The hydrodynamic stability of the developing laminar flow in the entrance region of a parallel-plate channel is investigated using the theory of small disturbances. The stability of the fully developed flow is also re-examined. A wide range of analytical (i.e. asymptotic) and numerical methods are employed in the stability investigation. Among the asymptotic methods, each of three viscous solutions (singular, regular and composite) is used along with the inviscid solution to provide critical Reynolds numbers and complete neutral stability curves. Two numerical methods, finite differences and stepwise integration, are applied to calculate critical Reynolds numbers. The basic flow in the development region is treated from two stand-points: as a channel velocity profile and as a boundary-layer velocity profile. Extensive comparisons among the various methods and flow models disclose their various strengths and ranges of applicability. As a general result, it is found that the critical Reynolds number decreases monotonically with increasing distance from the channel entrance, approaching the fully developed value as a limit.

This paper presents the results of an experimental investigation of the behaviour of artificial disturbances produced by an oscillating ribbon in the free convection boundary layer over a vertical uniform flux plate. The boundary layer was observed using a Mach Zehnder interferometer. The observations resulted in the approximate location of a neutral curve which is in good agreement with calculations from the linear stability theory.

Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y, and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion.

Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ2w/k1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.

The light-scatter technique facilitates study of the concentration field when one of the streams entering a mixing region is marked with colloidal particles. The present paper provides basic information for the effective application of the technique. The system response is analysed theoretically. The problems of noise and spatial resolution are examined and experimental data are presented from which the response parameters are evaluated numerically. The capabilities of the technique for characterizing turbulent concentration fluctuations are described. The technique is excellent in the convection region of the turbulence spectrum but fails where molecular diffusion is important.

The light-scatter technique has been used to study the nozzle-fluid concentration field in an isothermal, turbulent, axisymmetric air/air free jet with the nozzle air marked by an oil smoke. The data on the mean concentration field appear to be the most accurate yet obtained, due to the peculiar advantages of the technique. The turbulent concentration fluctuations have been characterized as to intensity, spectral distribution, and two-point correlation. The intermittency factor has been measured and the properties of the turbulent fluid computed. Comparison with the results of other investigators who used heat to mark the nozzle fluid indicates a close similarity between the concentration and temperature fields.

Drag reduction caused by dilute, distilled water solutions of five polyethylene oxides, molecular weights from 80,000 to 6,000,000, in turbulent pipe flow was studied experimentally in 0·292 and 3·21 cm ID pipes. It was found that the onset of drag reduction occurs at a well-defined wall shear stress related to the random-coiling effective diameter of the polymer. Laminar to turbulent transition is not, in general, delayed. The extent of drag reduction induced by a homologous series of polymers in a given pipe is a universal function of concentration, flow rate, and molecular weight. The maximum drag reduction possible is limited by an asymptote that is independent of polymer and pipe diameter. Flow structure measurements in a single polymer solution, 1000 ppm of molecular weight 690,000, showed that the mean flow follows an ‘effective slip’ model. In this, the mean velocity profile consists of a ‘Newtonian plug’ convected along at an additional, ‘effective slip’ velocity. The turbulent flow structure follows the ‘effective slip’ model towards the pipe wall, but is significantly different from Newtonian towards the pipe axis; in particular, the inertial subrange observed in isotropic Newtonian turbulence was absent in an energy spectrum taken on the pipe axis in the polymer solution.

The two-dimensional internal wave pattern produced by a small disturbance moving with constant velocity along a line of arbitrary inclination in an inviscid, density stratified liquid is studied. It is shown how the far field wave pattern evolves as the inclination changes from the extreme of horizontal motion to that of vertical motion. It is found that, in general, waves propagate ahead of the disturbance.

An analysis is described for convection from a circular cylinder subjected to transverse oscillations relative to the fluid in which it is immersed. The analysis is based upon use of the acoustic streaming flow field. It is assumed that the frequency involved is sufficiently small that the acoustic wavelength in the fluid is much larger than the cylinder diameter, and that there is no externally imposed mean flow across or along the cylinder. Solutions are presented which are appropriate for a wide range of Prandtl number, and the cases of small and of large streaming Reynolds number are distinguished. The analysis compares favourably with experiments when the influence of natural convection is small.

The fluid is assumed to be inviscid and to be confined within two parallel planes, each perpendicular to the axis of rotation. A sphere is set moving, relative to the rotating fluid, in a straight line with uniform velocity and the temporal development of the flow structure examined. It is found that ultimately the flow has different properties inside and outside the cylinder [Cscr ], circumscribing the sphere and having its generators parallel to the axis of rotation. Inside [Cscr ] the fluid moves with the sphere as if solid; in early experiments of Taylor (1923) this phenomenon was observed. Outside [Cscr ] the motion is a two-dimensional potential flow past [Cscr ] as if it were solid. Then the asymmetry observed by Taylor and predicted in an earlier theory of the author for an unbounded fluid (1953) is not borne out. A partial explanation is offered.

Experiments in which a horizontal layer of convecting air is probed by one beam of a Michelson interferometer are described. When the localized interference fringes are horizontal, they indicate that the beam is wide enough to provide a suitable horizontal average. When the fringes are oriented nearly vertically, quantitative temperature measurements may be made. Results are presented for ratios (λ) of Rayleigh number to critical Rayleigh number of 1·48, 3·81 and 16·0. The temperature profile becomes more distorted from linear as the Rayleigh number is increased. An isothermal central region and thermal boundary regions each occupy one-third of the layer at λ = 3·81. By λ = 16·0 each boundary region occupies only one-quarter of the layer thickness, and the central region shows a reversed gradient. No full calculation is presently available to compare to the measurements. However, the shape assumption, using the first eigenfunctions of the linear stability problem, predicts the profile rather well for λ = 1·48 and 3·81 if Nusselt number agreement is imposed.

The paper deals with the regular refraction of a plane shock at a gas interface for the particular case where the reflected wave is an expansion fan. Numerical results are presented for the air–CH4 and air–CO2 gas combinations which are respectively examples of ‘slow–fast’ and ‘fast–slow’ refractions. It is found that a previously unreported condition exists in which the reflected wave solutions may be multi-valued. The hodograph mapping theory predicts a new type of regular–irregular transition for a refraction in this condition. The continuous expansion wave type of irregular refraction is also examined. The existence of this wave system is found to depend on the flow being self-similar. By contrast the expansion wave becomes centred when the flow becomes steady. Transitions within the ordered set of regular solutions are examined and it is shown that they may be either continuous or discontinuous. The continuous types appear to be associated with fixed boundaries and the discontinuous types with movable boundaries. Finally, a number of almost linear relations between the wave strengths are noted.

Measurements of the aerodynamic pressure distribution at the interface between air and simple progressive water waves are obtained with the use of a pressure sensor that follows the water surface. The theory of Miles (1957, 1959) and Benjamin (1959) on shear flows past a wavy boundary predicts a phase shift between the pressure distribution along the boundary and the boundary itself. An experimental verification of this theory is sought especially. A wind–wave facility 115 ft. long, 6 ft. high and 3 ft. wide was used. The facility is equipped with an oscil-lating-plate wave-generator which is capable of generating sinusoidal or arbitrary wave-forms, and a suction fan which can produce wind velocities up to 80 ft./sec when the water is at a nominal depth of 3 ft. The pressure sensor used for the measurements of pressure, was mounted on an oscillating device such that the sensor could be maintained at a fixed small distance (within 1/4 in.) above a propagating wavy surface at all times. The perturbation pressure over progressive waves is extracted from recorded data sensed by the moving sensor. The results compare favourably with the theoretical predictions of Miles (1959).