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The current work analyses the onset characteristics of Rayleigh–Bénard convection in confined two-dimensional two-layer systems. Owing to the interfacial interactions and the possibilities of convection onset in the individual layers, the two-layer systems typically exhibit diverse excitation modes. While the attributes of these modes range from the non-oscillatory mechanical/thermal couplings to the oscillatory standing/travelling waves, their regimes of occurrence are determined by the numerous system parameters and property ratios. In this regard, the current work aims at characterising their respective influence via methodical linear and fully nonlinear analyses, carried out on fluid systems that have been selected using the concept of balanced contrasts. Consequently, the occurrence of oscillatory modes is found to be associated with certain favourable fluid combinations and interfacial heights. The further branching of oscillatory modes into standing and travelling waves seems to additionally rely on the aspect ratio of the confined cavity. Specifically, the modulated travelling waves have been observed to occur (amidst standing wave modes) at discrete aspect ratios for which the onset of oscillatory convection happens at unequal fluid heights. This behaviour corresponds to the typical $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}m$:$n$ resonance where the critical wavenumbers of convection onset in the layers are dissimilar. Based on all of these observations, an attempt has been made in the present work to identify the oscillatory excitation modes with a reduced number of non-dimensional parameters.

The results of an experimental investigation of a turbulent vortex street in the range 103 [lsim ] Re [lsim ] 2 × 104 are presented. The vortex street was created by the motion of a circular cylinder in a motionless fluid (mercury). Photographs obtained showed that the turbulent street, created by the vortex shedding behind the cylinder, persisted at longer downstream distances and higher Reynolds numbers than previously reported in the literature. A theory was developed to account for the experimental measurements pertaining to the change of the geometrical characteristics, h (distance between the two rows of vortices) and α (longitudinal distance between two consecutive vortices on the same row), of the street in the downstream direction. The implications of the structure of the vortex street on the entrainment mechanism of the turbulent wake are discussed. Some observations of the flow in the formation region of the vortices are discussed in relation to existing work.

Temperature-sensitive constant-current wires operating at very low resistance ratios have been tested for temperature fluctuation response. A significant step in the response was found to occur with a centre-frequency of typically 1/6 Hz. The step size was observed to be as large as 30% and grew from zero to its maximum value in about a decade. Analysis shows that this phenomenon is associated with axial conduction of heat to and from the prongs. If it is recognized that prongs have finite thermal inertia then a modification of the boundary conditions to the equations of Betchov (1948) predicts this step, in agreement with the simple asymptotic analysis of Maye (1970).Experiments indicate that a similar phenomenon occurs with velocity-sensitive wires. Axial conduction appears to be the most likely cause. Aeroelastic deflexions and non-uniform cooling caused by bowing of the wire make precise predictions impossible. Here the differences in step size between wires were observed to be as large as 10% (or 20% in mean-square energy), the centre-frequency was usually beyond 10 Hz for the wires tested and the step extended over a much broader frequency range than in the temperature-sensitive case. The effect occurred at all velocities, resistance ratios and wire geometries. An analysis based on non-uniform cooling of the wire filament predicts the correct frequency range and shows that steps of 10% in frequency response are quite plausible.

The laminar pulsatile flow over a semi-infinite flat plate, on which is located a small (steady) surface distortion is investigated; triple-deck theory provides the basis for the study. The problem is of direct relevance to the externally imposed acoustic excitation of boundary layers. The investigation is primarily numerical and involves the solution of the nonlinear, unsteady boundary-layer equations which arise from the lower deck. The numerical method involves the use of finite differencing in the transverse direction, Crank-Nicolson marching in time, and Fourier transforms in the streamwise direction, and as such is an extension of the spectral method of Burggraf & Duck (1982). Supersonic and incompressible flows are studied. A number of the computations presented suggest that the small surface distortion can excite a large-wavenumber, rapidly growing instability, leading to a breakdown of the solution, with the wall shear at a point seeming to increase without bound as a finite time is approached. Rayleigh modes for the basic (undisturbed) velocity profile are computed and there is some correlation between the existence and magnitude of the growth rate of these unstable modes, and the occurrence of the apparent singularity. Streamline plots indicate that this phenomenon is linked to the formation of closed (or ‘cats-eye’) eddies in the main body of the boundary layer, away from the wall. Tollmien-Schlichting instabilities are clearly seen in the case of incompressible flows.

We study the initial-value problem posed by the small-amplitude (linearized) free oscillations of free drops, gas bubbles, and drops in a host liquid when viscous effects cannot be neglected. It is found that the motion consists of modulated damped oscillations, with the damping parameter and frequency approaching only asymptotically the results of the normal-mode analysis. The connexion with the normal-mode method is demonstrated explicitly and the experimental relevance of our results is discussed.

Oscillating flow in a tapered channel was studied experimentally by observing the deformation of a dye streak within a Plexiglas channel during piston induced, volume-cycled oscillations. The observed steady streaming was compared to theoretical calculations. Both the theoretical and experimental results show bi-directional drift for all frequencies, with characteristics dependent upon the value of the Womersley parameter, α = b(ω/ν)½. For large values of α, e.g. α > 10, the fluid near the walls and along the centreline drifted towards the narrow end of the channel, while fluid in an intermediate region drifted towards the wide end of the channel. For small values of α, e.g. α < 5, the fluid drifted towards the narrow end at the wall and the wide end of the channel along the centreline. Applications to mass transport in the lung are discussed.

The change by an order of magnitude of the oscillating properties of the flow past a circular cylinder in the Reynolds number range 2*103 to 5*104 is demonstrated experimentally. It is shown that in this range these properties are highly susceptible to small disturbances of the frequency of the transition waves which precede turbulence in the shear layers just downstream of the cylinder. It is suggested that this susceptibility is responsible for the different lift coefficient values measured by various workers.The effect of disturbances on the mean flow properties is also described.The frequency-determining mechanism and the characteristic length of the oscillating flow are discussed.