A new approach to determine stability of multiple steady-state similarity solutions corresponding to laminar flows is introduced and applied to laminar flows in cold, pure water at temperature T∞ °C (near 4 °C) adjacent to a vertical, isothermal, plane surface at temperature T0 °C when 0 < R ≡ (4−T∞)/(T0−T∞) < 0.5, the region of buoyancy-force reversals. The results show that the steady-state similarity solutions recently found in this region by El-Henawy et al. (1982) are unstable, and thus should not be observed experimentally; while those solutions found earlier by Carey, Gebhart & Mollendorf (1980) may be stable. No unstable modes corresponding to their solutions were found. Some flows for R in the range of strong buoyancy-force reversals, 0.14 < R < 0.32 at Prandtl number Pr = 11.6, have been observed, for example at R = 0.143,0.254 and 0.317 by Carey & Gebhart (1981) and Wilson & Vyas (1979). The latter found time-varying flows in this region of strongest flow reversals.

The advantages of the method introduced are reduction of mathematical shortcomings of the traditional approach and relative ease of numerical calculation of the real eigenvalues and eigenfunctions. The disadvantage is that information on downstream, selective frequency, exponential growth of amplitude is lost. The theory presented may be regarded as an asymptotic limit of the standard hydrodynamic theory as the frequency of perturbations approaches zero.

It is shown that the vortex filament in background shear considered in Aref & Flinchem (1984) is unstable to infinitesimal disturbances, and that the numerical results described therein are consistent with the characteristics of the instability.

This is a theoretical and experimental study of the basic hydraulics of two flowing layers. Unlike single-layer flows, two-layer flows respond quite differently to bottom depth as opposed to width variations. Bottom-depth changes affect the lower layer directly and the upper layer only indirectly. Changes in width can affect both layers. In fact for flows through a contraction control two distinct flow configurations are possible; which one actually occurs depends on the requirements of matching a downstream flow. Two-layer flows can pass through internally critical conditions at other than the narrowest section. When the two layers are flowing in the same direction, the result is a strong coupling between the two layers in the neighbourhood of the control. For contractions a particularly simple flow then exists upstream in which there is no longer any significant interfacial dynamics; downstream in the divergent section the flow remains internally supercritical, causing one of the layers to be rapidly accelerated with a resulting instability at the interface. A brief discussion of internal hydraulic jumps based upon the energy equations as opposed to the more traditional momentum equations is included. Previous uniqueness problems are thereby avoided.

The motion of a viscous drop in a vertical Hele-Shaw cell is studied in a limit where the effect of surface tension through contact-angle hysteresis is significant. It is found that a rectangular drop shape is a possible steady solution of the governing equations, although this solution is unstable to perturbations on the leading edge. Even though the unstable edge is one where a viscous fluid is moving into a less viscous fluid, in this case air, this is shown to be a special case of the well-known Saffman—Taylor instability. An experiment is performed with an initially circular drop in which it is observed that the drop shape becomes approximately rectangular except at the leading edge, where it becomes rounded and sometimes has a ragged appearance.

A drop sliding down a vertical Hele-Shaw cell is an example of a system where the action of surface tension is not always one of smoothing, since in this case it leads to the formation of right-angle corners at the back of the drop (rounded only slightly on the lengthscale of the gap thickness of the cell).

This paper presents numerical calculations of the self-excited oscillations of an incompressible planar jet impinging upon a wedge for a Reynolds-number range of 250–650. For this Reynolds-number range these flows are experimentally observed to be two-dimensional and laminar. A finite-difference vorticity/stream-function formulation of the Navier-Stokes equations is employed. The self-sustained flow oscillations result in not just one but several well-defined flow frequency components due to nonlinear interaction of two primary components: the most unstable frequency (β) of the jet shear layer and a low-frequency modulating component ($\frac{1}{3}\beta $). The modulating component results from vortex-vortex interaction at the impingement edge of both like and counter-rotating vortices. Although the interaction pattern varies through the Reynolds-number range studied, the pattern adjusts itself to maintain the modulating component $\frac{1}{3}\beta $ which has a strong upstream influence. The numerical results, in agreement with experimental results, strongly suggest the occurrence of such phenomena as frequency jumps and hysteresis. Pressure at the wedge surface has been calculated and compared with experimental results. Numerical results for wedge torque and lift, which have not been experimentally measured, have also been obtained.

Incompressible moderate-Reynolds-number flow in periodically grooved channels is investigated by direct numerical simulation using the spectral element method. For Reynolds numbers less than a critical value Rc the flow is found to approach a stable steady state, comprising an ‘outer’ channel flow, a shear layer at the groove lip, and a weak re-circulating vortex in the groove proper. The linear stability of this flow is then analysed, and it is found that the least stable modes closely resemble Tollmien–Schlichting channel waves, forced by Kelvin–Helmholtz shear-layer instability at the cavity edge. A theory for frequency prediction based on the Orr–Sommerfeld dispersion relation is presented, and verified by variation of the geometric parameters of the problem. The accuracy of the theory, and the fact that it predicts many qualitative features of low-speed groove experiments, suggests that the frequency-selection process in these flows is largely governed by the outer, more stable flow (here a channel), in contrast to most current theories based solely on shear-layer considerations. The instability of the linear mode for R > Rc is shown to result in self-sustained flow oscillations (at frequencies only slightly shifted from the originating linear modes), which again resemble (finite-amplitude) Tollmien-Schlichting modes driven by an unstable groove vortex sheet. Analysis of the amplitude dependence of the oscillations on degree of criticality reveals the transition to oscillatory flow to be a regular Hopf bifurcation.

A numerical method has been developed to represent unsteady boundary layers with large flow reversal. It makes use of the characteristic box scheme which examines the finite-difference grid in relation to the magnitude and direction of local velocity and reaches and implements a decision to ensure that the Courant, Friedricks & Lewey stability criterion is not violated. The method has been applied to the problem of an impulsively started circular cylinder and the results, though generally consistent with those of van Dommelen & Shen obtained with a Lagrangian method, show some differences. The time step is identified as very important and, with the present intelligent numerical scheme, the results were readily extended to times far beyond those previously achieved with Eulerian methods. Extrapolation of the results suggests that the much-discussed singularity for this unsteady flow is the same as that of the corresponding steady flow.

A similarity solution is found which describes the flow impinging on a flat wall at an arbitrary angle of incidence. The technique is similar to a method used by Jeffery (1915) and discussed more recently by Peregrine (1981).

This is an experimental investigation of vortex excitation of prisms with elongated rectangular, H- and [vdash ]-shaped cross-sections, where the depth parallel to the flow is much greater than the height perpendicular to the flow. Measurements are made of free oscillations in a wind tunnel and flow visualizations in a water tank. The flow around elongated bluff prisms is dominated by the impinging-shear- layer instability where the separated shear layers become unstable in the presence of different kinds of shape of the rear part of the cross-section, which may include sharp trailing edges. The two unstable shear layers interact with each other when they meet together downstream of the prism, thereby forming Kármán vortices with the same frequency of oscillation. The former impinging-shear-layer instability is largely responsible for vortex excitation of elongated bluff prisms.

The behaviour of a binary mixture of a vapour and an inert gas around the spherical condensed-phase droplet is studied analytically using kinetic theory. By the singular-perturbation method, the linearized Boltzmann equation of B–G–K type is first solved for problems with spherical symmetry under the diffusive boundary condition when the Knudsen number of the problem is small. The macroscopic equations and the appropriate boundary conditions in the form of the temperature and partial-pressure jumps on the interface between the droplet and the gas phase, which enable us to treat the problems at the level of ordinary fluid dynamics, are derived together with the Knudsen-layer structure formed near the interface. Then the velocity, temperature and pressure fields around the droplet are explicitly obtained, as well as the mass, heat and energy flows from it. The results obtained are capable of describing the transition from the diffusion-control to the kinetic-control mechanism in the mass-transfer process. The negative-temperature-gradient phenomenon, a common phenomenon for pure-vapour cases (absence of inert gas), is also possible, manifesting itself more easily as the kinetic-control mechanism becomes prevalent and the critical condition for its existence is given. The present analysis could be applied to other problems with spherical symmetry as well.

We report a study of the flow patterns associated with Rayleigh—Bénard convection in rectangular containers of approximate proportions 10 × 5 × 1 at Prandtl numbers σ between 2 and 20. The flow is studied at Rayleigh numbers ranging from the onset of convective flow to the onset of time dependence; Nusselt-number measurements are also presented. The results are discussed in the content of the theory for the stability of a laterally infinite system of parallel rolls. We observed transitions between time-independent flow patterns which depend on roll wavenumber, Rayleigh number and Prandtl number in a manner that is reasonably well described by this theory. For σ [lsim ] 10, the skewed-varicose instability (which leads directly to time dependence in much larger containers) is found to initiate transitions between time-independent patterns. We are then able to study the approach to time dependence in a regime of larger Rayleigh number where the instabilities in the flow are found to have an intrinsic time dependence. In this regime, the onset of time dependence appears to be explained by the recent predictions of Bolton, Busse & Clever for a new set of time-dependent instabilities.

An experimental study of the developing structural characteristics of a two-dimensional jet in an extremely quiet environment was performed. The jet, at an exit Reynolds number of 6000 and with fluctuation intensity under 0.2% at the mouth, was operated within a large anechoic room. Measurements of energy spectra, fluctuation phase angles and two-dimensionality led to the inference of structural patterns in the flow. These patterns are initially characterized by relatively strong symmetric modes exhibiting limited two-dimensionality and oriented parallel to the mouth of the jet. Subsequent downstream evolution led to the formation of an antisymmetric pattern beyond the jet potential core and the associated development of extended structures possessing a definite large lateral inclination. The results of this work suggest a developing large-scale structural pattern more complicated than previously supposed.

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier–Stokes equations for the attachment-line flow have been solved using a Fourier–Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

Experiments were performed in the highly turbulent and disturbed flow over a bluff plate with a long splitter plate in its plane of symmetry. The flow separates at the sharp bevelled edge of the bluff plate, forms a free shear layer on top of the reverse-flow region which is bounded on its other side by the splitter plate, and reattaches on the splitter plate over a narrow region curved in spanwise direction. Downstream of reattachment the shear flow adjusts slowly to the wall boundary conditions.

Measurements of mean velocity, Reynolds-shear-stress and Reynolds-normal-stress distributions were carried out by hot-wire and pulsed-wire anemometry. The latter technique was used in those regions of the flow where reverse flow occurred or where the flow was highly turbulent. Spectra and integral lengthscales were measured to investigate the state and structure of the flow. The large-eddy structure in the inner region of the flow had lengthscales in the two cross-stream directions which were approximately equal, indicating a fast break-up of spanwise structures just downstream from separation.

Mean and fluctuating quantities showed a self-similar behaviour in a short region upstream of reattachment and ‘profile similarity’ in the separated shear layer and along the splitter plate downstream from reattachment. Probability-density distributions of skin friction were measured and used to calculate mean and fluctuating values. No flapping of the reattaching shear layer could be observed. Pulsed-wire measurements revealed that the logarithmic law of the wall does not hold either in the reverse-flow region or in a region about half the length of the bubble downstream from reattachment.

A viscous/inviscid interaction method is described and has been used to calculate flows around four distinctly different airfoils as a function of angle of attack. It comprises an inviscid-flow method based on conformal mapping, a boundary-layer procedure based on the numerical solution of differential equations and an algebraic eddy viscosity. The results are in close agreement with experiment up to angles close to stall. In one case, where the airfoil thickness is large, small difficulties were experienced and are described. The method is shown to be capable of obtaining results with large flow separation and quantifies the role of transition on the lift coefficient.

A set of second-order modelled equations for the motion of particles are presented. We consider the effects of the particle inertia and the crossing-trajectories effect on the particle dispersion. A simple case of a particle mixing layer in a decaying homogeneous turbulence for light and heavy particles is calculated. The results show that the crossing-trajectories effect on particle dispersion is very significant, while inertia only has a slight effect. This behaviour has been observed in experiments (Wells & Stock 1983) and is well predicted by an asymptotic analysis (Csanady, 1963). The calculation also shows that there is a significant difference between Favre-averaged particle velocity and conventional-averaged particle velocity in the low-particle-concentration region. All calculations are in good agreement with Wells & Stock's experimental data.

Following a review of the difficulties associated with the measurement and interpretation of statistics of the small-scale motion, the evidence for and against local isotropy is assessed in the light of measurements in a turbulent plane jet at moderate values of the Reynolds and Péclet numbers. These measurements include spatial derivatives with respect to different spatial directions of the longitudinal velocity fluctuation and of the temperature fluctuation. Relations between mean-square values of these derivatives suggest strong departures from local isotropy for both velocity and temperature. In contrast, the locally isotropic forms of the vorticity and temperature dissipation budgets are approximately satisfied. Possible contamination of the fine-scale measurements by the anisotropic large-scale motion is assessed in the context of the measured structure functions of temperature and of the measured skewness of the streamwise derivative of temperature. Structure functions are, within the framework of local isotropy, consistent with the average frequency and amplitude of temperature signatures that characterize the quasi-organized large-scale motion. Conditional averages associated with this motion account, in an approximate way, for the skewness of the temperature derivative but make negligible contributions to the skewness of velocity derivatives. The degree of spatial organization of the fine structure is inferred from conditional statistics of temperature derivatives.

Measurements by Freymuth & Uberoi (1971) of the terms in the transport equation for the temperature variance in a plane turbulent wake indicated approximate equality for the three components of the temperature dissipation, thus indicating isotropy for that quantity. This result was in sufficient disagreement with the results obtained in several other turbulent shear flows to warrant further measurements of the temperature dissipation in the wake. The present measurements indicate that the dissipation is larger than the isotropic value by about 50 % near the wake centreline and nearly 100 % near the region of maximum production. The magnitude of this ratio is similar to that obtained in other turbulent shear flows. The present measured ratio of total dissipation to isotropic dissipation leads to a satisfactory closure of the temperature variance budget for our experiments and also for the plane-wake measurements of Fabris (1974). It is concluded that the temperature dissipation is not isotropic.

Flow of red blood cells along narrow cylindrical vessels, with inside diameters up to 8 μm, is modelled theoretically. Axisymmetric cell shapes are assumed, and lubrication theory is used to describe the flow of the suspending fluid in the gaps between the cells and the vessel wall. The models take into account the elastic properties of the red blood cell membrane, including its responses to shear and bending. At moderate or high cell velocities, about 1 mm/s or more, the membrane stress may be approximated by an isotropic tension which is maximal at the nose of the cell and falls to zero at the rear. Cell shape and apparent viscosity are then independent of flow rate. At lower flow velocities, membrane shear and bending stresses become increasingly important, and models are developed to take these into account. Apparent viscosity is shown to increase with decreasing flow rate, in agreement with previous experimental and theoretical studies.

We extend the numerical methods of a previous paper to the study of the α-effect in a turbulent plasma. In the frozen-turbulence case the α-effect vanishes for zero molecular diffusivity. The value of α is, however, found to depend very sensitively on the molecular diffusivity. The same is true for the turbulent magnetic diffusivity β. The theoretical predictions of the first-order smoothing and the Markovian approximations are well satisfied in the appropriate limits, for both α and β.