An aerodynamic investigation was conducted to determine the laminar-flow drag coefficient of spheres of various sizes in a subsonic wind tunnel. The tests were conducted using the M.I.T.-N.A.S.A. prototype magnetic-balance system. By measuring the drag of different sized spheres without model support interference the tunnel wall effect can be deduced. The present results indicate that the classical wind tunnel correction does not completely account for the effects of model size and wall interference. That is, the corrected drag coefficient data for the different sphere sizes differ among themselves in the region of Reynolds number overlap.

A comparison of the present sphere drag results with those of numerous other investigations including free-flight and ballistic-range data is given. The drag coefficients presented here are slightly lower than those of other workers for Reynolds numbers ranging from 20 000 to 150 000, but fall between the limits of experimental scatter for Reynolds numbers from 150 000 to 260 000.

An analysis of the estimated error in the present data indicates the primary source to be measurement of the wind tunnel parameters rather than errors resulting from the balance system.

In this paper the linear stability of the flow between two long eccentric rotating circular cylinders is considered. The problem, which is of interest in lubrication technology, is an extension of the classical Taylor problem for concentric cylinders. The basic flow has components in the radial and azimuthal directions and depends on both of these co-ordinates. As a consequence the linearized stability equations are partial differential equations rather than ordinary differential equations. Thus standard methods of stability theory are not immediately useful. However, there are two small parameters in the problem, namely δ, the clearance ratio, and ε, the eccentricity. By letting these parameters tend to zero in such a way that δ½ is proportional to ε, a global solution to the stability problem is obtained without recourse to the concept of ‘local instability’, or ‘parallel-flow’ approximation, so commonly used in boundary-layer stability theory. It is found that the predictions of the present theory are at variance with what is given by a ‘local’ theory. First, the Taylor-vortex amplitude is found to be largest at about 90° downstream of the region of ‘maximum local instability’. This result is given support by some experimental observations of Vohr (1968) with δ = 0·1 and ε = 0·475, which yield a corresponding angle of about 50°. Second, the critical Taylor number rises with ε, rather than initially decreasing with ε as predicted by local stability theory using the criteria of maximum local instability. The present prediction of the critical Taylor number agrees well with Vohr's experiments for ε up to about 0·5 when δ = 0·01 and for ε up to about 0·2 when δ = 0.1.

The existence of a new time scale t = σ-¼(L2/kN)½, where σ, k, L and N are the Prandtl number, the thermometric conductivity, a typical length and the Brunt-Väisälä frequency, respectively, is clarified for a temperature adjustment process of a Boussinesq fluid in a circular cylinder.

Measurements of static pressure and wave height are used to describe the waveinduced pressure field above generating sea waves. A large hump in the pressure spectra is observed at the wave frequencies. The amplitude of this hump increases and the rate of its vertical decay decreases as the mean wind speed increases. The phase difference between the pressure and the waves during active generation is about 135°, pressure lagging the waves, and does not change vertically for measurements at heights greater than the wave crests. In the present data, active wave generation appears to occur only when the wind at a height of 5 metres is greater than or about equal to twice the phase speed of the waves.

The effect of turbulence on the structure of weak shock waves is investigated. The equilibrium structure is shown to be governed by a balance between nonlinear steepening and the turbulent scattering of acoustic energy out of the main wave direction. The scattered energy appears as perturbations behind the shock front. For conditions typical of sonic booms in atmospheric turbulence the wave structure is governed by a Burgers equation similar to that describing viscous shocks, except that parameters related to the turbulence appear instead of the viscosity coefficient. The magnitude of the perturbations following a shock is estimated from first-order scattering applied to a thickened shock. Predictions of shock thicknesses and perturbations compare favourably with available experimental data. The approach used in the analysis of shock structure is to account for energy scattered from a single wave propagating a long distance through turbulence. This avoids difficulties of physical interpretation which arise if an ensembleaveraged structure is calculated, which is the usual approach in turbulent scattering analysis.

An experimental study has been made of the flow produced by an internal heat source as it moves around a fixed annulus of fluid. The mean surface flow relative to the annulus is found to be in the opposite direction to the movement of the heat source. The variation in its magnitude with changes in the external parameters is investigated. Thermocouple measurements and streak photography are used to examine the interior temperature and flow structure.

The equations describing the statistical features of small amplitude waves in a turbulent shear flow are derived from the Navier-Stokes equations. Closure is achieved through a postulated constitutive equation for the alteration of the statistical properties of the turbulence by the organized wave. The theory is applied in an examination of the stability of a hypothetical wake consisting of small-scale turbulence enclosed within a steady uncontorted superlayer. A set of superlayer jump conditions is derived from fundamental considerations, and these are of more general interest. For this hypothetical flow the analysis predicts largescale instabilities and superlayer contortions reminiscent of large-eddy structures observed in real flows. These instabilities therefore offer an explanation of the presence of large-scale organized motions in turbulent free shear flows.

Errors in static pressure measurements caused by taps which protrude beyond the wall and disturb the boundary layer locally are investigated experimentally. The resulting error is presented as a function of the wall shearing stress, the protrusion height and the probe diameter in a representation similar to the calibration curve of Preston tubes. If suitably plotted, the present results can be made to fit this calibration curve to within the experimental accuracy, in spite of the differences between the geometries being compared.

A similarity solution is presented which describes the internal waves generated by a simple-harmonic localized disturbance in a stably stratified viscous fluid. Some experimental results support the theoretical predictions for the waves in a linearly stratified salt solution.

The energy flux in gravity-capillary wave spectra has been obtained using Hasselmann's (1962) perturbation analysis for a homogeneous Gaussian sea. As expected, resonant interactions now appear at second order, and a third-order perturbation analysis shows that energy is redistributed from waves with intermediate wavelengths (in the neighbourhood of 1·7 cm) toward gravity and capillary waves. Numerical computations are also obtained for the energy flux and the interaction time of a sharply peaked spectrum consisting of wavenumbers concentrated around a single wavenumber, superposed on a smooth background spectrum. The range of validity of the inviscid results is discussed.

Bounds on the heat transport in a porous layer are derived using the variational method of Howard (1963) and Busse (1969b). The relatively simple structure of the variational problem in the case of porous convection allows one to formulate the theory more simply and to investigate some of the mathematical questions posed by the earlier work. A precise characterization of the solution with N wavenumbers is given. The variational problem is solved exactly among functions with a single overall wavenumber and this solution is in good agreement with a nonlinear perturbation solution of the governing equations and with experiments. An N-wavenumber solution is constructed for large Nusselt numbers by boundary-layer methods. The asymptotic solution is compared with a numerical solution of the problem for N = 2. The comparison supports the boundary-layer assumptions introduced in the asymptotic analysis.

Conjugate flows have been defined generally as flows uniform in the direction of streaming that separately satisfy the relevant hydrodynamical equations, so allowing a transition from one flow to its conjugate to be consistent with mass and energy conservation. In previous studies of various examples, certain general principles have been found to apply to conjugate flows: in particular, one in a pair of such flows is subcritical (subsonic) and the other supercritical (supersonic), the former having greater flow force (i.e. momentum flux plus pressure force). In this paper these principles are confirmed in another field of application, for which the theory of conjugate flows takes a novel course.

The theoretical model defined in § 2 consists of a straight duct of arbitrary cross-section filled with a perfect fluid whose constitutive properties vary with cross-sectional position, and whose primary, prescribed flow is axial with a velocity distribution that may be non-uniform. In § 3 the possibility of a conjugate flow in the same duct is investigated, and its principal properties relative to those of the primary flow are deduced from certain simple inequalities between integrals over the cross-section. A Lagrangian description of the conjugate flow is essential, but the properties in question are established without the necessity of determining this flow explicitly. At the end of § 3, a modification of the model is discussed accounting for dissipative, flow-force conserving transitions (shocks). The application of the theory to flows of non-uniform suspensions of gas bubbles is considered in § 4.

The present work is concerned with the flow past spheres in the Reynolds number range 5 × 104 [les ] Re [les ] 6 × 106. Results are reported for the case of a smooth surface. The total drag, the local static pressure and the local skin friction distribution were measured at a turbulence level of about 0·45%. The present results are compared with other available data as far as possible. Information is obtained from the local flow parameters on the positions of boundary-layer transition from laminar to turbulent flow and of boundary-layer separation. Finally the dependence of friction forces on Reynolds number is pointed out.