The research summarized in this paper is an experimental study of the velocity and turbulence fields in the gap between two parallel co-rotating or stationary disks with a source in the centre. Detailed hot-wire measurements over a wide range of source strengths and disk speeds are presented; the average velocity components are correlated in terms of dimensionless quantities; and the radial pressure distribution is analysed. Also, transition phenomena and conditions under which similarity in the velocity profiles can be expected are discussed.

For locally isotropic, homogeneous fluid turbulence, a digital Fourier analysis method of measuring directly the net scalar and velocity spectral transfer Tn(k) of scalar and kinetic energy to a pa;rticular wavenumber from all other wave-numbers is described and applied to heated-grid turbulence. The technique uses the imaginary part of a particular cross-spectrum to obtain the one-dimensional net spectral transfer function Ln(k1) of velocity and scalar turbulence, and is a refinement of that used previously by Van Atta & Chen for measuring the velocity kinetic energy transfer.

The detailed spectral transfer Tn(k, k′) from one wavenumber to any other is related to the imaginary part of a particular three-dimensional bispectrum. Tn(k, k′) can be, in principle, computed from a particular two-dimensional triple correlation. Unlike Tn(k), which can be obtained from Ln(k1), Tn(k, k′) cannot be determined from the measurable one-dimensional bippectrum B1, n, n (k1, k1′) nor the one-dimensional transfer spectrum Ln(k1, k1′).

The measured net transfer spectra Tn(k) have been used to determine the extent of validity for heated-grid turbulence of the dynamical equations for the three-dimensional power spectra of temperature and velocity in locally isotropic turbulence. The measured temperature transfer spectrum is also compared with those obtained from the power spectra of velocity and temperature by using various simple hypotheses.

The steady flow of an ideal gas with finite conductivity past a thin wedge section in an aligned magnetic field is considered within the linearized theory. The wedge is assumed to be an insulator or a perfect conductor. The flow field around the obstacle is found by numerical integration of the Fourier transform for various values of the Mach number, the Alfven Mach number and the magnetic Reynolds number in the main stream. The outer flow is estimated by the method of asymptotic expansions. These results disclose how the inner flow including gas-dynamic features changes to the magnetohydrodynamic outer flow.

A similarity solution is found for the distribution of layer thickness in viscous source flow down an inclined plane. With this soldion a t lowest order, an asymptotic expansion in inverse powers of the downstream co-ordinate x allows a small correction for upstream influence. A simple experiment confirms the major features of the similarity solution: (i) a parabolic cross-stream variation in the layer thickness; (ii) spreading of the flow according to an $x^{\frac{3}{7}}$ power law; (iii) thin-ning of the layer along streamlines like $x^{-\frac{1}{7}}$; and (iv) surface velocities which vary as the square of the layer thickness. Deviations of the layer-thickness measurements from the parabolic profile follow the trend predicted by the first-order corrections, whereas systematically high measured values are explained qualitatively in terms of waves at the free surface.

Two-dimensional convection in a Boussinesq fluid confined between free boundaries is studied in a series of numerical experiments. Earlier calculations by Fromm and Veronis were limited to a maximum Rayleigh number R 50 times the critical value R, for linear instability. This range is extended to 1000Rc. Convection in water, with a Prandtl number p = 6·8, is systematically investigated, together with other models for Prandtl numbers between 0·01 and infinity. Two different modes of nonlinear behaviour are distinguished. For Prandtl numbers greater than unity there is a viscous regime in which the Nusselt number $N \approx 2(R/R_c)^{\frac{1}{3}}$, independently of p. The heat flux is a maximum for cells whose width is between 1·2 and 1·4 times the layer depth. This regime is found when $5 \leqslant R/R_c \lesssim p^{\frac{3}{2}}$. At higher Rayleigh numbers advection of vorticity becomes important and N ∞ R0·365. When p = 6·8 the heat flux is a maximum for square cells; steady convection is impossible for wider cells and finite amplitude oscillations appear instead, with periodic fluctuations of temperature and velocity in the layer. For p < 1 it is also found that N ∞ R0·365, with a constant of proportionality equal to 1·90 when p [Lt ] 1 and decreasing slowly as p is increased. The physical behaviour in these regimes is analysed and related to astrophysical convection.

In this paper, the first of two parts on solutions to the non-relativistic de Hoffmann-Teller relations, a unified notation is developed and used to produce new analytical solutions for one-dimensional unsteady and two-dimensional crossed-fields representations. A simple numerical solution method for the non-aligned two-dimensional representation is also included. These solutions are explicit in the upstream parameters and a single strength parameter. Unification of reality, entropy and evolutionary conditions is also carried out. The resulting single criterion is used to derive algorithms by which the correct solution is obtained, in every case without previous computation and elimination of non-physical solutions. Classifications of the solutions are discussed in relation to previous schemes.

We apply the perturbation theory which was recently developed and justified by Joseph & Sattinger (1972) to determine the form of the time-periodic solutions which bifurcate from plane Poiseuille flow. The results a t lowest significant order seem to be in good agreement with those following from the formal perturbation method of Stuart (1960) as extended by Reynolds & Potter (1967). Given the numerical results of the present calculation, the rigorous theory guarantees that the only time-periodic solution which bifurcates from laminar Poiseuille flow is a two-dimensional wave. The wave which bifurcates at the lowest Reynolds number exists, but it is unstable when its amplitude is small. Solutions which escape the small domain of attraction of laminar Poiseuille flow snap through this unstable time-periodic solution with a small amplitude to solutions of larger amplitudes.

A gas in a tube is excited by a reciprocating piston operating at or near a resonant frequency. Damping is introduced into the system by two means: radiation of energy from one end of the tube and rate dependence of the gas. These define a lumped damping coefficient. It is shown that in the small rate limit the signal in the periodic state suffers negligible distortion in one travel time, and hence its propagation according to acoustic theory is valid. The shape of the signal is determined by a nonlinear ordinary differential equation. The small rate condition provides a test of the applicability of the theory to given experimental conditions. When there is no damping, shocks are a feature of the flow for frequencies in the resonant band. For a given amount of damping an upper bound on the piston acceleration which ensures shockless motion is given. The resonant band is analysed for both damped and undamped cases. The predictions of the theory are compared with experiment.

The horizontal, linearly stratified, non-diffusive, high Reynolds number flow of an unbounded fluid over a two-dimensional vertical barrier is studied for a range of internal Froude numbers (Fi) under the Oseen and Boussinesq approximations. For F1 > 0·47 the most prominent feature of the flow is the system of large amplitude lee waves located downstream of the barrier with crests tilted in the upstream direction. For 0·47 < F1 < 0·6 the crests actually extend upstream of the barrier and appear as flows of alternating direction over the barrier. For 0·47 < Fi < 0·5 reversed flows due to these waves actually extend far upstream. For Fi < 0·47 a blocking column upstream of the obstacle, as well as large amplitude lee waves, is present. For even smaller 3. the amplitude of the lee-wave system diminishes but the blocking column remains. It is also shown that the steady-state solution obtained by Trustrum (1964, 1971) for the density and pressure field is drastically altered if a small viscosity is retained in the transient analysis.

An experimental study was made of the interaction produced by the collision, in still air, of two diametrically opposed plane turbulent wall jets. Distributions of time-average velocity, longitudinal turbulence and static pressure on the wall were measured. Simple universal relations giving the position of interaction and the maximum wall static pressure are deduced from the measurements and are explained in terms of the ‘frozen-flow’ concept. There is little or no loss of momentum due to mixing in the interaction process. The free jet that results from the interaction has the same velocity distribution as a conventionally generated two-dimensional free jet, but its rate of spread and turbulence level are about three times larger.

The effects of a wavy permeable boundary on turbulent flow are investigated theoretically and experimentally, mainly in terms of the pressure distribution along the wavy boundary and the friction factors. A simplified theoretical analysis based on potential flow theory and a linear Darcy equation shows that the perturbations of the flow field have a phase shift relative to the wavy surface and that, owing to this phase shift, there results a net form resistance on the wavy surface. Experiments were conducted in two pipelines with different sizes of granular material lining the inside of the pipe walls. The diameter of the porous conduits varied sinusoidally. The experimental results show that there is a phase shift between the boundary wave form and the pressure distribution and that friction factors increase with Reynolds number even though the flow is within the normal fully rough regime.