In a large range of Reynolds numbers, 6 × 104 < Re < 5 × 106, the flow around single cylinders with smooth surfaces has been investigated. The high values of the Reynolds numbers were obtained in a test channel which could be pressurized up to 40 bar of static pressure. New experiments were performed to measure the local pressure and skin friction distribution around the cylinder. From these results the total drag, the pressure drag and the friction drag were calculated. By means of the skin friction distribution the position of the separation points, separation bubbles or transition points can be localized. These data allow one to define three states of the flow: the subcritical flow, where the boundary layer separates laminarly; the critical flow, in which a separation bubble, followed by a turbulent reattachment, occurs; and the supercritical flow, where an immediate transition from the laminar to the turbulent boundary layer is observed at a critical distance from the stagnation point. According to the total drag coefficient the values found in this paper connect the subcritical region represented by the measurements of Wieselsberger (1923) and Fage & Warsap (1930) with the supercritical range in which Roshko (1961) carried out his experiments.

A numerical solution is presented for predicting the flow and heat transfer due to free convection in the entry region of a cooled vertical pipe, open at both ends. Following Lighthill (1953) the Kármán-Pohlhausen method is used in this analysis. Velocity and temperature profiles are assumed satisfying the physical boundary conditions, and the integrated forms of the equations of motion and the equations themselves at the axis and the walls of the pipe are used to calculate the various parameters involved in the profiles assumed. Two cases of constant wall temperature and linearly decreasing temperature with height were considered. Cooling decelerates the fluid in the boundary layer that forms at the wall and the fluid in the core is accelerated by virtue of continuity. As cooling progresses, at Rayleigh number O(103) the fluid in the boundary layer starts reversing at first and then assumes progressively increasing velocities. Graphs are presented for the development of the predicted velocity and temperature profiles and the other parameters involved, for a situation when the boundary layer fills the whole pipe.

The surge studied in this paper is due to the sudden closure of the sink of a bathtub vortex. Experimental evidence established that the surge is not initially a wave but is in fact a slug of fluid which has, for a very short period of time, a distinctive motion of its own. The purpose of this paper is to present the salient features of an experimental investigation of the effect of circulation, geometry, and viscosity on the speed of the surge and to report some rather unexpected observations.

This paper concerns the stability characteristics of laminar natural convection in external flows. Until recently, very little was known about such stability because of the inherent complexity of temperature-coupled flows and because of the complicated mechanisms of disturbance propagation. In this work the stability of the laminar natural convection boundary layer is examined more closely in an attempt to predict the experimental results recently obtained. In particular, it is shown that an important thermal capacity coupling exists between the fluid and the wall which generates the flow. This thermal capacity coupling is shown to have a first-order effect for particular Grashof-number wave-number products. Solutions are obtained for a Prandtl number of 0·733 and several values of relative wall thermal capacity. These solutions indicate the important role of this wall coupling. In particular, the results predict the experimental data previously obtained.

In addition, solutions with ‘zero wall storage’ are obtained for a range of Prandtl numbers from 0·733 to 6·9. The relative disturbance u-velocity and temperature amplitudes and their phases are shown for Pr = 0·733 and several wall-storage parameters, and for Pr = 6·9 with zero wall storage. A comparison between the disturbance temperature distribution and the data obtained from a recent experimental investigation shows close agreement when the thermal capacity of the wall is taken into account.

In the appendix, it is shown that for temperature-coupled flows and wall-coupled boundary conditions the flow is unstable at a lower Grashof number for two-dimensional disturbances than it is for three-dimensional disturbances. This result has been supported by the recent experimental observations.

Stewartson's theory for axisymmetric hypersonic flow of a model gas over slender bodies with strong viscous interaction and strong shock wave is extended to power-law viscosity variation and Prandtl numbers other than one. Flow properties at the body surface and shock are obtained without recourse to numerical integration. Numerical computations are presented for axisymmetric flow over a three-quarter power-law body with strong shock wave and viscous interactions that range from weak to strong.

The results of a theoretical treatment are presented for the slow flow of a viscous fluid through a circular cylinder within which a small spherical particle is confined. The sphere is situated in an arbitrary position within the cylinder, rotates with an arbitrary constant angular velocity and moves at constant velocity parallel to the wall. Approximate expressions are presented which give the frictional force, torque, and permanent pressure drop caused by the presence of this obstacle in the original Poiseuillian field of flow.

An eccentricity function for the torque on a sphere in a circular cylinder was evaluated numerically. It can be used to predict the wall-effect for the torque as well as the angular velocity with which a ‘dense’ spherical particle will rotate. Expressions are presented which predict the angular velocity of ‘dense’ as well as neutrally buoyant hydrodynamically supported spherical particles.

The theory of wave action conservation is summarized, and its interpretation in terms of the working, against the rate of strain of the basic flow, of an interaction stress associated with the waves is discussed. Usually this interaction stress is identical with the radiation stress of a uniform plane wave. The problem of internal gravity wave propagation in an incompressible, stratified Boussinesq liquid is considered in detail for a more general basic flow than has hitherto been treated, and the interaction stress is derived. One component of the interaction stress tensor is only equal to the corresponding component of the radiation stress tensor if we include in the latter, in addition to the Reynolds stress, a term associated with the redistribution of matter, on the average, by the wave. Two other components of the radiation stress tensor are modified in a similar manner, but the corresponding components of the interaction stress tensor are undefined, and so no comparison is possible.

A linear three-dimensional model of the wind-driven ocean circulation is treated by boundary-layer methods. The interior flow, below the Ekman layer, differs from the classical gyres of Munk (1950). There is a north-eastwards transport of fluid from the western boundary current of the southern gyre across the latitude of zero wind stress curl into the northern gyre. A return flow in the Ekman layer preserves continuity.

A co-ordinate system consisting of the left-running characteristics (α = const.) and the streamlines (ϕ = const.) is used. The governing equations are derived in terms of α and ϕ for a two-dimensional steady supersonic rotational inviscid flow of a perfect gas. The equations are applied to the problem of an initially parallel supersonic rotational flow which expands around a convex corner. The velocity of the incoming flow at the wall is considered to be either supersonic (case 1) or sonic (case 2). For each case, solutions uniformly valid in the region near the leading characteristic and in the region near the corner, are found for the Mach angle and flow deflexion angle in terms of their values on the leading characteristic and at the corner. In case 2, a transonic similarity solution is found and composite solutions are constructed for each region. Comparisons are made with existing exact numerical results.

The dynamics of long water waves are considered in a curved geometry representing a canal bend. The presence of the bend is found to produce a spectrum of transverse oscillations in the canal. The associated dominant amplitudes are evaluated for both tidal periods and higher frequencies representative of tsunamis. It is found that low-frequency waves do not lead to significant transverse amplitudes. For tsunamis, the presence of the bend may result in considerable changes in the local wave amplitude.

High-frequency plane sound waves in ideal gases with internal dissipation are discussed. Particular applications to dissociating diatomic gases and gases displaying vibrational relaxation are considered. A criterion in the form of an inequality is derived for the validity of the high-frequency approximation and an asymptotic analysis is developed.

The scattering of a gravity wave of wave number k by a circular dock of radius a and draft d – h in water of depth d is calculated through a variational approximation. The total and differential scattering cross-sections, the peripheral displacement, and the lateral force on the dock are presented as functions of ka with d/a and h/d as parameters and compared with the classical results for a circular cylinder (h = 0). A pronounced resonance is found near ka = 2 for certain values of d/a and h/d.

Laminar flow of a stably stratified fluid with uniform upstream velocity and density gradient past a flat plate is investigated experimentally and theoretically. In the experimental study, the flat plate, parallel to the direction of motion, is towed horizontally at uniform speeds in a tank of stratified salt water at uniform density gradients. The horizontal velocity in front of, above, and behind the flat plate is measured with a flow visualization technique. One of the striking phenomena is the strong upstream influence (the upstream wake) of an obstacle in a flow of stably stratified fluid when the gravity effect is comparable to, or more than the inertial effect. The velocity profiles of the upstream wake and boundary layer above the flat plate are wavy and found to be governed by the ratio of Reynolds number Be to Richardson number Ri. The problem is also analysed theoretically with Boussinesq's approximation and two-parameter perturbation expansions for the upstream wake and the boundary layer. The solutions for the upstream wake and for the boundary layer are compared with measurements.

The velocities, accelerations and drag forces experienced by two equal spheres falling along their line of centres in a viscous fluid were determined for three groups of Reynolds numbers R in the range where it is commonly assumed that Stokes's approximation applies. For all groups, with R ranging between 0·060 and 0·216, both spheres continually acclerated as they fell, and the upper sphere fell faster and accelerated more than the lower one. In contrast to Stimson & Jeffery's (1926) theory, which is based on the Stokes approximation, and to most earlier experimenters, the drag-force coefficients of the upper sphere computed from the experiments were significantly smaller than those for the lower sphere. Oseen's theory for this case agreed with the experiments in some respects, but contrary to it the drag-force coefficient varied with R for the upper sphere as well as the lower sphere.