A technique by which the effect of the random phase fluctuations or Doppler ambiguity can be removed from measurements of turbulence intensities by the laser-Doppler velocimeter is proposed. Because the ambiguity is often much broader band than the turbulence, it is proposed that a sequence of low-pass filters at frequencies above those of the turbulence be used in the measurement of turbulence intensities. The true turbulence intensity is given by the extrapolation of these measurements to zero frequency.

Simultaneous measurements of the longitudinal (sx) and transverse (sz) components of the turbulent fluctuating velocity gradient at the wall of a pipe are presented for ten locations in the transverse direction. Separate measurements of sx and of sz are also presented for twenty locations. The sz pattern reveals alternating positive and negative values over lengths Λ of the magnitude suggested by the spacing of the streaky wall structure observed in a number of laboratories. Of particular interest is the observation of regular eddies for which the sz pattern is accompanied by a spatial variation of sx out of phase by about 1/4Λ. These regular eddies are associated with intermittent production of Reynolds stress and with the occurrence of large negative values of sx which could be identified with wall bursts previously reported. The time response of the axial flow appears to influence the development of these regular eddies in that the development of an sx pattern lags behind that of an sz pattern. Measurements of spatial correlations of sx and sz with different time delays, as well as direct observations of the temporal variation of sx and sz patterns, support these notions.

A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here.

Rotational flow of an inviscid fluid over an irregularity in the bottom is investigated. The flow is regarded as a perturbed unidirectional flow, and the shape of the irregularity is described using Fourier transforms. The velocity profile in the unidirectional flow is determined using the eddy-viscosity concept and a finite wall slip velocity.

Two different examples of irregularities are considered: (a) an infinitely long straight irregularity which forms an arbitrary angle with the direction of the basic flow and (b) a hump in a channel with impermeable walls. The influence of rotation on the two- and three-dimensional waves which are formed downstream of these irregularities is analysed and experimentally verified. Further, it is shown that the gradient of the basic velocity profile increases the transverse movement of the fluid particles at the bottom, while at the surface this transverse movement is decreased.

An experimental study of transitions from steady bimodal convection to time-dependent forms of convection is described. Using controlled initial conditions for the onset of bimodal convection two mechanisms of instability can be separated from the effects of random noise. The oscillatory instability of bimodal cells introduces standing waves closely resembling those occurring in low Prandtl number convection. The collective instability introduces spoke-pattern convection which is characteristic for turbulent large Prandtl number convection. Both instabilities originate primarily from the momentum advection terms in the equations of motion, as is evident from the strong Prandtl number dependence of the critical Rayleigh number Rt for the onset of oscillations. The results are discussed in relation to previous experiments and recent theoretical work.

Waves of small but finite amplitude in shallow water can occur as periodic wave trains of permanent shape in two known forms, either as Stokes waves for the shorter wavelengths or as cnoidal waves for the longer wavelengths. Calculations are made here of the periodic wave trains of permanent shape which span uniformly the range of increasing wavelength from Stokes waves to cnoidal waves and beyond. The present investigation is concerned with the stability of such permanent waves to periodic disturbances of greater or equal wavelength travelling in the same direction. The waves are found to be stable to infinitesimal and to small but finite disturbances of wavelength greater than the fundamental, the margin of stability decreasing either as the fundamental wave becomes more nonlinear (i.e. contains more harmonics), or as the wavelength of the periodic disturbance becomes large compared with the fundamental wavelength. The decreasing margin of stability is associated with an increasing loss of spatial periodicity of the wave train, to the extent that small but finite disturbances can cause a form of interaction between consecutive crests of the disturbed wave train. In such a case, a small but finite disturbance of wavelength n times the fundamental wavelength converts the wave train into n interacting wave trains. The amplitude of the disturbance subharmonic is then nearly periodic, the time scale being the time taken for repetitions of the pattern of interactions. When the disturbance is of the same wavelength as the permanent wave, the wave is found to be neutrally stable both to infinitesimal and to small but finite disturbances.

Two-dimensional waves are incident upon a pair of vertical flat plates intersecting the free surface in a fluid of infinite depth. An asymptotic theory is developed for the resulting wave reflexion and transmission, assuming that the separation between the plates is small. The fluid motion between the plates is a uniform vertical oscillation, matched to the outer wave field by a local flow at the opening beneath the plates. It is shown that the reflexion and transmission coefficients undergo rapid changes, ranging from complete reflexion to complete transmission, in the vicinity of a critical wavenumber where the fluid column between the obstacles is resonant.

Using a test-particle Monte Carlo method the general features of a gas expanding from a circular nozzle into a vacuum were investigated. Calculations were performed by considering the flow to be uniform and axial at the exit plane of the nozzle with an exit Mach number of 3 and a throat Reynolds number of 25. Results are presented for the density, mean flow velocity and kinetic temperature of the gas. Near the axis of the jet the calculated density distributions were found to agree well with those given by Robertson & Willis. Results are also presented for regions far from the jet's axis where no other solution is available.

We observed a gradual change in the structure of a shock wave passing through a long tube of bubbly liquid, which we attribute to the motion of the bubbles relative to the liquid. We show that the effect of the motion on the structure of a shock wave is like that of thermal relaxation on gasdynamic shock waves: the pertinent relaxation time is the time viscous forces in the fluid take to alter the velocity of a bubble to that of the fluid. Our theory predicts certain changes in the speed of the shock wave and in its structure. We could not verify the prediction as to wave speed: in dilute mixtures it is too small to be measured. But we report experiments on the structure of the wave, which support our theoretical conclusion that the observed changes are due to the relative motion.

The application of slender-body theory to the evaluation of the three-dimensional surface velocities induced by a boundary layer on an elliptic cylinder is considered. The method is applicable when the Reynolds number is sufficiently large so that the thin-boundary-layer approximation is valid. The resulting potential problem is reduced to a two-dimensional consideration of the flow over an expanding cylinder with porous boundary conditions. The limiting solutions for a flat plate of finite span and a nearly circular cross-section are obtained in a simple analytic form. In the former case, within the limitations of slender-body theory, the results are in exact agreement with the complete three-dimensional solution for this geometry.

The near wall jet produced by directing a uniform axisymmetric jet of air normally onto a large flat plate has been investigated experimentally and theoretically for four jets in the Mach number range 1·64–2·77. Detailed measurements of the surface pressure and shadowgraph and surface flow pictures are presented. The results show that the mechanism which mainly determines the supersonic near wall jet is the jet-edge expansion and its reflexions from the sonic line and the wall-jet boundaries. The near wall jet is found to consist of an alternating series of expansion and recompression regions whose strengths depend on the jet Mach number and decay with distance. At Mach numbers of 2·4 and above, shock waves are observed in the first recompression region and at a Mach number of 2·77 the boundary layer separates locally. Further out, viscous effects become increasingly important and a constant-pressure shear flow is established at a distance which increases with jet Mach number. The application of the method of characteristics in an approximate manner reproduces a number of the features of the near wall jet which are observed experimentally.

Pressure distributions obtained in the shock layer show that a stagnation bubble can occur and that its occurrence depends on factors such as the flow upstream of the nozzle. The wall-jet region is found to be largely independent of whether or not a bubble occurs in the shock layer.

A cryogenic shock tube has been developed as a tool for research in fluid mechanics and low-temperature physics. The shock tube was designed to operate with the test section immersed in a cryogenic liquid. A unique diaphragm-changing mechanism makes this shock tube an economical and practical device. There are several advantages in operating a shock tube at cryogenic temperatures. Shock waves of very large Mach number can be produced. The flow field can be accurately calculated using ideal-shock-tube/perfect-gas theory. Boundary-layer effects are decreased, so that long test times are possible.

The cases that were studied are test-gas temperatures of 300, 77, 4·2 and 2·3 °K. Helium was used as both test and driver gas. The largest Mach numbers observed range from 2·4 at 300 °K to 32 at 2·3 °K (several runs at 1·46 °K produced Mach 40 shocks). As the temperature of the test gas was decreased, the observed Mach numbers approached those calculated using the ‘shock-tube equation’.

As a laboratory tool, the cryogenic shock tube may be applied in many areas and modified for use in even more. Shock waves with large Mach numbers and flows with large Reynolds numbers can be produced with this device. The rapid increase in temperature and pressure across the shock wave is useful for studies of sublimation, evaporation or chemical reactions. Quantum-mechanical effects in cryogenic materials, superconductors or superfluid helium can also be investigated.

The objective of this paper is to show how to formulate a bifurcation theory for pipe flows in terms of the friction factor. We compute the slope of the friction factor vs. Reynolds number curve and the frequency change for the time-periodic solution which bifurcates from Poiseuille flow through annular ducts.