Experiments on transition to turbulence in a purely oscillatory pipe flow were performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude Û, from 19 to 1530 (or for values of the Reynolds number Re, defined using the pipe diameter d and Û, from 105 to 5830) and for values of the Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·19. Three types of turbulent flow regime have been detected: weakly turbulent flow, conditionally turbulent flow and fully turbulent flow. Demarcation of the flow regimes is possible on Rλ, λ or Re, λ diagrams. The critical Reynolds number of the first transition decreases as the Stokes parameter increases. In the conditionally turbulent flow, turbulence is generated suddenly in the decelerating phase and the profile of the velocity distribution changes drastically. In the accelerating phase, the flow recovers to laminar. This type of partially turbulent flow persists even at Reynolds numbers as high as Re = 5830 if the value of the Stokes parameter is high.

A conditional averaging technique to extract the underlying vortex pattern from a turbulent bluff body wake is described. Ensemble averages of wake velocities are developed on the basis of a reference phase position, determined from the outer flow irrotational fluctuations. The method is applied to the wakes of a stationary and oscillating D-shape cylinder, where, in the latter case, the vortex shedding is locked to the frequency of body movement. Direct comparisons of average circulation and vortex street spacings are obtained and these demonstrate the significant change in wake structure that accompanies and sustains vortex-induced vibrations. It is observed in both conditions that only 25% of the estimated shed vorticity is found in the fully developed wake. In addition the analysis produces profiles of vorticity and velocity in an ‘average vortex cycle’. A model, developed to help interpret these results, suggests that a good representation of an average wake situation is obtained by the addition of considerable mean shear to a street of finite area axisymmetric vortices.

This paper considers the general problem of laminar, steady, horizontal, Oseen flow at large distances upstream and downstream of a two-dimensional body which is represented as a line source of horizontal or vertical momentum, or as a line heat source or heat dipole. The fluid is assumed to be incompressible, diffusive, viscous and stably stratified. The analysis is focused on the general properties of the horizontal velocity component, as well as on explicit calculation of the horizontal velocity profiles and disturbance stream-function fields for varying degrees of stratification. For stable stratifications, the flow fields for all four types of singularities exhibit the common feature of multiple recirculating rotors of finite thicknesses, which leads to an alternating jet structure both upstream and downstream for the horizontal velocity component and to leewaves downstream in the overall flow. The self-similar formulae for the velocity, temperature and pressure at very large distances upstream and downstream are also derived and compared with the Oseen solutions.

A study has been made of the wake of a cylinder vibrating in line with an incident steady flow. The Reynolds number for the experiments was 190, and the vortex shedding was at all times synchronized with the vibrations of the cylinder, which were in a range of frequencies near twice the Strouhal shedding frequency for the stationary cylinder. Two distinct vortex wake patterns were encountered. The first is a complex regime in which two vortices are shed during each cycle of the vibration and form an alternating pattern of vortex pairs downstream. The second pattern is an alternating street which results from the shedding of a single vortex during each cycle of the cylinder's motion. The street geometry in the latter case shares many basic characteristics with the wake of a cylinder vibrating in cross-flow. These include the effects of vibration amplitude and frequency on the longitudinal and transverse spacing of the vortices. The results obtained from these experiments in air are in agreement with previous findings from free- and forced-vibration experiments in water at both higher and lower Reynolds numbers.

The axisymmetric streaming Stokes flow past a body which contains a surface concave to the fluid is considered for the simplest geometry, namely, a spherical cap. It is found that a vortex ring is attached to the concave surface of the cap regardless of whether the oncoming flow is positive or negative. A stream surface ψ = 0 divides the vortex from the mainstream flow, and a detailed description of the flow is given for the hemispherical cup. The local velocity and stress in the vicinity of the rim are expressed in terms of local co-ordinates.

A vertical plate oscillating vertically in a statically stably-stratified fluid induces an internal wave damped by viscous forces. A two-dimensional linear stability analysis of this time-dependent state shows that the wave is highly unstable when the buoyancy and forcing frequencies are comparable. This gravitational (buoyancy) instability is due to the presence of the background stratification. The neutral curve is calculated and the system energetics are explored. Excellent agreement is obtained with the recent experimental observations of Robinson & McEwan.

The stability of the decaying laminar flow in a suddenly blocked channel is investigated. The partial differential system governing the stability of the flow is solved using a WKB type of approach. It is shown that the first term of the WKB expansion of the disturbance velocity field is just that obtained by a quasi-steady approach. The flow is found to be unstable at quite small Reynolds numbers. This instability is associated with the inflexional nature of the velocity profiles of the decaying flow.

This study was motivated by the focal tendency of atherosclerotic plaque to appear near arterial junctions. A two-dimensional bifurcation was selected to provide preliminary information on branch flow dynamics. Superseding previous steady flow estimates in similar branches, digital solutions for two flux waves have been obtained to reveal temporal and spatial distributions of shear and separation in pulsatile flow. Marked differences from steady flow are illustrated as well as variation due to flux-wave shape.

The dispersion relation for a random gravity wave field is derived using the complete system of nonlinear equations. It is found that the generally accepted dispersion relation is only a first-order approximation to the mean value. The correction to this approximation is expressed in terms of the energy spectral function of the wave field. The non-zero mean deviation is proportional to the ratio of the mean Eulerian velocity at the surface and the local phase velocity. In addition to the mean deviation, there is a random scatter. The root-mean-square value of this scatter is proportional to the ratio of the root-mean-square surface velocity and the local phase velocity. As for the phase velocity, the nonzero mean deviation is equal to the mean Eulerian velocity while the root-mean-square scatter is equal to the root-mean-square surface velocity. Special cases are considered and a comparison with experimental data is also discussed.

The exact equations of steady inviscid flow past a ship hull are formulated in a reference domain, onto which the flow domain is mapped. A thin-ship perturbation analysis is performed in the reference domain, and the first- and second-order solutions are derived. The classical thin-ship theory is obtained as the consistent, mapping-independent, perturbation solution in the physical space. Guilloton's method is interpreted as an inconsistent, mapping-dependent, second-order approximation. A new inconsistent approximation is obtained by exploiting the freedom in the mapping of the flow domain onto the reference domain. Further improvements are suggested.

The flow field produced by a shock wave reflecting from a helium gas-liquid interface was investigated using a cryogenic shock tube. Incident and reflected shock waves were observed in the gas; transmitted first- and second-sound shocks were observed in the liquid. Wave diagrams are constructed to compare the data with theoretical wave trajectories. Qualitative agreement between data and theory is shown. Quantitative differences between data and theory indicate a need for further analysis of both the gas-liquid interface and the propagation of nonlinear waves in liquid helium.

This work was a first step in the experimental investigation of a complex non-equilibrium state. The results demonstrate clearly the usefulness of the cryogenic shock tube as a research tool. The well-controlled jump in temperature and pressure across the incident shock wave provides unique initial conditions for the study of dynamic phenomena in superfluid helium.

The stability of the conduction regime of natural convection of a fluid contained in a narrow rotating annulus with a heated inner wall has been investigated according to the linear theory. The results include computations for Prandtl numbers P = 0, 0·72 and 6·7 over a large range of the rotational parameters. For low rotation rates the instability sets in as multicellular convection with the cell axes horizontal in the absence of rotation but tilting monotonically towards the vertical as the rotation rate is in creased. Two other types of instability were found at high rotation rates. For large Froude numbers the unstable thermal stratification leads to a Bénard type of convection with vertically oriented rolls. For large Taylor numbers, through a mainly hydrodynamic mechanism, a nearly vertically oriented cellular structure develops in the flow which is destabilized as a result of rotation.