An experimental investitition was made of the entry flow in a curved pipe under conditions wherein a pulsatile component of flow was superimposed on a steady mean flow. Two experiments were conducted, one in a pipe of curvature ratio $\delta = \frac{1}{20}$ under conditions of Womersley parameter αw = 8·0 and alternative Dean number κ = 120, the second in a pipe of $\delta = \frac{1}{7}$ for αw = 12·5 and κ = 372. Laser-velocimetry measurements of the axial and secondary velocities were made throughout the cross-section at different instants of time within the cycle and at several axial locations downstream from the pipe entrance.

The flow in the first experiment was found to be quasisteady, with axial and secondary velocities varying in time at the several axial stations proportionally to the instantaneous mean velocity, but essentially the same in character as low-Dean-number steady entry flow. The flow in the second experiment was more complex, with separation of the axial flow appearing at the inner bend during deceleration, starting downstream and propagating upstream toward the pipe entrance. Helical motions imbedded within the Dean circulation were also observed, and during certain portions of the cycle the secondary motions within the central core took on a jet-like structure.

It suggested that the classifications employed by Smith to describe the different regimes of fully-developed pulsatile flow in curved pipes may also be useful to distinguish between different entry-flow regimes.

Experiments are described in which a grid is towed horizontally along a large tank filled first with water and then with a stably stratified saline solution. The decay rates of the r.m.s. turbulent velocity components (w’, v’) perpendicular to the mean motion are measured by a ‘Taylor’ diffusion probe and are found to be unaffected by the stable stratification over distances measured from 5 to 47 mesh lengths (M) downstream, and over a range of Froude number U/NM of ∞ and 8·5 to 0·5, U being the velocity and N the buoyancy frequency. The Reynolds number Mw’/ν of the turbulence was about 103, where v is the kinematic viscosity. The vertical velocity fluctuations produced near the grid were reduced by the stratification by up to 30% when U/MN ≈ 0·5. Large-scale internal wave motion was not evident from the observations within about 50 mesh lengths of the grid.

The turbulent diffusion from a point source located 4·7 mesh lengths downstream was studied. σy, σz, the horizontal and vertical plume widths, were measured by a rake of probes. σy was found to be largely unaffected by the stratification and grew like t½, while σz was found in all cases to reach an asymptotic limit σz∞ where 0·5 [les ] σz∞N/w’s [les ] 2, w’s being the r.m.s. velocity fluctuations at the source; the time taken for σz to reach its maximum was about 2N−1. These results are largely in agreement with the theoretical models of Csanady (1964) and Pearson, Puttock & Hunt (1983).

The stability of a parallel flow periodic in the direction normal to the stream is investigated theoretically. Critical Reynolds numbers are calculated for a general velocity profile including widely separated wakes. The critical mode of disturbance is found to have the same period as the basic flow. Growing modes with much larger periods exist, however, at slightly supercritical values of the Reynolds number. The analysis of various limiting cases explains the qualitative difference in the shape of the neutral curves depending on the period of the disturbance. In connection with the results obtained in this paper, the stability of non-parallel periodic flows is briefly discussed.

The method of matched asymptotic expansions is used to study the generation of Tollmien-Schlichting waves by free-stream disturbances incident on a flat-plate boundary layer. Near the leading edge, the motion is governed by the unsteady boundary-layer equation, while farther downstream it is governed (to lowest order) by the Orr-Sommerfeld equation with slowly varying coefficients. It is shown that there is an overlap domain where the Tollmien-Schlichting wave solutions to the Orr-Sommerfeld equation and appropriate asymptotic solutions of the unsteady boundary-layer equation match, in the matched-asymptotic-expansion sense. The analysis explains how long-wavelength free-stream disturbances can generate Tollmien-Schlichting waves of much shorter wavelength. It also leads to a set of scaling laws for the asymptotic structure of the unsteady boundary layer.

A mechanism previously proposed for the possible interaction between a rotating sheet of fluid and a rotating environment is re-investigated using the normal-mode method. Only azimuthal modes are considered. Stability of such a flow, if any, will appear as the neutral condition, i.e. the stability domain will be present as a stability boundary. The stability boundary for the present flow exists only for one azimuthal mode with no density inhomogeneity. For general heterogeneous rotating flows subject to non-axisymmetric disturbances, a semi-ellipse theorem is derived with a restriction. In contrast with the semicircle theorem in two-dimensional stratified flows, the restriction suggests that the semicircle in the complex phase-velocity plane does not in general provide an upper bound on all unstable waves. For rigidly rotating flows all unstable waves lie on a semicircle in the complex phase-velocity plane regardless of the density distributions.

An exact solution of the equations of motion of a two-phase fluid is given which describes separation in a centrifugal force field. A retrograde rotation is always produced in the settling process, which is characterized by propagating kinematic shocks and a time-dependent volume fraction of the mixture.

Experiments have shown that bubbles approaching an air–water interface give rise to axisymmetric jets projected upwards into the air. Similar jets occur during the collapse of cavitation bubbles near a solid surface. In this paper we show that such jets are well modelled by a Dirichlet hyperboloid, a hyperbolic form of the better-known ellipsoid. The vertex angle of the hyperboloid is calculated as a function of time and found to agree with the observations of Blake & Gibson (1981) and others.

The jet is initiated, according to this model, when the vertex angle passes through 2 arctan √2, or 109·47°, at which instant the fluid accelerations become large. This compares with a vertical angle of 90° in the corresponding two-dimensional flow.

Further experiments demonstrate that an axisymmetric standing wave, when driven beyond its maximum amplitude, can break by throwing up a jet of the same hyperbolic form. Hyperbolic jets may occur commonly in free-surface flows.

Schlieren visualization and laser-anemometry experiments are presented which demonstrate that a two-dimensional positive corona discharge interacts with the flow of a wire–plate electrostatic precipitator to produce a non-turbulent secondary flow in a plane perpendicular to the discharge wires. Smoke-wire visualization and hot-wire anemometry experiments are then described which show that negative-corona-discharge non-uniformities are responsible for producing both secondary flow in a plane parallel to the discharge wire and also turbulence. The significance of these results to the performance of electrostatic precipitators is discussed.

Three-dimensional solutions are computed describing convection in a layer of a Boussinesq fluid of infinite Prandtl number. Rigid boundaries of constant temperature are assumed. As many as four physically different solutions are found for a given rectangular horizontal periodicity interval. These are two solutions describing bimodal convection, and two ‘square-pattern’ solutions which correspond to two orthogonally superimposed convection rolls of nearly equal amplitude. The Galerkin method used in obtaining the steady solutions can also be employed for the investigation of their stability. The stability of the bimodal solutions agrees with the experimental determination of the stability region by Whithead & Chan (1976). The square-pattern solution is unstable in the investigated parameter range, even though it exhibits the highest Nusselt number.

An analysis is presented of the steady states of two-dimensional convection near threshold in a laterally finite container with aspect ratio 2L [Gt ] 1. It is shown that the allowed wavevectors which can occur in the bulk of the container are reduced from a band |q| ∼ [(R − R0)/R0]½ in the laterally infinite system to a band |q| ∼ (R − R0)/R0 in a system with sidewalls (R is the Rayleigh number and R0 its critical value in the infinite system). The analysis involves an expansion of the hydrodynamic equations in the small parameter [(R − R0)/R0]½, and leads to amplitude equations with boundary conditions, which generalize to higher order those previously obtained by Newell & Whitehead and Segel. The precise values of the allowed wavevectors depend on the Prandtl number of the fluid and the thermal properties of the sidewalls. For certain values of these parameters all the allowed wavevectors are less than the critical value q0. The applicability of the results to convection in a rectangular container is briefly discussed.

An experimental and theoretical investigation has been conducted to determine the stability and disturbance-amplification characteristics of the combined forced and free convection flow adjacent to a vertical uniform-heat-flux surface in a uniform free stream. Previous studies of the stability of mixed convection flows have been limited to linear stability analysis of the effect of weak buoyancy on the neutral stability of a stronger forced flow. Here we consider circumstances where forced-convection effects are small compared with buoyancy effects. The flow behaviour is analysed using linear stability theory. The analysis incorporates a new formulation which permits the calculation of amplification contours for a given flow circumstance. The governing equations have been solved numerically to generate stability planes including the neutral curve and constant amplification contours. Stability planes are presented for assisting and opposed flows at Prandtl numbers Pr of 0·733 and 6·7. In air (Pr = 0·733), the presence of a weak free stream is found to cause the disturbance-amplification rates and the filtered frequency to deviate strongly from those found in purely free-convection flow. In water (Pr = 6·7), the effect of a free stream is much weaker. In addition, hot-wire and thermocouple measurements of the filtered frequencies and the disturbance-amplitude distributions are presented for aiding mixed convection flow in air. The measurements are found to be in very good agreement with the calculated results of the stability analysis.

The motion of a slender body near a flat interface between two immiscible fluids of different viscosities and densities is considered. The force distributions along a slender body are derived for the two cases when the instantaneous motion of the slender body is parallel to, and normal to, the interface. In some cases the slender body will rotate, the magnitude and direction of rotation being a function of the ratio of the two viscosities and the distance from the interface. For a narrow band of viscosity ratios the direction of rotation for a normally oriented slender body will change with distance from the interface. Two mechanisms for the interface-induced rotation are discussed.

Unsteady separating turbulent boundary layers are of practical interest because of unsteady aerodynamic phenomena associated with blades in compressors and with helicopter rotors in translating motion during high-loading conditions. Extensive measurements of a steady free-stream, nominally two-dimensional, separating turbulent boundary layer have been reported by Simpson, Chew & Shivaprasad (1981a, b) and Shiloh, Shivaprasad & Simpson (1981). Here measurements are reported that show the effects of sinusoidal unsteadiness of the free-stream velocity on this separating turbulent boundary layer at a practical reduced frequency of 0·61. The ratio of oscillation amplitude to mean velocity is about 0·3.

Upstream of flow detachment, single- and cross-wire, hot-wire anemometer measurements were obtained. A surface hot-wire anemometer was used to measure the phase-averaged skin friction. Measurements in the detached-flow zone of phase-averaged velocities and turbulence quantities were obtained with a directionally sensitive laser anemometer. The fraction of time that the flow moves downstream was measured by the LDV and by a thermal flow-direction probe.

Upstream of any flow reversal or backflow, the flow behaves in a quasisteady manner, i.e. the phase-averaged flow is described by the steady free-stream flow structure. The semilogarithmic law-of-the-wall velocity profile applies at each phase of the cycle. The Perry & Schofield (1973) velocity-profile correlations fit the mean and ensemble-averaged velocity profiles near detachment.

After the beginning of detachment, large amplitude and phase variations develop through the flow. Unsteady effects produce hysteresis in relationships between flow parameters. As the free-stream velocity during a cycle begins to increase, the Reynolds shearing stresses increase, the detached shear layer decreases in thickness, and the fraction of time $\hat{\gamma}_{{\rm p}u}$ that the flow moves downstream increases as backflow fluid is washed downstream. As the free-stream velocity nears the maximum value in a cycle, the increasingly adverse pressure gradient causes progressively greater near-wall backflow at downstream locations, while $\hat{\gamma}_{{\rm p}u}$ remains high at the upstream part of the detached flow. After the free-stream velocity begins to decelerate, the detached shear layer grows in thickness and the location where flow reversal begins moves upstream. This cycle is repeated as the free-stream velocity again increases.

Numerical solutions for the impulsively started spin-up from rest of a homogeneous fluid in a cylinder for small Ekman numbers are presented. The basic analytical theory for this spin-up flow is due to Wedemeyer (1964). Wedemeyer's solution shows that the interior flow is divided into two regions by a moving front which propagates radially inward across the cylinder. The fluid ahead of the front remains non-rotating, while the fluid behind the front is being spun up. Experimental observations have shown that Wedemeyer's model captures the essential dynamics of the azimuthal flow, but that it is not a quantitative model. Wedemeyer made several assumptions in formulating an Ekman compatibility condition, and inconsistencies exist between these assumptions and his solution. Later workers attempted to improve the analytical theory, but their work still included the same basic assumptions made by Wedemeyer.

No previous work has provided a comprehensive and accurate set of three-dimensional flow-field data for this spin-up problem. We chose to acquire such data using a numerical model based on the Navier–Stokes equations. This model was first checked against accurate laser-Doppler measurements of the azimuthal flow for spin-up from rest. New flow-field data over a range of Ekman numbers 9·18 × 10−6 [les ] E [les ] 9·18 × 10−4 are presented. Diagnostic studies, which reveal the various contributions to spin-up of the separate inviscid and viscous terms as functions of radius and time, are also presented. The plots of the viscous-diffusion term reveal the moving front, which is identified as a layer of enhanced local viscous activity. Immediately after the impulsive start, viscous diffusion is seen to be the major contributor to spin-up, then the nonlinear radial advection term takes over, and, finally, when spin-up is well progressed, the linear Coriolis force dominates. In the vicinity of the front, the inward radial flow is a maximum, and the vertical velocity is very small. Strong radial gradients of the vertical velocity are observed across the front and behind the front at the edge of the Ekman layer, and the azimuthal flow behind the front shows strong departures from solid-body rotation. These results enable us to fill in details of the flow not accurately given by Wedemeyer's model and its extensions.

A previous study by Forbes & Schwartz (1982) on flow under gravity of a fluid over a submerged semicircular disturbance is generalized to include the effects of surface tension. A linearized theory is presented, in which the existence of three different branches of solution is predicted. The solution of the fully nonlinear problem by a boundary-integral technique supports this prediction. The wave resistance experienced by the obstacle is computed for the linearized and nonlinear theories.

An analysis is presented that describes a model of the flow field of a rotating compressible fluid in a cylinder with internal sources or sinks of mass, momentum or energy, A solution of the mathematical model is obtained using an expansion in eigenfunctions of the corresponding homogeneous equation. The internal sources or sinks produce countercurrent flows analogous to flows generated by boundary conditions in the classical analysis of the problem. The application of this model to the flow driven by a feed stream or a scoop is discussed. Some sample calculations are presented that illustrate the countercurrent flow produced by sources of mass, the three components of momentum, energy and a mass source/sink combination. Calculations simulating feed introduction and a tails-removal scoop have been performed and the fluid-dynamics solutions have been used to calculate the optimum separative performance of the example centrifuge.

In the auscultatory technique, the most widely used clinical method to measure the arterial blood pressure, the systolic and diastolic blood pressures are estimated based on the beginning and cessation of the so-called Korotkoff sound emitted from the artery. Despite the widespread use of the technique, the mechanism by which Korotkoff sound is generated has not been well understood. In this report, a series of model experiments and a one-dimensional wave-propagation analysis have been conducted in order to elucidate the mechanism. As a result, the clear thud sound, heard when the cuff pressure is in the vicinity of the diastolic blood pressure, has been found to be generated by the sudden expansion of the vessel due to the shock wave that is formed at the wave front by compression-wave overtaking during wave propagation through the partially collapsed vessel segment under the cuff. Because of the strong nonlinear characteristics of the tube law, the sudden change in the vessel compliance around the near-zero transmural pressure, the shock wave is formed only when the cuff pressure, externally applied to the vessel, is nearly equal to or higher than the diastolic blood pressure and the vessel is partially collapsed in the late diastolic phase. The shock strength at the distal end of the partially collapsed vessel segment increases with the cuff pressure and the collapsed-vessel segment length within some limits. The waveform of the sound is well correlated with the time differential of the pressure waveform.

The purpose of the present paper is to investigate the structure of the laminar–turbulent transition region for the three-dimensional boundary layer along a 30° cone rotating in external axial flow. Spiral vortices, which were assumed as small disturbances in the present stability analysis, are observed experimentally in the transition region. The process of transition to a turbulent boundary layer is visualized in detail. When the ratio of rotational speed to external axial flow is increased, the critical and transition Reynolds numbers decrease remarkably. The spiral angle and the number of vortices appearing on the cone decrease as the rotational speed ratio is increased.

A linear stability analysis and experiments were carried out for the laminar–turbulent transition of three-dimensional incompressible boundary layers induced on the surface of a cone rotating around the axis of symmetry with constant angular speed in still fluid. Five cones having total angle of 30°–150° were tested. The results show that the critical and transition Reynolds numbers, the direction of spiral vortices appearing in the transition region and their number on a cone increase as the cone angle is increased, and they tend to the values for the case of a rotating disk. Flow visualizations were made for the transitional process and also for cross-sectional flows of spiral vortices.

The stability of an interface between a liquid metal and an insulating atmosphere, in which an inductor generates a uniform alternating magnetic field, is investigated, with particular attention given to the influence of the electrical conductivity of the liquid. In a range of high frequencies, a quasi-steady approximation is justified, in which the pulsation of the electromagnetic forces is negligible compared with their mean part, and the unsteadiness of the magnetic field only appears through the skin effect. By means of a linear analysis, the influence of the alternating magnetic field on a perturbation of the interface is found to be neutral for wavevectors perpendicular to the magnetic field, and stabilizing for any other orientation. The stabilizing effect is largest when the angle between the wavevector and the magnetic field is zero, and it increases with increasing wavenumber. This effect, maximum for an infinitely conducting medium, quickly decreases with the electrical conductivity.