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.

The paper presents the outcome of experimental research on turbulence-induced secondary flows in square-sectioned ducts. The main emphasis of the experiments has been on the measurement of the secondary flows in a duct with equally roughened surfaces. Here the secondary flow is a substantially larger proportion of the axial flow than is the case in smooth-walled ducts. With the secondary velocities normalized by the friction velocity, however, the resultant profiles for smooth and rough surfaces are the same, within the precision of the measurements.

A detailed study has been made of the solutions to cone boundary-layer equations in the symmetry plane in order to increase understanding of the mathematical nature and physical meaning of these solutions. A typical set of symmetry-plane solutions is presented. Included in this set are various solution branches not previously published. A double-valued solution curve is found which has not been studied prior to this time except at one trivial point. The extension of an existing solution branch through a removable singular point has also been accomplished. The solutions presented are categorized according to whether they are dependent on or independent of the boundary layer outside the symmetry plane. The region in which no solutions to the usual symmetry-plane equations exist is examined. Solutions in which the usual boundary-layer model predicts that conservation of mass is not satisfied at the symmetry plane are discussed. Non-analytical behaviour at the symmetry plane is also investigated. In both of these cases a boundary region exists at the symmetry plane.

Some numerical solutions of a variable-coefficient Korteweg-de Vries equation are presented. This particular equation was derived by the author recently (Johnson 1972) in an attempt to describe the development of a single solitary wave moving onto a shelf. Soliton production on the shelf was predicted and this is confirmed here. Results for two and three solitons are reproduced and two intermediate shelf depths are also considered. In these latter two cases both solitons and an oscillatory wave occur. One of the profiles corresponds to the integrations performed by Madsen & Mei (1969) and a comparison is made.

The acceleration of a shock wave in an ideal gas of decreasing density has previously been studied. The problem is reconsidered here with empirical inclusion of real-gas effects for strong shocks in hydrogen. Experimental results suggest that previous shock acceleration models are valid only for a limited range of the Knudsen number in finite geometries and that for large final-state Knudsen numbers a free-expansion model best describes the experimental results.

The stability of Poiseuille flow in a pipe of circular cross-section to azimuthally varying as well as axisymmetric disturbances has been studied. The perturbation velocity and pressure were expanded in a complete set of orthonormal functions which satisfy the boundary conditions. Truncating the expansion yielded a matrix differential equation for the time dependence of the expansion coefficients. The stability characteristics were determined from the eigenvalues of the matrix, which were calculated numerically. Calculations were carried out for the azimuthal wavenumbers n = 0,…, 5, axial wavenumbers α between 0·1 and 10·0 and αR [les ] 50000, R being the Reynolds number. Our results show that pipe flow is stable to infinitesimal disturbances for all values of α, R and n in these ranges.

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.

Semi-infinite double rows of vortices are used to study the periodic wake of both oscillating and stationary two-dimensional bodies immersed in a uniform incompressible stream. Analytical expressions for the induced Velocities on the body, for trails with constant spacing, which are valid for small values of the oscillation amplitude are presented while, for the general case of vortex shedding, an iterative procedure for the representation of trails of variable spacing is developed and used. Vortex streets due to oscillating bodies are obtained as a function of three non-dimensional parameters: the Strouhal number (initial spacing ratio), a non-dimensional vortex strength and the downstream spacing ratio. Criteria establishing when such trails are expected to widen, become narrow or stay of constant width are presented, as well as expressions for the induced velocities.

The trails and their induced velocities enable the calculation of the vortex strength from measurable quantities. Thus they can serve as a method for estimating the hydrodynamic forces on the airfoil due to large amplitude oscillations, such as those observed in the propulsive movements of fish and cetaceans, as well as the small amplitude oscillations due to hydroelastic interactions.

A theoretical study of the spatial stability of Poiseuille flow in a rigid pipe to infinitesimal disturbances is presented. Both axisymmetric and non-axisymmetric disturbances are considered. The coupled, linear, ordinary differential equations governing the propagation of a disturbance that has a constant frequency and is imposed at a specified location in the fluid are solved numerically for the complex eigenvalues, or wavenumbers, each of which defines a mode of propagation. A series solution for small values of the pipe radius is derived and step-by-step integration to the pipe wall is then performed. In order to ascertain the number of eigenvalues within a closed region, an eigenvalue search technique is used. Results are obtained for Reynolds numbers up to 10000. For these Reynolds numbers it is found that the pipe Poiseuille flow is spatially stable to all infinitesimal disturbances.

Experiments have been conducted to determine the effect of density stratification upon certain characteristic features of so-called Taylor columns. The interior structure of the homogeneous Taylor column is first of all described and compared with flow patterns obtained when the fluid is stratified. Qualitative features of the horizontal and vertical motion (in particular, the attenuation with height of the distortion created by the obstacle) are then described for values of the stratification parameter S (defined as S = N/2 Ω, whereN and Ω are the Brunt-Väisälä and rotation frequencies respectively) in the range 0 [les ] S [les ] 0·24. The effect of density stratification upon, specifically, the length of the column is then described. A working definition for the existence of a Taylor column in a given experimental situation is formulated, enabling the strength of the column to be quantified at a particular height above the obstacle. Using this method the column length is measured as a function of S in the range 0 [les ] S [les ] 0·24. It is shown that even very slight stratification is sufficient to produce noticeable modification of all aspects of the flow. In particular, the column length is considerably reduced by weak stratification.

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.

Messiter's thin shock layer approximation for hypersonic wings is applied to several non-conical shapes. Two calculation methods are considered. One gives the exact solution for a particular three-dimensional geometry which possesses a conical planform and also a conical distribution of thickness superimposed upon a surface cambered in the chordwise direction. Agreement with experiment is good for all cases, including that where the wing is yawed. The other method is a more general approach whereby the solution is expressed as a correction to an already known conical flow. Such a technique is applicable to conical planforms with either attached or detached shocks but only to the non-conical planform for the region in the vicinity of the leading edge when the shock is attached.

The motion of a rigid sphere responding to the passage of an acoustic pulse is considered by means of a simple approximate model which neglects the diffraction of the pulse front. The model is based on a solution of the equivalent inviscid problem and assumes that, initially, the flow field around the sphere corresponds to the steady incompressible flow of an inviscid fluid over a sphere at rest. For t > 0, the motion is studied by means of the unsteady Stokes equations. Results for the sphere's velocity, displacement and drag are obtained in closed form in terms of tabulated functions and compared with results obtained by using the Stokes drag. It is found that, when the ratio of gas density to sphere material density is finite, the initial response of the sphere differs considerably from that predicted by the use of the Stokes drag. However, when the ratio of gas density to sphere material density is infinitesimal, the differences disappear. These results may be of some importance in the study of shock-induced droplet collisions in aerosol clouds.

The present work is an analytical study of the stability of interfaces between fluids in motion, special attention being given to the role of surface tension without consideration of viscous effects. A variational approach based upon the principle of minimum free energy, which was first formulated for stagnant fluids, is applied to fluids in motion. This generalization is possible if viscous and inertia effects are unimportant as far as stability is concerned. One stability problem is studied in detail: a gas jet impinging on a free liquid. The analytical results obtained by this variational technique lie within the range of accuracy (15%) of the experimental results for this gas-jet problem. The method is very general and therefore can be applied to quite a number of interface stability problems.

The steady, two-dimensional motion which can occur when a body moves horizontally at large Richardson number is examined. Theoretical evidence is presented for two propositions: (i) The nature of the motion depends on whether the vertical thickness of the body is large compared with an intrinsic length scale of the motion. (ii) If the body is sufficiently thick, then diffusion or heat conduction are important, even if the Schmidt or Prandtl number is large. The notion of ‘near-similar’ solutions (§4) is used to obtain a description of the motion past a thick body which is likely to approximate the real motion everywhere except fairly close to the body surface (§5). It predicts a very long wake, at the core of which is a blocking column, both fore and aft of the body (§5). The same prediction is implied for the two-dimensional Taylor column in a rotating system (§6).

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.

The formation of convective cells in a fluid between two horizontal rigid boundaries with time-periodic temperature distribution is studied by the use of the Floquet theory. Numerical results for the critical Rayleigh number are given for a Prandtl number of 0·73 (air) and for various values of the frequency and magnitude of the primary temperature oscillation. Some numerical results for a Prandtl number of 7·0 (water) are also given. The most striking feature of the results is that the disturbances (or convection cells) oscillate either synchronously or with half frequency.

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.

Two-dimensional upstream and downstream wakes are produced by extremely slowly moving cylinders in a tank containing a linearly stratified salt solution. The upstream and downstream wakes appear to be of comparable strength, consistent with the symmetry predicted by theories that take account of density diffusion as well as viscosity. This contrasts with the quasi-non-diffusive régime recently studied experimentally by Browand & Winant (1972). The present velocity profiles are essentially similar to those predicted by diffusion theories, althought the magnitudes of the velocities appear to be greatly attenuated by the proximity of the upstream and downstream walls.

The average roll diameter in Rayleigh convection for 2000 < R < 31000, where R is the Rayleigh number, has been measured from photographs of three convecting fluids: air, water and a silicone oil with a Prandtl number σ of 450. For air the average dimensionless roll diameter was found to depend uniquely upon R and to increase especially rapidly in the range 2000 < R < 8000. The fluids of larger σ exhibited strong hysteresis but also had average roll diameters tending to increase with R. The increase in average roll diameter with R tended to decrease with σ. Through use of two-dimensional numerical integrations for the case of air it was found that the increase in average roll diameter with R provides an explanation for the usual discrepancy in heat flux observed between experiment and two-dimensional numerical calculations which prescribe a fixed wavelength.