Detailed studies are reported of the free and forced oscillation of disks and a right-circular cylinder constrained to rotate about a fixed diametrical axis passing through the centre of the body and normal to the free-stream direction. When a disk is free to rotate, it oscillates at a definite frequency with slowly varying amplitude and phase. A right-circular cylinder also oscillates at a definite frequency but with rapidly increasing amplitude. When the amplitude becomes large, after a few cycles of oscillation, the cylinder rotates steadily in one direction.

Analogue computer elements, position sensors and a dynamic moment balance were used to study the static restoring moment, dynamic restoring moment, average damping moment, statistical properties of the disk motion and power spectrum of the turbulent moment. The behaviour of the disk and cylinder are explained using the measurements and the theory for random excitation of a linear system. The turbulent exciting moment is caused by the unsteady flow in the wake and can be changed by placing disks and splitter plates in the wake. A model is proposed for the unsteady flow field in the wake behind the disk. The model relates the turbulent moment to the vortex shedding process in the wake.

The onset of convection in a rotating cylindrical annulus with sloping conical boundaries is studied in the case where this slope increases with the radius. The critical modes assume the form of drifting spiralling columns attached to the inner cylindrical wall at moderate and large Prandtl numbers, but they become attached to the outer wall at low Prandtl numbers. These latter ‘equatorially attached’ modes are multicellular at intermediate rotation rates. Through a perturbation analysis which is validated by a numerical code, we show that all equatorially attached modes are quasi-inertial modes and analyse the physical mechanisms leading to multicells. This is done for both stress-free and no-slip boundary conditions. At finite amplitudes the convection generates a Reynolds stress which leads to the development of a mean zonal flow, and a geometrical analysis of the mechanisms leading to this zonal flow is presented. The influence of Ekman friction on the zonal flow is also studied.

The isopycnal elevation ζ of a stratified incompressible fluid constitutes a generalized co-ordinate in terms of which the dynamics can be described in Hamiltonian form. The description is complete, and no additional variables are necessary, when the isopycnal circulation vanishes and when there are no remote sources of flow. The Hamiltonian, constructed in a co-ordinate system that coincides with the isopycnal surfaces, generates nonlinear equations of motion for ζ and its conjugate variable π which are formally exact for arbitrary displacements of the fluid and which are equivalent at lowest order to the usual linearized equations of internal waves. The appropriate scaling parameters for the nonlinearity are the isopycnal slope [dtri ]ζ and vertical strain ∂zζ, which emerge as the expansion parameters of an explicit powerseries representation of the Hamiltonian.

The incompressible laminar flow in the neighbourhood of the trailing edge of an aerofoil undergoing sinusoidal oscillations of small amplitude in a uniform stream is described in the limit as the Reynolds number R tends to infinity. It is shown that if the frequency parameter is of any order less than R¼ the viscous correction to the Kutta condition and hence to the lift and moment may be determined from the results for the steady case. Justification of this correlation requires discussion of the flow in an additional region not encountered in previous studies.

The selection of long air bubbles propagating steadily in a strongly collapsed fluid-filled elastic tube is investigated experimentally in a benchtop model of airway reopening. Localized regions of strong collapse are likely in the lung, because collapsing fluid-elastic instabilities promote extensive deformation of the airway cross-section beyond the point of opposite wall contact. We find that radical changes in the reopening mechanics occur at this point. We build on the recent identification by Heap & Juel (Phys. Fluids, vol. 20, 2008, article no. 081702) of three different steadily propagating bubbles (asymmetric, double-tipped and pointed) that are selected successively for increasing values of the capillary number (Ca, ratio of viscous to surface tension forces) in tubes initially collapsed beyond the point of opposite wall contact. The asymmetric bubble is also observed in less collapsed tubes for small values of Ca, and we show that it bifurcates super-critically from the usual parabolic-tipped bubble as Ca increases. We also characterize the mechanisms underlying the discontinuous transitions between asymmetric and double-tipped bubbles, and double-tipped and pointed bubbles. In particular, we find that the tube must reopen to a critical height for double-tipped bubbles to be selected. The length of the precursor fingers in the double-tipped bubble decreases with Ca, and the bubble loses stability to pointed bubbles when this length is less than the height of the tube at the point where the fingers merge. By contrast with the asymmetric and double-tipped bubbles, the pointed bubble infiltrates the most collapsed part of the tube to yield the rapid reopening of the airway at low pressure, with the potential to reduce ventilation-induced lung damage.

A rational theory is developed to describe the reattachment of a laminar shear layer in supersonic flow. In the neighbourhood of reattachment the flow develops a threetiered or ‘triple-deck’ structure analogous to that which occurs at a point of separation (Stewartson & Williams 1969) and, as in the separation problem, the local flow pattern may be found independently of the flow in the surrounding regions. The fundamental problem of the reattachment triple deck reduces to the solution of the incompressible boundary-layer equations in the lower deck, which is of streamwise and lateral dimensions O(R−⅜) and O(R−⅝), where R [Gt ] 1 is a representative Reynolds number for the flow. Pressure variations in this region are O(R−¼). Asymptotic solutions in terms of x, the scaled streamwise lower-deck variable, are derived to confirm the transition from a reverse flow profile at x = 0+, through reattachment, to a forward flow as x → ∞, the attainment of the required asymptotic form downstream (as x → ∞) being shown to depend crucially upon the correct choice of the finite part of the pressure in the lower deck at x = 0+. The lower-deck solution is singular at x = 0+ and assumes a complicated multi-structured form which is shown to match upstream with the solution in a largely inviscid region of dimension O(R−½) where the pressure is O(1) and the major part of the flow reversal takes place. Solutions are presented for reattachment at a wall and for symmetric reattachment behind a wedge or bluff body. In the former case the results also explain the apparent ignorance of upstream conditions in the expansive triple-deck solution formulated by Stewartson (1970) in the context of supersonic flow around a convex corner.

It is known that certain configurations which possess curvature are prone to a class of instabilities which their ‘flat’ counterparts will not support. The main thrust of the study of these centrifugal instabilities has concentrated on curved solid boundaries and their effect on the fluid motion. In this article attention is shifted towards a fluid-fluid interface observed within a curved incompressible mixing layer. Experimental evidence is available to support the conjecture that this situation may be subject to centrifugal instabilities. The evolution of modes with wavelengths comparable with the layer's thickness is considered within moderately curved mixing layers. The high Taylor/Görtler number régime is also discussed which characterizes the ultimate fate of the modes.

We investigate the weakly nonlinear spatial evolution of helical disturbances of an axisymmetrical jet which are the analogue of three-dimensional disturbances, such as a single oblique wave (the wave vector is directed at an angle to the main flow velocity) in plane-parallel flows. It is shown that when a supercriticality is large enough, the perturbation amplitude A grows in the streamwise direction (along z) explosively: A ∼ (z0 — z)−5/2, though more slowly than in the case of essentially three-dimensional disturbances in the form of a pair of oblique waves (A ∼ (z0 — z)−3; Goldstein & Choi 1989). The nonlinearity needed for such a growth, is due equally to the cylindricity of shear layer and to the spatial character of the evolution (in the temporal problem the ‘evolution’ contribution is absent). At a smaller supercriticality, the evolution equation has a non-local (integral in z) nonlinearity, unusual for the regime of a viscous critical layer. Scenarios of disturbance development for different levels of supercriticality are studied, with proper account taken of viscous broadening of the flow.

The performance of a circular electrochemical wall shear rate probe under unsteady flow conditions is analysed through a combined experimental, numerical and analytical approach. The experiments arc performed with a ferri- and ferrocyanide redox couple and compared to finite element analyses of the two-dimensional time-dependent convection—diffusion equation. The results are related to the analytical Lévêque solution for steady flow and for some cases to Pedley's model for heat transfer in reversing shear flow (Pedley 1976).

The steady flow analyses showed that in our experiments axial diffusion is only of minor importance but that for the lower Péclet numbers (< 104) three-dimensional effects, like tangential diffusion, may not be neglected. A similar result is found for the oscillating case. A fair agreement is found between experimental and numerical data during flow acceleration, but during flow reversal remarkable (about 15%) deviations are found. The observed insensitivity of the transducer during flow reversal is quite well predicted by Pedley's model. Finally, the performance of the probe may be improved somewhat by a decrease in cathode length and cathode—anode distance.

The transition process of mechanically generated regular waves into wind waves is investigated in a wind-wave tunnel. Modulations of characteristic quantities of the waves are examined in both space and time using wave-gauge arrays. The transition begins with the occurrence of wave breaking, and it is associated with the following two processes: (i) the irregularization, i.e. the generation and amplification of a random modulation whose wave height and period are in phase; and (ii) the frequency shift to the lower side by the mutual coalescence of waves through the amplification of the modulation, the coalescence occurring at the troughs of the period modulation. The modulational properties under the effect of wind with wave breaking are thus in part different from the theoretical prediction of modulational instability of a freely travelling wavetrain. It is concluded that the mechanism of the transition is the modulational instability coupled with the wind effects.

The occurrence of new unstable modes of quasigeostrophic baroclinic oscillation of rotating stratified shear flow over a wavy bottom is examined. To obtain a tractable mathematical problem, the bottom topography is considered as a perturbation modifying the oscillations. It is found that combinations of a top-intensified and a bottom-intensified Eady mode, each stable without topography, can be destabilized by topography if certain resonant conditions are met. These are that (i) the two modes possess the same wavefrequency, and (ii) topography possesses a wavenumber c bridging the gap between the wavenumbers of the modes a, b, i.e. c = a – b. Growth rate of this instability (called type A) is proportional to the amplitude of the topographic component. There are two special cases: (i) when one of the basic modes is a marginally neutral mode – according to the classical analysis without topography – the instability is stronger (type M) with growth rate proportional to the 2/3-power of topographic amplitude; (ii) when both modes are marginally neutral the instability is even stronger (type M2) with growth rate proportional to the square root of topographic amplitude.

These topographic instabilities, like classical baroclinic instability, draw their energy from the available potential by transporting buoyancy down the mean gradient associated with the geostrophic shear flow.

High frequency surface waves are generated by the forced heaving of either two half-immersed spheres in infinite water or by a half-immersed sphere in a hemispherical lake. The virtual-mass coefficients can be found, to leading order, in terms of wave-free limit potentials.

The interaction of free-surface bores and an erodible porous channel bed in a shallow-water flow is analysed based on the assumption of weak coupling between free-surface discontinuities and bed discontinuities and on the simplest closure for the sediment transport rate (cubic with the mean flow velocity). It is shown that free-surface bores with finite cross-stream extent can evolve over the erodible bed by generating vertically oriented macrovortices in a manner similar to, but more complex than, that of free-surface bores of finite cross-stream extent over a rigid channel bottom. An equation for the potential vorticity is derived, which shows that on an erodible bed the vortices are generated by a combination of various mechanisms related to energy dissipation of both surface bores and bed discontinuities. The model is verified and the physics explored by comparison with a number of numerical simulations, typical of both riverine (dam-break test and pit test) and nearshore (bore on a beach test) flows, and with previously published experimental results. For all cases a fairly good agreement is found between the analytically estimated potential vorticity and that computed numerically.

The dispersion relation is found for edge waves in a rotating stratified fluid over a constant sloping bottom. The dispersion relation is then extended to the case of arbitrary gentle bottom bathymetry. Superinertial trapped modes do not exist in the rigid-lid Boussinesq case. The effect of some of the approximations that have been made in this problem is discussed.

Townsend has derived a relation between mean vorticity and Reynolds stress valid in the wall layer of a turbulent flow. The vorticity Ω appears as a function of the local stress τ and its gradient. Such a relation is better suited for use in the vorticity equation than in the momentum equation. The Rayleigh problem, whose vorticity equation is simply ∂Ω/∂t = ∂2τ/∂y2, is introduced as a setting for Townsend's theory. Certain wall speed programmes are shown to generate Rayleigh layers that are exactly self-similar in the fully turbulent part of the flow. Those layers correspond to Clauser's equilibrium boundary layers. A formal analogy between the two families is found; the analogy becomes quantitatively exact in the limit of infinite Reynolds number. The Rayleigh problem is posed in similarity form. A composite non-linear, ordinary differential equation for the stress profile is deduced from a two-layer model incorporating Townsend's relation for the wall layer and Clauser's constant eddy-viscosity assumption for the outer layer. The profile depends on the wall-speed programme selected and on two empirical constants: the combination λ = √(k)/k of Clauser's k and Kármán's k, and Townsend's constant B. Closed-form solutions for arbitrary λ and B are obtained in two important cases: constant wall stress, analogous to constant pressure above a boundary layer, and zero wall stress, corresponding to continuous separation. The velocity profile in the wall region of a continuously separating Rayleigh layer is found to depend sensitively on B.

An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract energy via resonant triad interactions while in contact with the underlying beam, and the mean flow is assumed to be small so that its advection effect on the perturbations is as important as dispersion, triad nonlinearity and viscous dissipation. In this ‘distinguished limit’, the perturbation dynamics are governed by the same evolution equations as those derived in Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402), except for a mean flow term that affects the group velocity of the perturbations and imposes an additional necessary condition for PSI, which stabilizes very short-scale perturbations. As a result, it is possible for a small amount of mean flow to weaken PSI dramatically.

Following weak plane shock diffraction at a knife-edge situated in a duct, a two-dimensional vortex sheet springs from the salient edge. The method of ‘vortex discretization’ is used, in conjunction with a Schwarz-Christoffel transformation, to develop a two-dimensional potential model for this constrained form of vortex generation. The analysis is independent of empirical parameters and describes, qualitatively, the pattern of streamlines through the orifice.

Flow-visualization photographs are presented which illustrate the spiral shape of the starting vortex. Although of a limited nature, quantitative experimental vortex growth rates have been obtained and are compared with initial growth rates predicted theoretically. The results are discussed together with other aspects of the problem, including the limitations of the theory.

An extension of vortex discretization is developed whereby the pressure distribution remote from the vortex sheet can be calculated. The combination of flow separation and the associated static wall pressure distribution gives theoretical insight into the mechanism of flow through an orifice.

Complementary variational formulations are developed for the scattering of a gravity wave by a circular dock. These formulations, which are based on assumed distributions of the radial velocity and the potential, respectively, on the projection of the cylindrical boundary, yield lower and upper bounds to an impedance parameter that determines the difference between the scattered wave for the dock and the corresponding wave for a circular cylinder. Numerical results, using trial functions based on the incident wave, are compared with the results implied by a Galerkin solution (Garrett 1971). The maximum errors in the variational approximations to the total scattering cross-section are found to be of the order of 2% for a typical depth/radius ratio, draft/depth ratios of 0, ½ and 1, and all wavelengths. The axisymmetric component of the scattering cross-section is found to be very close to the value for scattering by a circular cylinder (dock extending to bottom). The intensity of the scattered wave on the forward axis for long wavelengths and a certain range of the geometric parameters is significantly less than that for a circular cylinder, and may vanish for critical combinations of these parameters.