three-dimensionality in this regime is reminiscent of mode-B three-dimensionality. It is observed that the high degree of spanwise coherence that exists in regime H breaks down in regime L. Based on detailed numerical flow visualization we conjecture that the formation of streamwise and spanwise vortices is not in perfect synchronization and that the low-frequency unsteadiness is the result of this imbalance (or phase mismatch).

One-dimensional small-amplitude waves in which the local value of the fundamental derivative changes sign are examined. The undisturbed medium is taken to be a Navier–Stokes fluid which is at rest and uniform with a pressure and density such that the fundamental derivative is small. A weak shock theory is developed to treat inviscid motions, and the method of multiple scales is used to derive the nonlinear parabolic equation governing the evolution of weakly dissipative waves. The latter is used to compute the viscous shock structure. New phenomena of interest include shock waves having an entropy jump of the fourth order in the shock strength, shock waves having sonic conditions either upstream or downstream of the shock, and collisions between expansion and compression shocks. When the fundamental derivative of the undisturbed media is identically zero it is shown that the ultimate decay of a one-signed pulse is proportional to the negative 1/3-power of the propagation time.

An analytical model is presented for the direct initiation of gaseous detonations by a blast wave. For stable or weakly unstable mixtures, numerical simulations of the spherical direct initiation event and local analysis of the one-dimensional unsteady reaction zone structure identify a competition between heat release, wave front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the wave front. The quasi-steady assumption is thus shown to be incorrect for direct initiation. The numerical simulations also suggest a non-uniqueness of critical energy in some cases, and the model developed here is an attempt to explain the lower critical energy only. A critical shock decay rate is determined in terms of the other fundamental dynamic parameters of the detonation wave, and hence this model is referred to as the critical decay rate (CDR) model. The local analysis is validated by integration of reaction-zone structure equations with real gas kinetics and prescribed unsteadiness. The CDR model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models of the critical energy, this equation is not dependent on other experimentally determined parameters and for evaluation requires only an appropriate reaction mechanism for the given gas mixture. For different fuel–oxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude.

We use resolvent analysis to design active control techniques for separated flows over a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of $23\,000$ and a free-stream Mach number of $0.3$ are considered at two post-stall angles of attack of $6^{\circ }$ and $9^{\circ }$. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. To provide physics-based guidance for the effective choice of these control input parameters, we conduct global resolvent analysis on the baseline turbulent mean flows to identify the actuation frequency and wavenumber that provide large perturbation energy amplification. The present analysis also considers the use of a temporal filter to limit the time horizon for assessing the energy amplification to extend resolvent analysis to unstable base flows. We incorporate the amplification and response mode from resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. This metric is compared to the results from a large number of three-dimensional large-eddy simulations of open-loop controlled flows. With the agreement between the resolvent-based metric and the enhancement of aerodynamic performance found through large-eddy simulations, we demonstrate that resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. We believe that the present resolvent-based approach provides a promising path towards mean flow modification by capitalizing on the dominant modal mixing.

The scattering of plane sound waves by a vortex is investigated by solving the compressible Navier–-Stokes equations numerically, and analytically with asymptotic expansions. Numerical errors associated with discretization and boundary conditions are made small by using high-order-accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computations of flow fields with acoustic waves of amplitude five orders of magnitude smaller than the hydrodynamic fluctuations is directly verified. The properties of the scattered field are examined in detail. The results reveal inadequacies in previous vortex scattering theories when the circulation of the vortex is non-zero and refraction by the slowly decaying vortex flow field is important. Approximate analytical solutions that account for the refraction effect are developed and found to be in good agreement with the computations and experiments.

Experiments have been undertaken to investigate dam-break flows where a thin plate separating water at different levels is withdrawn impulsively in a vertically upwards direction. Depth ratios of 0, 0.1 and 0.45 were investigated for two larger depth values of 10 cm and 36 cm. The resulting sequence of surface profiles is shown to satisfy approximately Froude scaling. For the dry-bed case a horizontal jet forms at small times and for the other cases a vertical, mushroom-like jet occurs, none of which have been observed previously. We analyse the initial-release problem in which the plate is instantaneously removed or dissolved. Although this shows singular behaviour, jet-like formations are predicted. Artificially smoothing out the singularity enables a fully nonlinear, potential-flow computation to follow the jet formation for small times. There is qualitative agreement between theory and experiment.

In the experiments, after a bore has developed downstream as a result of highly complex flow interactions, the surface profiles agree remarkably well with exact solutions of the shallow-water equations which assume hydrostatic pressure and uniform velocity over depth.

The uniform steady flow of an incompressible, viscous, electrically conducting fluid is distorted by the presence of a symmetrically oriented semi-infinite flat plate. The ambient magnetic field is coincident with the ambient velocity field. The description of the resulting fields depends on the physical co-ordinates measured in units of Reynolds number and on the two parameters ε = ωμν and β = μH2/ρv2. This description of the fields is approximated in three different ways and essentially covers the full range of ε and β. In particular, when β [Gt ] 1, no steady flow which is uniform at large distances from the plate exists.

A small drop of liquid 1 falls through a less dense liquid 2 and approaches the horizontal interface between liquid 2 and an underlying layer of liquid 1. After a short time the drop will be brought to rest (or nearly) in a hollow in the interface. Before the drop can coalesce with its bulk phase, the thin film of liquid 2 trapped between them must be squeezed out, and become sufficiently thin that rupture can occur. This is the film drainage problem. Early calculations, based on simple lubrication theory, fail to take proper account of two effects which are investigated here and shown to be decisive. They are the circulation induced in the drop and in the lower bulk fluid, which tends to speed up drainage, and the constriction in the film thickness at its periphery, which tends to slow it down. This constriction has been observed and some existing theories have attempted to model it in an ad hoc manner. We give here a physical explanation and calculate the minimum thickness explicitly. The effect of circulation in the adjacent fluids is also calculated.

We report large-eddy simulation (LES) of turbulent channel flow. This LES neither resolves nor partially resolves the near-wall region. Instead, we develop a special near-wall subgrid-scale (SGS) model based on wall-parallel filtering and wall-normal averaging of the streamwise momentum equation, with an assumption of local inner scaling used to reduce the unsteady term. This gives an ordinary differential equation (ODE) for the wall shear stress at every wall location that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stress due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the streamwise velocity at the top boundary of the near-wall averaged domain. This allows calculation of an instantaneous slip velocity that is then used as a ‘virtual-wall’ boundary condition for the LES. A Kármán-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for Reynolds numbers Reτ based on the friction velocity uτ and the channel half-width δ in the range 2 × 103 to 2 × 107. Results, including SGS-extended longitudinal spectra, compare favourably with the direct numerical simulation (DNS) data of Hoyas & Jiménez (2006) at Reτ = 2003 and maintain an O(1) grid dependence on Reτ.

Measurements of mean velocity, turbulent stress and static pressure were made in the mixing region of a jet of air issuing from a slot nozzle into still air. The velocity was low and the two-dimensional flow was effectively incompressible. The results are examined in terms of the unsimplified equations of fluid motion, and comparisons are drawn with the common assumptions and simplifications of free jet theory. Appreciable deviations from isobaric conditions exist and the deviations are closely related to the local turbulent stresses. Negative static pressures were encountered everywhere in the mixing field except in the potential wedge region immediately adjacent to the nozzle. Lateral profiles of mean longitudinal velocity conformed closely to an error curve at all stations further than 7 slot widths from the nozzle mouth. An asymptotic approach to complete self-preservation of the flow was observed.

A general continuum theory for particle-size segregation and diffusive remixing in polydisperse granular avalanches is formulated using mixture theory. Comparisons are drawn to existing segregation theories for bi-disperse mixtures and the case of a ternary mixture of large, medium and small particles is investigated. In this case, the general theory reduces to a system of two coupled parabolic segregation–remixing equations, which have a single diffusion coefficient and three parameters which control the segregation rates between each pair of constituents. Considerable insight into many problems where the effect of diffusive remixing is small is provided by the non-diffusive case. Here the equations reduce to a system of two first-order conservation laws, whose wave speeds are real for a very wide class of segregation parameters. In this regime, the system is guaranteed to be non-strictly hyperbolic for all admissible concentrations. If the segregation rates do not increase monotonically with the grain-size ratio, it is possible to enter another region of parameter space, where the equations may either be hyperbolic or elliptic, depending on the segregation rates and the local particle concentrations. Even if the solution is initially hyperbolic everywhere, regions of ellipticity may develop during the evolution of the problem. Such regions in a time-dependent problem necessarily lead to short wavelength Hadamard instability and ill-posedness. A linear stability analysis is used to show that the diffusive remixing terms are sufficient to regularize the theory and prevent unbounded growth rates at high wave numbers. Numerical solutions for the time-dependent segregation of an initially almost homogeneously mixed state are performed using a standard Galerkin finite element method. The diffuse solutions may be linearly stable or unstable, depending on the initial concentrations. In the linearly unstable region, ‘sawtooth’ concentration stripes form that trap and focus the medium-sized grains. The large and small particles still percolate through the avalanche and separate out at the surface and base of the flow due to the no-flux boundary conditions. As these regions grow, the unstable striped region is annihilated. The theory is used to investigate inverse distribution grading and reverse coarse-tail grading in multi-component mixtures. These terms are commonly used by geologists to describe particle-size distributions in which either the whole grain-size population coarsens upwards, or just the coarsest clasts are inversely graded and a fine-grained matrix is found everywhere. An exact solution is constructed for the steady segregation of a ternary mixture as it flows down an inclined slope from an initially homogeneously mixed inflow. It shows that for distribution grading, the particles segregate out into three inversely graded sharply segregated layers sufficiently far downstream, with the largest particles on top, the fines at the bottom and the medium-sized grains sandwiched in between. The heights of the layers are strongly influenced by the downstream velocity profile, with layers becoming thinner in the faster moving near-surface regions of the avalanche, and thicker in the slowly moving basal layers, for the same mass flux. Conditions for the existence of the solution are discussed and a simple and useful upper bound is derived for the distance at which all the particles completely segregate. When the effects of diffusive remixing are included, the sharp concentration discontinuities are smoothed out, but the simple shock solutions capture many features of the evolving size distribution for typical diffusive remixing rates. The theory is also used to construct a simple model for reverse coarse-tail grading, in which the fine-grained material does not segregate. The numerical method is used to calculate diffuse solutions for a ternary mixture and a sharply segregated shock solution is derived that looks similar to the segregation of a bi-disperse mixture of large and medium grains. The presence of the fine-grained material, however, prevents high concentrations of large or medium particles being achieved and there is a significant lengthening of the segregation distance.

Experiments were carried out in an axisymmetric turbulent jet from 2 to 6 diameters downstream at exit Reynolds numbers of 78 400, 117 600, and 156 800. Data were collected using the 138 hot-wire probe constructed by Citriniti & George (2000). The proper orthogonal decomposition (POD) was then applied to a double Fourier transform in time and azimuthal direction of the two-point velocity correlation tensor. Azimuthal mode-0, which dominated the dynamics at $x/D\,{=}\,3$ in the previous experiments, dies off rapidly downstream towards a non-zero value. For the higher azimuthal modes, the peak shifts from mode-6 towards lower azimuthal mode numbers with increasing downstream distance, until the peak is at mode-2 by the end of the potential core. The POD eigenspectra collapse in similarity variables for the mixing layer at all downstream positions, and are nearly independent of Reynolds number. Reconstruction of the full-field streamwise velocity component using the dominant POD modes shows clearly the evolution of the flow with downstream position, from ‘volcano-type’ eruptions at 2 to 3 diameters downstream to a ‘propeller-like’ pattern where the number of blades diminishes downstream.

The aero-optical distortions caused by compressible flows have been used by researchers for flow diagnostics and accepted by designers of airborne optical systems as a performance penalty. In order to estimate these distortions, an understanding of the optical distortion mechanism is required. This article examines the mechanisms which produce a variable-density field (and accompanying index-of-refraction field) in a nearly incompressible shear-layer flow. The two-dimensional-shear-layer velocity field was approximated using a discrete vortex model. From this ‘known’ velocity field, the pressure and density fields were determined by iteratively solving the unsteady Euler equations. The resulting index-of-refraction field produced simulated schlieren images which closely resemble experimental schlierens. Optical wavefronts computed from the simulation reasonably match the behaviour of large-scale aberrations measured in a transonic wind tunnel. Small-scale distortions in the experimental data may have been caused by boundary layers on the splitter plate and tunnel walls or by three-dimensional effects that were not simulated.

Turbulent energy spectra have been measured in a round air jet at high Reynolds numbers (Rλ = 710 to 780). The streamwise and cross-stream spectrum functions are well fitted by the (${\\frac{5}{3}$) power law predicted by the Kolmogoroff theory for an inertial subrange. The data are shown to be consistent with the local isotropy hypothesis and the constant in the Kolmogoroff spectrum function in the inertial subrange is evaluated. Effects of length and non-linear response of the hot-wire are considered.