Slow motion of a thin plate at a finite angle of attack in a rotating container filled with a viscous incompressible fluid is analysed. The Rossby and Ekman numbers are assumed to be small. The solution method is developed by studying horizontal translation of an elliptical plate. The plate is shown to carry a stagnant Taylor column with it as it moves. Detailed analysis of the structure of the vertical shear column bounding the Taylor column is circumvented by integrating the equations of motion across the shear column. A jump condition based upon mass conservation in the shear column which relates the geostrophic regions inside and outside the Taylor column results. This jump condition and its method of derivation can be used to analyse arbitrary (slow) motion of any thin plate at any angle of attack.

The fluid motion resulting when a disk moves using all six degrees of freedom at an infinitesimal angle of attack is discussed. The forces and moments on the disk are calculated and the streamlines of the geostrophic flow are displayed.

Effects of product dissociation and preferential diffusion on the structure, propagation and diffusional-thermal instability of the classical one-dimensional laminar flame have been studied by using activation energy asymptotics. Analytical expressions as functions of dissociation and diffusion parameters have been obtained for such bulk flame parameters as the flame temprature reduction and the propagation rate eigenvalue, and for the dispersion relation governing flame stability. Results on flame propagation show that while under most situations the flame speed is reduced due to product dissociation, it can attain values in excess of the non-dissociative limit for highly mobile product species which can preferentially back diffuse to the upstream portion of the reaction zone where they recombine and release the associated recombination heat. Results on flame stability show that it is promoted in the presence of product dissociation which has a moderating influence on the flame temperature fluctuations, and for highly-mobile product species because of the enhanced burning rate and curvature-induced concentration modification.

Steady flows of an incompressible, inviscid, and non-diffusive fluid of variable density in a gravitational field are first considered. By a transformation it is shown conclusively that there are infinitely many flows with the same flow pattern, provided the density gradients of these flows at any section (e.g. far upstream) differ only by a multiplicative constant. These flows have identical local internal Froude numbers at all corresponding points of the flows and, hence, identical local Richardson numbers. They are therefore dynamically similar. Every time a solution for one stratification is obtained, one has in fact obtained the solutions for infinitely many stratifications.

The creation of vorticity in steady stratified flows is then examined, and it is shown that this creation can be divided into two parts, one part being entirely due to the inertial effect and the other originating from the gravity effect of density variation.

Finally, compressibility is considered and the results on similarity of stratified flows and on vorticity and circulation are extended to apply to steady flows of gases stratified in entropy.

This paper presents a new nonlinear analytical method based on the Fourier-series expansion for cavity flows, by which we can systematically deal with curved bodies of arbitrary shape. Furthermore, in the present study, the momentum defect within the cavity wake is reasonably well estimated by the displacement effect through the momentum theorem. For two-dimensional symmetric flows around various bluff bodies, theoretical predictions are shown quantitatively and compared with experi- mental data, wherever possible.

A theoretical study has been made of the laminar boundary layer on a semi-infinite flat plate parallel to a stream consisting of a uniform steady component U∞ normal to its leading edge and a periodic sideslip component of the travelling-wave type, where the wave travels with velocity Q in the direction of the steady component. It is found that the longitudinal flow (that in planes perpendicular to the leading edge) is independent of the transverse flow, and satisfies the well-known Blasius equations. The transverse flow is governed by a linear partial differential equation which may be approximated in different ways for high and low values of the ‘reduced’ frequency $\overline{\omega}$. A series-expansion solution for small $\overline{\omega}$ appears to be valid up to about $\overline{\omega} = 2$; the solution for large $\overline{\omega}$ is applicable down to $\overline{\omega} \approx 10$. A third approximation has been developed which joins the others smoothly. Numerical solutions of the equations for the transverse flow are presented for $0 \leqslant\overline{\omega}\leqslant 40$ and Q/U∞ = 0.6 (the value appropriate to the Queen Mary College (QMC) ‘gust-tunnels’) and for $\overline{\omega} = 10$ and 0.4 [les ] Q/U∞ [les ] ∞. The value of Q/U∞ has a profound influence: for values less than about one there are large phase lags within the boundary layer; for large values there are phase leads throughout most of the layer. For Q/U∞ < 1 the amplitude of the oscillation within the boundary layer exceeds that of the external driving oscillation, this ‘overshoot’ increasing as the wave-speed ratio diminishes. At Q/U∞ = 0.6 peak velocities more than 3 times those outside appear within the viscous layer.

As $\overline{\omega} \rightarrow \infty $, the transverse viscous layer becomes thinner; the oscillatory boundary layer, here transverse, becomes a ‘Stokes layer’ and is virtually uncoupled from the longitudinal flow. Far downstream the amplitude of the transverse skin-friction grows as x½ and becomes comparable with the streamwise component even for moderate values of the sideslip amplitude.

Experiments were conducted in one of the QMC gust-tunnels for values of $\overline{\omega}$ up to 2.0. Measurements of the transverse velocity amplitude and phase profiles confirm the ‘low frequency theory’.

The method of matched asymptotic expansions is used to extend the short-wave asymptotics of the transmission coefficient T by the addition of the terms of order 1/N5, (logN)2/N6 and log N/N6 as N → ∞ (where N = wavenumber times cylinder radius). The result is the formula \begin{eqnarray*} T &=& \frac{2{\rm i}}{\pi N^4}\exp (-2{\rm i}N)\left[1+\frac{4\log N}{\pi N}-\frac{4}{\pi N} \bigg(2-\gamma-\log 2+\frac{{\rm i}\pi}{8}\bigg)+\frac{8(\log N)^2}{\pi^2N^2}\right.\\ && \left.-\frac{8\log N}{\pi^2N^2}\bigg(5-2\gamma - \log 4+\frac{{\rm i}\pi}{4}\bigg)\right] + O\bigg(\frac{1}{N^6}\bigg)\quad {\rm as}\;N\rightarrow \infty \end{eqnarray*} (where γ = Euler's constant). The first term above is that derived rigorously by Ursell (1961) using an integral-equation method; the second term is that added by Leppington (1973) using matched asymptotic expansions; and the next three terms are those derived in this paper. Significant agreement between numerical values of T obtained from the completed fifth-order asymptotics and those obtained using Ursell's multipole expansions is demonstrated for 8 [les ] N [les ] 20 (table 2). The extensions of the perturbation expansions for the potential in the various fluid sub-domains (used in the method of matched expansions) provide some interesting cross-checks, between the solutions for potentials occurring later in the series and determined at advanced matching stages, with those for potentials occurring earlier on and determined independently at an earlier stage in the matching process. Some examples are given.

Laboratory experiments and numerical modelling studies have been performed for a rotating, thermally driven fluid system in a cylindrical annulus with a vertical rotation vector and axis of symmetry. The thermal forcing was through the imposition of an axisymmetric temperature gradient on a thermally conducting lower boundary, with additional heating through the outer sidewall. The upper and inner walls were nominally insulating. Flow patterns were observed in the experiments through the use of small, reflective flakes (Kalliroscope) in the working fluid, which was water. The rotation rate and temperature difference were varied to construct a regime diagram in thermal Rossby number–-Taylor number space. The curve separating axisymmetric flow from wave flow is ‘knee-shaped’, similar to the side-heated and -cooled baroclinic annulus which has been extensively investigated previously. Very near the transition curve, the initial wavenumber persists indefinitely, but well into the wave regime the initial wavenumber is higher than the equilibrated value. Far enough into the wave regime, the initial waves have wavenumbers several times that of the equilibrated value, and the initial disturbances form near the outer wall very early in the experiment. Numerical studies indicate that these waves are effective in distributing heat and that they occur in a region of positive static stability. These waves rapidly grow inward to fill the annulus and reduce in number as weaker waves are absorbed by the stronger ones. The period of transition between these waves and the equilibrated long-wave pattern is characterized by irregular flow. Closer to the transition curve, the temporal transition to longer waves as the flow equilibrates is simpler, with initial waves filling the annulus. In that case, the transition is characterized by a slow process of individual waves weakening and merging with adjacent waves.