The results of an experimental investigation of the thermal transpiration effect (the thermomolecular pressure difference or t.p.d. effect) in a single glass capillary with a length-to-radius ratio of 250 are presented. The temperatures of the gas in the ‘cold’ and ‘hot’ chambers were 273·2°K and 293°K, respectively. A modified relative method has been used. To measure the t.p.d. effect, a capacitance differential digital micromanometer with sensitivity 4·5 × 10−5N/(m2Hz) was used. The gases investigated were He, Ne, Ar, Xe, H2, D2, N2, CO2, CH4 and SF6. It was discovered that in the intermediate flow regime the thermal-creep flow rate does not depend on the (non-isothermal) tangential momentum accommodation coefficient. From the experimental data on the viscous slip flow regime, the Eucken factors and the accommodation coefficients are calculated. For inert gases the Eucken factor is found to be equal to 2·5 within the experimental error, while the accommodation coefficients differ significantly from unity.

The investigation of the effects which a changing mean flow has on a uniform train of internal gravity waves (Thorpe 1978a) is continued by considering waves in a uniformly accelerating stratified plane Couette flow with constant density gradient. Experiments reveal a change in the mode structure and phase distribution of the waves, and their eventual breaking near the boundary where the mean flow is greatest, the phase speed of the waves being positive. A linear numerical model is devised which accurately describes the waves up to the onset of their breaking, and this is used to investigate their energetics. The working of the Reynolds stress against the mean velocity gradient results in a very rapid transfer of energy from the waves to the mean flow, so that by the time breaking occurs only a small fraction of their initial energy remains for possible transfer into potential energy of the fluid.

The consequences have important applications in oceanography and meteorology, to flow stability and flow generation, and explain some earlier laboratory observations.

A first-order analysis is presented for the propagation of a blast wave through a dilute spray of non-reactive liquid droplets that are suspended in a non-reactive gas-phase carrier. The analysis permits straightforward computation of decay rates and internal wave structure for wave strengths in the approximate Mach number range 4 ≤ Ms ≤ 15, and loading factors (mass of spray per unit mass of carrier) less than about 0·4. The droplets must be sufficiently small to completely change phase in a distance behind the shock that is at all times negligible compared with the wave radius. Representative calculations are presented and discussed. These show more rapid decay rates and higher pressures, densities, and particle velocities in two-phase blast waves when compared against equivalent gas-phase blast waves. A simplification of the analysis for the regime of higher wave Mach numbers (strong waves) is also given, which for that case allows direct algebraic calculation of early wave characteristics.

Previous measurements of the decay rate of the fluctuation intensity of passive scalars in grid-generated turbulence show large variation. New results presented here show that the decay rate of passive temperature fluctuations produced by heating the grid is a function of the initial temperature fluctuation intensity. Although a full reason for this is wanting, spectra of the temperature fluctuations show that, by varying the heat applied to the grid, the wavenumber of the maximum in the temperature spectrum changes, indicating that the geometry of the thermal fluctuations is being altered in some way. In these experiments the one-dimensional temperature spectrum shows an anomalous $-\frac{5}{3}$ slope. In order to eliminate the dependence of the decay rate of the temperature fluctuations on their intensity, we describe a new way of generating temperature fluctuations by means of placing a heated parallel array of fine wires (a mandoline) downstream from the unheated grid. Results of this experiment show that the decay rate of passive thermal fluctuations is uniquely determined by the wave-number of the initial temperature fluctuations. In this type of flow there appears to be no equilibrium value for the thermal fluctuation decay rate and hence for the mechanical/thermal time-scale ratio since the thermal fluctuation decay rate does not change within the tunnel length, which is the equivalent of nearly one turbulence decay time.

The spectral method of Orszag & Patterson has been extended to calculate the static pressure fluctuations in incompressible homogeneous decaying turbulence at Reynolds numbers Reλ [lsim ] 35. In real space 323 points are treated. Several cases starting from different isotropic initial conditions have been studied. Some departure from isotropy exists owing to the small number of modes at small wavenumbers. Root-mean-square pressure fluctuations, pressure gradients and integral length scales have been evaluated. The results agree rather well with predictions based on velocity statistics and on the assumption of normality. The normality assumption has been tested extensively for the simulated fields and found to be approximately valid as far as fourth-order velocity correlations are concerned. In addition, a model for the dissipation tensor has been proposed. The application of the present method to the study of the return of axisymmetric turbulence to isotropy is described in the companion paper.

The spectral method of Orszag & Patterson (1972a, b) is used here to study pressure and velocity fluctuations in axisymmetric, homogeneous, incompressible, decaying turbulence at Reynolds numbers Reλ [lsim ] 40. In real space 323 points are treated. The return to isotropy is simulated for several different sets of anisotropic Gaussian initial conditions. All contributions to the spectral energy balance for the different velocity components are shown as a function of time and wavenumber. The return to isotropy is effected by the pressure-strain correlation. The rate of return is larger at high than at low wavenumbers. The inertial energy transfer tends to create anisotropy at high wavenumbers. This explains the overrelaxation found by Herring (1974). The pressure and the inertial energy transfer are zero initially as the triple correlations are zero for the Gaussian initial values. The two transfer terms are independent of each other but vary with the same characteristic time scale. The pressure-strain correlation becomes small for extremely large anisotropies. This can be explained kinematically. Rotta's (1951) model is approximately valid if the anisotropy is small and if the time scale of the mean flow is much larger than 0·2 Lf/v, which is the time scale of the triple correlations (Lf = integral length scale, v = root-mean-square velocity). The value of Rotta's constant is less dependent upon the Reynolds number if the pressure-strain correlation is scaled by v3/Lf rather than by the dissipation. Lumley & Khajeh-Nouri's (1974) model can be used to account for the influence of large anisotropies. The effect of strain is studied by splitting the total flow field into large- and fine-scale motion. The empirical model of Naot, Shavit & Wolfshtein (1970) has been confirmed in this respect.

This paper presents an experimental study of the turbulent structure on the centre-line of a two-dimensional impinging jet. The mean velocity, turbulent stresses, triple velocity products and temporal derivatives were measured and the energy balances for the three fluctuating components were calculated. The results indicate a selective stretching of vortices in the direction in which the streamlines spread near the wall, causing anisotropy in this region. The distribution of energy among various frequencies was found from spectral measurements. These measurements revealed the existence of a neutral frequency above which the energy was attenuated by viscous dissipation and below which it was augmented by a vortex-stretching mechanism.

In the present investigation we consider hydromagnetic Stokes flow past a rotating sphere. The magnetic field is produced by a magnetic pole placed at the centre of the sphere. The problem is analysed by a combination of perturbation and numerical methods. It is seen that the flow reversal (due to rotation) at the rear portion of the sphere is enhanced as the strength of the magnetic field increases. In addition, we obtain the simultaneous effects of rotation and a magnetic field on the streamlines.

Faulted regions associated with geothermal areas are assumed to be composed of rock which has been heavily fractured within the fault zone by continuous tectonic activity. The fractured zone is modelled as a vertical, slender, two-dimensional channel of saturated porous material with impermeable walls on which the temperature increases linearly with depth. The development of an isothermal slug flow entering the fault at a large depth is examined. An entry solution and the subsequent approach to the fully developed configuration are obtained for large Rayleigh number flow. The former is characterized by growing thermal boundary layers adjacent to the walls and a slightly accelerated isothermal core flow. Further downstream the development is described by a parabolic system. It is shown that a class of fully developed solutions is not spatially stable.