Sir Geoffrey Ingram Taylor, O.M., F.R.S., who died on 27 June 1975 at the age of 89, was one of the great men of our subject. He was a likeable happy man with an uncomplicated character and a razor-sharp mind for which scientific investigation was a natural activity. He was engaged in research throughout the whole of his life – not only the ‘working'part of it – and the fruits of his enquiries are described in over 200 papers published between 1909 and 1974. Nearly all these papers have been republished by Cambridge University Press in the four volumes of G. I. Taylor: Scientific Papers, three of which are on the mechanics of fluids and one on the mechanics of solids. These four volumes are his legacy to us, and will be a store-house of information and a source of illumination for many years to come.

Shock discontinuities for which the upstream state is vapour and the downstream state is liquid are considered. The possibility of such shock waves is associated with a large number of molecular degrees of freedom: it is necessary that the ideal-gas specific heat cv [ges ] 24R at the critical temperature, a condition which is met by several common fluids. Shock properties are found from a corresponding-states thermodynamic model and from several calculations based on data for particular fluids. Condensation shock waves satisfy the usual stability conditions and should be found in laboratory experiments.

Using the method of matched asymptotic expansions, an expansion of the velocity potential for steady incompressible flow has been obtained to order ε4 for slender bodies of revolution at an angle of attack by representing the potential due to the body as a superposition of potentials of sources and doublets distributed along a segment of the axis inside the body excluding an interval near each end of the body. Also, expansions of the coefficients of longitudinal virtual mass and lateral virtual mass have been found. The pressure distributions over an ellipsoid of revolution of thickness ratio ε = 0·3 at zero angle of attack and at an angle of attack of 3° obtained by the present method are compared with results obtained from the exact theory and that of Van Dyke. The virtual-mass coefficients are also compared with those obtained from the exact theory and are found to be in good agreement up to ε = 0·3.

Steady plane periodic waves on the surface of an ideal liquid above a horizontal bottom are considered. The flow is irrotational. Let Q denote the volume flow rate, R the total head and S the flow force for the wave train. Bounds on wave properties are obtained in terms of the properties of (i) the conjugate streams with the same Q and R, and (ii) the conjugate streams with the same Q and S.

A body is started from rest and moves on an arbitrary path in an inviscid isothermal compressible atmosphere. The phase configuration of the internal waves and the gravity-modified acoustic waves which are generated by the body is studied using small amplitude wave theory. When the body moves at supersonic speeds and the background density gradient approaches zero, it is shown how the wave solutions approach the pure acoustic wave solutions of Lilley et al. (1953).

A procedure for obtaining numerical solutions to the equations describing thermal convection in a compressible fluid is outlined. The method is applied to the case of a perfect gas with constant viscosity and thermal conductivity. The fluid is considered to be confined in a rectangular region by fixed slippery boundaries and motions are restricted to two dimensions. The upper and lower boundaries are maintained at fixed temperatures and the side boundaries are thermally insulating. The resulting convection problem can be characterized by six dimension-less parameters. The onset of convection has been studied both by obtaining solutions to the nonlinear equations in the neighbourhood of the critical Rayleigh number Rc and by solving the linear stability problem. Solutions have been obtained for values of the Rayleigh number up to 100Rc and for pressure variations of a factor of 300 within the fluid. In some cases the fluid velocity is comparable to the local sound speed. The Nusselt number increases with decreasing Prandtl number for moderate values of the depth parameter. Steady finite amplitude solutions have been found in all the cases considered. As the horizontal dimension A of the rectangle is increased, the length of time needed to reach a steady state also increases. For large values of A the solution consists of a number of rolls. Even for small values of A, no solutions have been found where one roll is vertically above another.

Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Pressure-wave propagation through a separated gas-liquid layer at rest in a duct of constant rectangular cross-section and infinite length is considered. Such a system is dispersive, possessing an infinite number of modes which depend on the ratios of the densities, thicknesses and sound speeds of the two phases. The transitional variation of an infinitesimal disturbance initially having a step profile is investigated analytically and numerically. In addition, it is shown that a weak but finite disturbance is described asymptotically by the solution of the Korteweg-de Vries equation.

Measurements of the pressure drop and flow rate were obtained for dilute solutions of polyethylene oxide flowing through beds of packed beads. When the velocity was sufficiently high, the pressure drop was above that for a Newtonian fluid of equal viscosity, often considerably above, and this viscoelastic effect was explored by varying the concentration and molecular weight of the polymer, by testing solutions over a wide range of flow rates, and by using several bead sizes. The non-Newtonian behaviour was most pronounced at moderate flow rates; at the highest velocities, the data were pseudo-Newtonian in character, i.e. the pressure drop still exceeded that for a Newtonian fluid, but was linearly related to the velocity. For some solutions, the large deviation from Newtonian values occurred over such a short range of flow rates that there was an interval in which the pressure drop decreased with velocity. It was not possible, therefore, to obtain steady-state measurements in this regime and a gap appears in the data curve of pressure vs. velocity.

The pressure drop was monitored in steps along the test section, so that it was possible to detect molecular degradation of the solutions as they flowed through the porous media. In general, degradation was not extensive and the solutions became stably degraded by the midpoint of the test section. Degradation increased with velocity and, quite surprisingly, became more severe as the bead size increased.

A visual examination of the flow field revealed that the streamline pattern for the polymer solutions was the same as that for water. The large non-Newtonian effects were therefore due to changes in the stress field, and in an effort to understand these effects, an analysis was carried out which examined how the stresses generated by each component of the deformation, i.e. by shear and pure strain, influence the pressure drop. This analysis, combined with a study of onset data, indicates that onset and the sudden large departures from Newtonian values are probably due to an interaction between extensional and shearing deformation, and that the reduced viscoelastic effect of higher flow rates may be due to the dominance of extensional stresses.

A linearized theory, which treats unsteady motions of a wing of large aspect ratio at variable forward speed in an inviscid incompressible fluid, is developed, using the method of matched asymptotic expansions. The wing geometry and motions are specified; and the time-dependent lift and moment are obtained. Long-time asymptotic behaviour of an initial-value harmonic motion is presented, as are the short-time solutions of a wing starting from rest, with constant acceleration and with impulsive acceleration to constant speed. Some attention is given to flapping flight. Results are presented in quadrature form for a general class of unsteady wing motions.

Transition in a two-dimensional plane wall jet was examined for the range of exit Reynolds numbers between 100 and 600. The wall jet was produced by the flow of water, which issued either from a smoothly-contoured nozzle or from the end of a long parallel channel. Observations were recorded both visually and with a hot-film anemometer. Both natural and forced transition cases were studied. Natural transition generally occurred in the following stages: (i) formation of discrete vortices in the outer shear layer; (ii) coalescence of adjacent vortices in the outer shear layer, coupled with the rolling up of the inner shear layer; (iii) eruption of the wall jet off the surface of the flat plate into the ambient fluid; (iv) dispersion of the organized flow pattern by three-dimensional turbulent motions; and (v) re-laminarization of the upstream flow, until another vortex pairing occurred. The initial stages of transition are two-dimensional in nature; and are dominated by the mechanism of vortex pairing, which is commonly observed in free shear layers. The inner-region shear layer exerts a stabilizing influence on the velocity profile at low Reynolds numbers. Forced transition was essentially similar to natural transition, except for the elimination of the downstream intermittency and the establishment of a fixed downstream location for transition.

In an attempt to explain the discrepancies that have been observed in the spread of nominally axisymmetric jets, an experimental investigation has been carried out in which the effects of a number of factors which it was thought might be important to jet development have been studied. These factors included the nozzle boundary-layer thickness, turbulence level and convergence. However, over the limited range of the tests, it was found that none of these factors had a very strong influence on the jet development. By contrast, the insertion of small rectangular tabs into the jet flow on the nozzle perimeter was found to have a very profound effect on the jet development. In particular, it was found that just two tabs produced gross distortions in the jet development resulting in the jet almost splitting in two with high velocity regions on either side of the diameter joining the tabs. Some explanations for this effect based on further tests with wedges are put forward.

In addition to the measurements of the mean flow field, a few spectrum and correlation measurements are reported for jets both from a clean nozzle and also from a nozzle with two tabs. In the former tests, evidence additional to the results of other experimenters was found for the existence of flow structures which have some coherence around the entire circumference of the jet. It has been suggested that these ‘vortex rings’ or ‘puffs’ may be of some importance in producing jet noise and it seems that the effect of inserting tabs is to prevent the occurrence of these structures.

The evolution of the power spectrum of surface gravity waves is described by means of an energy transport equation. A slowly varying, prescribed ocean current and wind source are assumed to account for spatial inhomogeneities in the surface wave spectrum. These inhomogeneities lead to a new nonlinear wave-wave interaction mechanism.