Kr, Xe and SiCI4 have been investigated for convective instabilities in closed vertical cylinders with conductive walls heated from below. Critical Rayleigh numbers NiRa for the onset of various convective modes (including the onset of marginally stable and periodic flow) have been determined with a high resolution differential temperature sensing method. Flow patterns were deduced from a multiple sensor arrangement. For the three lowest modes (i = 1, 2, 3) good quantitative agreement with linear stability theory is found. Stable oscillatory modes (periodic fluctuations of the mean flow) with a period of approximately 5 s are found for a relatively narrow range of NRa. The critical Rayleigh number NoscRa for the onset of oscillatory temperature fluctuations is 1348 ± 50 for an aspect ratio (height/radius) of 6.

Non-reactive binary gas mixtures (Xe + He, SiCl4 + H2) have been investigated for convective instabilities in closed vertical cylinders with conductive walls heated from below. Critical Rayleigh numbers NiRa for the onset of various convective modes (including the onset of marginally stable and periodic flow) have been determined with a high resolution differential temperature sensing method. It is found that the second component can significantly alter the hydrodynamic state of the fluid compared to the monocomponent behaviour. Considerably lower critical thermal Rayleigh numbers for steady and time dependent convective modes are observed. The Xe : He system shows stable oscillatory modes similar to those observed in monocomponent gases (periodic disturbances of the mean flow, T0 ≈ 5 s) from NRa = 713 to 780, where a new mode with T0 = 15 s sets in. The frequency of these slower temperature oscillations can be fitted by an equation of the form f2 = k’(NRa − N0Ra) where k’ and N0Ra are constants, which supports the contention that these oscillations are the result of vertical vorticity. For SiCl4 : H2 the high frequency oscillations occur only as a transient mode eventually evolving into the low frequency mode characteristic of binary gas mixtures. This low frequency state is degenerate with a stable time-independent state over a considerable range of NRα. Finite amplitude perturbations can lead to (1) transient oscillatory phenomena accompanied by reorientations of the roll cells with mean periods of 3–5 min; and (2) stable oscillatory flow at NRa 's considerably below NoscRα. The unique behaviour of these binary fluids is tentatively assigned to thermal diffusion.

Surface streamline patterns on a spheroid have been examined at several angles of attack. Most of the tests were performed at low Reynolds numbers in a hydraulic flume using coloured dye to make the surface flow visible. A limited number of experiments was also carried out in a wind tunnel, using wool tufts, to study the influence of Reynolds number and turbulent separation. The study has verified some of the important qualitative features of three-dimensional separation criteria proposed earlier by Maskell, Wang and others. The observed locations of laminar separation lines on a spheroid at various incidences have been compared with the numerical solutions of Wang and show qualitative agreement. The quantitative differences are attributed largely to the significant viscous-inviscid flow interaction which is present, especially at large incidences.

The small amplitude stability analysis for the onset of double-diffusive convection when the density gradient is gravitationally stable is extended to include a third diffusing component. Special attention is given to systems with κ1 [Gt ] κ2, κ3 and Pr [Gt ] κ/κ1, where κi is the molecular diffusivity of the ith component and Pr is the Prandtl number based on the largest of the Ki. It is found that the boundary for the onset of overstability is approximated by two straight lines in a Rayleigh number plane. Small concentrations of a third property with a smaller diffusivity can have a significant effect upon the nature of diffusive instabilities, the magnitude of this effect being proportional to κ1/Ki. Oscillatory and direct ‘salt-finger’ modes are found to be simultaneously unstable under a wide range of conditions when the density gradients due to the components with the greatest and smallest diffusivities are of the same sign.

Details of flow visualization, aerodynamic forces and pitching moment, static pressure and skin friction measurements have been carried out on a symmetrical aerofoil at fixed angle of incidence in longitudinal oscillations parallel to the uniform airstream of a wind-tunnel.

This investigation shows weak unsteady effects at incidences below that of static stall. For higher incidences, strong unsteady effects appear and depend on the frequency and amplitude of the oscillations. The measurements indicate an overshoot of the instantaneous lift and drag which is explained by a strong vortex shedding process occurring during the dynamic stall encountered by the aerofoil in decelerated motion, as observed for profiles oscillating in pitch through stall. When the aerofoil is going forward in accelerated motion dynamic reattachment may be observed at very high incidence over a short part of the period of oscillation.

Dynamic stall and dynamic reattachment contribute to a favourable effect of unsteadiness on the mean lift coefficient, which increases as compared to the steady state one, and which is expressed through an empirical formula involving incidence, frequency and amplitude of oscillations. At given incidence, optimization of this feature is achieved by matching the frequency and the amplitude of oscillation, respectively with the frequency linked with the highest peak of energy in the wake, and with the distance between two consecutive vortices in the mean wake when modelled as a von Kármán's vortex street.

We consider the evolution of packets of water waves that travel predominantly in one direction, but in which the wave amplitudes are modulated slowly in both horizontal directions. Two separate models are discussed, depending on whether or not the waves are long in comparison with the fluid depth. These models are two-dimensional generalizations of the Korteweg-de Vries equation (for long waves) and the cubic nonlinear Schrödinger equation (for short waves). In either case, we find that the two-dimensional evolution of the wave packets depends fundamentally on the dimensionless surface tension and fluid depth. In particular, for the long waves, one-dimensional (KdV) solitons become unstable with respect to even longer transverse perturbations when the surface-tension parameter becomes large enough, i.e. in very thin sheets of water. Two-dimensional long waves (‘lumps’) that decay algebraically in all horizontal directions and interact like solitons exist only when the one-dimensional solitons are found to be unstable.

The most dramatic consequence of surface tension and depth, however, occurs for capillary-type waves in sufficiently deep water. Here a packet of waves that are everywhere small (but not infinitesimal) and modulated in both horizontal dimensions can ‘focus’ in a finite time, producing a region in which the wave amplitudes are finite. This nonlinear instability should be stronger and more apparent than the linear instabilities examined to date; it should be readily observable.

Another feature of the evolution of short wave packets in two dimensions is that all one-dimensional solitons are unstable with respect to long transverse perturbations. Finally, we identify some exact similarity solutions to the evolution equations.

A theoretical framework is given, upon which to examine the dispersion relation of random gravity waves. First a weakly nonlinear theory is developed to the third-order for a statistically stationary and homogeneous field of random gravity waves. Both the spectrum of forced waves and the nonlinear dispersion relation are expressed in terms of the spectrum of free waves under the assumption of the Gaussian process for the first-order surface displacement. Next a method is proposed by which to separate each of the spectra of free and forced waves from the measured spectrum. This gives practical and powerful means of investigating the statistical structure of wind waves.

Random waves are generated by wind in the first half of a wind-wave flume. The latter half of the flume is kept free from wind to measure the waves unaffected by the wind and wind-generated current. The random waves in the latter area are measured with a linear array of wave gauges, and their phase velocities and coherences are determined by a usual technique of the cross-spectral analysis. The measured results are compared with the nonlinear theory of two-dimensional random waves, which has been presented in part 1 of this paper (Masuda, Kuo & Mitsuyasu 1979). Agreement between the theory and the experiment is satisfactory, and observed characteristics of the phase velocity and coherence of the spectral components can be attributed to the effects of the nonlinearity and angular dispersion of the random waves.

Previous analyses of natural convection in a porous medium have drawn seemingly contradictory conclusions as to whether the motion is two- or three-dimensional. This investigation uses numerical results to show the relationship between previous contending observations, and demonstrates that there exists more than one mode of convection for any particular physical configuration and Rayleigh number. In some cases, a particular flow situation may be stable even though it does not maximize the energy transfer across the system.

The methods used are based on the efficient numerical solution of the governing equations, formulated with the definition of a vector potential. This approach is shown to be superior to formulating the equations in terms of pressure.

For a cubic region the flow pattern at a particular value of the Rayleigh number is not unique and is determined by the initial conditions. In some cases there exist four alternatives, two- and three-dimensional, steady and unsteady.

Numerical solutions for the irrotational flow of an incompressible fluid about a circular cylinder accelerated from rest below a free surface are presented. The usual restriction to linearized free-surface boundary conditions has been avoided. The transient period from the start to a local steady state or to the development of a very steep wave slope is investigated in terms of free-surface profiles and body-surface pressure distributions. Linear and nonlinear results are used to illustrate the transition from deep submergence when nonlinear effects are small to shallow submergence when linearized analysis is inaccurate.