An experimental investigation of flows of a large number of inert and polyatomic gases in various channels, a non-ideal orifice, flat slits with different surface roughnesses and wall materials, capillary packets with molten walls and a capillary sieve, has been made.

The unsteady flow method and a highly sensitive capacitance micromanometer were used (the sensitivity being ∼ 3 × 10−4N/m2Hz). Measurements were made in a range of Knudsen numbers 5 × 104–10−3 at ∼ 293 °K, and some measurements for flow through a non-ideal orifice were carried out at 77.2°K.

It was found that, both in the viscous slip-flow and free-molecule regimes for the channels with molten walls, the experimental conductivities were higher (by ∼ 15%) than theoretical ones calculated assuming diffuse molecular scattering by the walls. We have also observed that the channel conductivity essentially depends on the channel surface roughness and on the kind of gas. The larger the roughness height, the lower the conductivity. From the experimental data the tangential momentum accommodation coefficients were calculated.

The purpose of this study is to generalize the experimental method for deciding when a fluid motion can be considered turbulent. The rationale advanced for processing a transducer signal, which indicates the intermittent nature of a turbulent field, is given a probabilistic outlook. In addition an improved detector function is introduced which uses information from longitudinal and lateral fluctuation components.

A two-dimensional stability analysis of the flow in a straight alluvial channel has been carried out, using the vorticity transport equation. In the analysis an attempt has been made to account for the influence of gravity on bed-load transport, and this turned out to change the stability quite significantly.

In the case of instability, the further growth of the dunes has been investigated using a second-order approximation, This nonlinear theory explains the experimental fact that the dunes very soon become asymmetric.

The steady streaming generated in a pipe of slowly varying cross-section when a purely oscillatory pressure difference is maintained between its ends is considered. It is assumed that the perturbation of the pipe wall in the r, θ plane is small compared with the characteristic thickness of the Stokes layer associated with the oscillatory motion of the fluid. The first-order steady streaming is evaluated for the cases when this characteristic thickness is large and small compared with a typical radius of the pipe. In both these limits it is found that the geometry of the pipe is crucial in determining the nature of the induced steady streaming. If the ends of the pipe have the same mean radius it is found that the steady streaming consists of regions of recirculation between the nodes of the pipe. Otherwise the steady streaming is of a larger order of magnitude and has a component which represents a net flow towards the wider end of the pipe.

We consider the motion of the mass of fluid ejected through a sharp-edged orifice by the motion of a piston. The vorticity formed by viscous forces within the separated flow at the sharp edge rolls up to form a concentrated vortex which, after a development period, consists of a core of very fine scale turbulence surrounded by a co-moving bubble of much larger scale turbulence. This bubble entrains outer fluid, mixes with it, and deposits the majority into a wake together with some small fraction of the total vorticity of the ring. Enough fluid is retained to account for the slow growth of the whole fluid mass. A theory which takes account of both the growth process and the loss of vorticity is proposed. By comparison with experimental measurements we have determined that the entrainment coefficient for turbulent vortex rings has a value equal to 0.011 ± 0.001, while their effective drag coefficient is 0.09 ± 0.01. These results seem to be independent of Reynolds number to within experimental accuracy.

A detailed study of the intermittency in the outer region of a flat-plate turbulent boundary layer has been carried out using digital sampling and processing techniques. Conditional averages are used to generate mean and fluctuating components for the turbulent and non-turbulent zones of fluid. More particularly, point averages of these variables, taken with reference to the instantaneous position of the turbulent/non-turbulent interface, have been made to show the distribution of various quantities through the turbulent front. The results indicate that significant differences exist at leading and trailing edges of the turbulent bursts and a more complete picture of the motion of an average large eddy is deduced.

Linear stability theory is applied to the natural convection of slightly, elastic, viscous fluids in an infinitely long vertical slot. Travelling, as well as stationary, disturbances are considered. It is found that the elasticity (i) slightly stabilizes the stationary disturbances while strongly destabilizing the travelling disturbances, (ii) strongly increases the wave speed while slightly decreasing the wavenumber and (iii) reduces the transition Prandtl number, which separates the stationary cells from the travelling waves, from its value of 12.7 for Newtonian fluids.

Experiments are carried out with a viscoelastic fluid prepared by mixing Separan AP30 with water, giving a Prandtl number of about 30. This fluid is shown to produce wave instability at a Grashof number between 3900 and 4300. Under the same conditions, a Newtonian fluid is shown to remain stable to both stationary and travelling disturbances.

We consider the rapid rotation, in the sense of large Reynolds number ε−1, of a gravitating solid sphere in a monatomic gas. The flow is characterized by a thin boundary layer on the sphere and a thin, swirling, buoyant, radial jet in the equatorial plane. When the Prandtl number σ is of order unity, the boundary layer and jet are to first order uncoupled from the outer flow. For sufficiently small Prandtl number (which may be interpreted as approximating an optically thick radiating gas), the outer flow is boundary-layer driven. The parameter boundary between these two dissimilar steady states is σ = O(ε⅙).

Measurements of the intermittency factor γ and in particular the crossing frequency fγ of the turbulent/non-turbulent interface in the outer regions of various turbulent shear flows depend strongly on the settings of the intermittency meter used. Two methods of calibrating an intermittency meter of conventional design are described. In the first, turbulent and non-turbulent signals are simulated and switched at random times using an analog computer. Particular attention is given to the spectra of the switching and turbulent signals but the non-turbulent signal is assumed to have the same spectrum as the turbulent signal. In the second method, the same switching process is applied to two real signals, obtained in the fully turbulent and irretational flow regions associated with a turbulent jet with a co-flowing external air stream. A rather simple calibration procedure derived using the results of both methods is applied to the measurements of γ and fγ in the same jet. It is suggested that the simulation process adopted here could be useful in inferring properties of intermittent turbulent flows.

In this paper an infinite waving sheet is used to model a micro-organism swimming either parallel to a single plane wall, or along a channel formed by two such walls. The sheet surface, which undergoes small amplitude waves, can represent either a single flagellum or the envelope of the tips of numerous cilia. Two different solutions of the equations of motion are presented, depending upon whether or not the wave amplitude is small compared with the separation distances between the sheet and walls. It is found that the velocity of propulsion is bounded by the velocity of wave propagation by the sheet. Both the propulsive velocity and rate of working by the sheet increase as the separation distances decrease. However, it is demonstrated that suitable alterations in wave speed or wave shape can fix the rate of working while still causing increases in propulsive velocity. Reductions in propagated wave speed, i.e. beat frequency, are particularly effective in this regard.

The averaged equations of slow flow in random arrays of fixed spheres are developed as a hierarchy of integro-differential equations, and an iteration procedure is described for obtaining the mean drag in the case of small volume concentration c. The leading approximation is that given by Brinkman's model of flow past a single fixed sphere, in which the effects of all other spheres are treated as a Darcy resistance. The higher approximations take account of the modification to the mean flow, particularly in the near field, due to the localized nature of the actual resistance. Thus the second approximation finds the change due to a second sphere, and averages over all its possible positions. The result for the mean drag confirms Childress’ terms in clogc and c (apart from an arithmetical correction to the latter), but indicates that for practical values of c numerical evaluation of integrals is needed, rather than expansion in powers of c and log c. The last section of the paper develops the corresponding results for flow through random arrays of fixed parallel circular cylinders.

We discuss the theory of Kelvin wave propagation along an infinitely long coast-line which is straight except for small deviations which are treated as a stationary random function of distance along the coast. An operator expansion technique is used to derive the dispersion relation for the coherent Kelvin wave field. For the subinertial case σ = ω/f < 1 (ω = wave frequency, f = Coriolis parameter), it is shown that the wave speed is always decreased by the coastal irregularities. Moreover, while the coherent wave amplitude is unaltered, the energy flux along the coast is decreased by the irregularities. For the case σ > 1, however, we show that in the direction of propagation the wave is attenuated (with the energy being scattered into the random Poincaré and Kelvin wave modes) and that the wave speed is again decreased. Applications of the theory are made to the California coast and North Siberian coast to determine the decrease in phase velocity due to small coastal irregularities. For the California coast the percentage decrease is only about 1%. For the Siberian coast, however, the percentage decrease is about 25% for the K1 tide, and a minimum of 25% for the M2 tide. The attenuation of a Kelvin wave, however, appears to be due to very large scale irregularities. An estimate of the actual attenuation rate is not possible, though, because of the relatively short extent of coastal contours available for spectral analysis.

Although attention in this paper has been focused on Kelvin wave propagation, the method developed could readily be used to study the behaviour of other classes of waves trapped against a randomly perturbed boundary.

Fully developed turbulent flow through three concentric annuli was investigated experimentally for a Reynolds-number range Re = 2 × 104−2 × 105. Measurements were made of the pressure drop, the positions of zero shear stress and maximum velocity, and the velocity distribution in annuli of radius ratios α = 0.02, 0.04 and 0.1, respectively. The results for the key problem in the flow through annuli, the position of zero shear stress, showed that this position is not coincident with the position of maximum velocity. Furthermore, the investigation showed the strong influence of spacers on the velocity and shear-stress distributions. The numerous theoretical and experimental results in the literature which are based on the coincidence of the positions of zero shear stress and maximum velocity are not in agreement with reality.

The properties of convective flow driven by an adverse temperature gradient in a fluid-filled porous medium are investigated. The Galerkin technique is used to treat the steady-state two-dimensional problem for Rayleigh numbers as large as ten times the critical value. The flow is found to look very much like ordinary Bénard convection, but the Nusselt number depends much more strongly on the Rayleigh number than in Bénard convection. The stability of the finite amplitude two-dimensional solutions is treated. At a given value of the Rayleigh number, stable two-dimensional flow is possible for a finite band of horizontal wavenumbers as long as the Rayleigh number is small enough. For Rayleigh numbers larger than about 380, however, no two-dimensional solutions are stable. Comparisons with previous theoretical and experimental work are given.

The low-speed combustion of initially unmixed gaseous reactants under an irreversible two-step chain reaction is examined. Both equilibrium burning, in which two spatially separated flames of zero thickness arise, and near-equilibrium burning, in which two spatially separated flames of small but finite thickness arise, are studied by limit-process expansion techniques. Two time-dependent flows are examined: the first is (one-dimensional) transient mixing flow; and the second is (two-dimensional) transient counterflow. The latter flow, in which there is an impressed finite strain parallel to the flame, such that the flame itself is longitudinally stretched, is discussed as elucidating the characteristics of combustion in non-equilibrium turbulent shear flow.

Turbulent convection for a rotating layer of fluid heated from below is studied in this paper. The boundaries of the fluid layer are taken to be free. The underlying principle, used is the Malkus hypothesis that the flow tends to transport the maximum amount of heat possible, subject to certain constraints. By taking the Prandtl number to be infinite, a linear differential constraint and an integral constraint are used. The variational problem that follows then depends on two dimensionless parameters, the Taylor number T and the Rayleigh number R.

Asymptotic analysis for the turbulent regime shows that the flow arranges itself so as to tend to offset the stabilizing effect of the rotational constraint, at least in so far as the heat flux is concerned. The dimensionless heat flux, or the Nusselt number, has in general different dependence on T and R, depending on the particular region in the parameter space. For T [les ] O(R), the flow is essentially non-rotating. For O(R) [les ]T [les ] O(R4/3), the flow will always have finitely many horizontal wavenumbers, though the total number of modes increases as T increases in this region. For O(R4/3) [les ] T [les ] O (R3/2), the Nusselt number has a functional dependence proportional to R3/T2, having essentially infinitely many horizontal modes as both R and T increase indefinitely in this region. The last expression is particularly interesting, as it agrees qualitatively with results in finite-amplitude laminar convection. It is also linearly dependent on the layer thickness, as one might expect from dimensional argument. It is suggested that, in the context of the maximum principle, the result in this region of the parameter space may be applicable as well to the same fluid layer with rigid boundaries through the existence of an Ekman layer that is thinner than the thermal layer.

The time development of non-axisymmetric disturbances on a shear layer in a uniformly rotating fluid is studied theoretically. It is assumed that the Rossby number, Ekman number, shear-layer length scale, and initial disturbance amplitude are small, and that disturbances grow if vorticity transfer from the shear flow exceeds Ekman-layer vorticity dissipation, a mechanism investigated by Busse (1968). Expressions for the ultimate instability amplitude are determined for specified relations among the small parameters, using the volume-integrated energy equation, the shape assumption, and approximations for the spatial dependence of disturbances. Disturbance growth is limited by modification of the initially-unstable shear-layer profile, and the eventual amplitude is shown to be fairly insensitive to the specific form of the profile. Using data from observations by Hide & Titman, the predicted maximum velocity amplitude of the non-axisymmetric motions for their experiments is approximately one-quarter of the velocity of the shear flow at the point of maximum gradient.

Experimental results for dissociating nitrogen flow over a wedge, obtained in a free-piston shock tunnel, are described. Interferograms of the flow show clearly the curvature of the shock wave and the rise in fringe shift after the shock associated with the dissociation. It is shown that the shock curvature a t the tip of the wedge can be used to calculate the initial dissociation rate and that it is a more sensitive indication of the rate than can be obtained from fringe shift measurements under the prevailing experimental conditions. Because the free-stream dissociation fraction can be adjusted in the shock tunnel, the dependence on atomic nitrogen concentration of the dissociation rate can be determined by the shock curvature method. A detailed calculation of the flow field by an inverse method, starting from the measured shock shape, shows good agreement with experiments.

A linear stability analysis is applied to a stably stratified, thermally radiating shear layer. The grey Milne–Eddington approximation is employed as a radiation model. In contrast to a previously reported optically thin analysis, no inviscid instability exists, in the limit of vanishing horizontal wavenumber, for this selfabsorbing model. The inviscid neutral-stability boundary (Richardson number us. dimensionless wavenumber) for the Milne–Eddington approximation converges to the optically thick limit as the optical depth of the shear layer is increased. As the optical depth of the shear layer is decreased, the inviscid Milne–Eddington neutral-stability boundary approaches the optically thin limit, although not uniformly in the wavenumber. For fixed mean velocity gradient and fluid properties, the inviscid critical Richardson number approaches infinity as the optical depth of the shear layer approaches zero. Viscous effects neutralize this radiative destabilization, and the critical Richardson number eventually returns to zero as the optical depth continues to decrease. A shearlayer thickness exists for which the viscous critical Richardson number is a maximum. For shear depths greater than this thickness, self-absorption effects increase the stability; and for shear depths less than this thickness, viscous effects increase the stability. Results of the analysis are applied to the atmospheres of Venus and the earth. A critical Richardson number somewhat above the non-radiating value of 3 (although below the previously reported optically thin value) is found for the lower troposphere of the earth. No substantial effect is found for the earth's lower stratosphere or for the 100 km level above Venus.

In an experimental and theoretical study, we model a phenomenon observed in the summer Arctic, where a fresh-water layer at a temperature of 0°C floats both over a sea-water layer at its freezing point and under an ice layer. Our results show that the ice growth in this system takes place in three phases. First, because the fresh-water density decreases upon supercooling, the rapid diffusion of heat relative to salt from the fresh to the salt water causes a density inversion and thereby generates a high Rayleigh number convection in the fresh water. In this convection, supercooled water rises to the ice layer, where it nucleates into thin vertical interlocking ice crystals. When these sheets grow down to the interface, supercooling ceases. Second, the presence of the vertical ice sheets both constrains the temperature T and salinity s to lie on the freezing curve and allows them to diffuse in the vertical. In the interfacial region, the combination of these processes generates a lateral crystal growth, which continues until a horizontal ice sheet forms. Third, because of the T and s gradients in the sea water below this ice sheet, the horizontal sheet both migrates upwards and increases in thickness. From one-dimensional theoretical models of the first two phases, we find that the heat-transfer rates are 5–10 times those calculated for classic thermal diffusion.