Using the slender-body theory for Stokes flow, the equations of motion are developed for a small flexible inextensible thread. The nearly straight thread is examined analytically, and is shown to straighten rapidly. In a simple shear flow the distortions decay less rapidly, but rapidly enough not to rotate the thread through the plane of flow. Numerical studies of simple shear with more substantially distorted threads show the same qualitative behaviour. Additionally some differences are revealed in the nonlinear regime between the buckling and stretching processes which occur in the compressive and tensile quadrants of the flow.

An experimental and theoretical-numerical investigation has been carried out to extend existing knowledge of velocity and temperature distributions and local heat-transfer coefficients for naturel convection within a horizontal annulus. A Mach—Zehnder interferometer was used to determine temperature distributions and local heat-transfer coefficients experimentally. Results were obtained using water and air at atmospheric pressure with a ratio of gap width to inner-cylinder diameter of 0·8. The Rayleigh number based on the gap width varied from 2·11 × 104to 9·76 × 105. A finite-difference method was used to solve the governing constant-property equations numerically. The Rayleigh number was changed from 102 to 105 with the influence of Prandtl number and diameter ratio obtained near a Rayleigh number of 104. Comparisons between the present experimental and numerical results under similar conditions show good agreement.

A constant-pressure axisymmetric turbulent boundary layer along a circular cylinder of radius a is studied at large values of the frictional Reynolds number a+ (based upon a) with the boundary-layer thickness δ of order a. Using the equations of mean motion and the method of matched asymptotic expansions, it is shown that the flow can be described by the same two limit processes (inner and outer) as are used in two-dimensional flow. The condition that the two expansions match requires the existence, at the lowest order, of a log region in the usual two-dimensional co-ordinates (u+, y+). Examination of available experimental data shows that substantial log regions do in fact exist but that the intercept is possibly not a universal constant. Similarly, the solution in the outer layer leads to a defect law of the same form as in two-dimensional flow; experiment shows that the intercept in the defect law depends on δ/a. It is concluded that, except in those extreme situations where a+ is small (in which case the boundary layer may not anyway be in a fully developed turbulent state), the simplest analysis of axisymmetric flow will be to use the two-dimensional laws with parameters that now depend on a+ or δ/a as appropriate.

Accurate measurements of the density distribution in Ar and N2 shock waves have been made in a shock tube for the Mach number range from 1.55 to 9 and 10 respectively by the absorption of an electron beam. A modified absorption law has been used for data reduction. The density profiles were corrected for the influence of shock curvature and density rise behind the shock wave. The measurements in Ar agree to within 1% with those of Schmidt (1969) in the mean range of Ms but give a slightly smaller density gradient for Ms = 9. Comparison with various theories shows very good agreement with Bird's Monte Carlo simulation in the whole Mach number range for a simple repulsive intermolecular force law. Further, the agreement with the Mott-Smith density profile for the same interaction law is also good, and surprisingly is found to be better for lower than for higher Mach numbers. Qualitative agreement is obtained with the solutions of Hicks & Yen for hard-sphere and Maxwell molecules. The Navier-Stokes and BGK solutions are found to differ significantly from the present experiments even for the lowest measured Mach number (1·55), whereas the Burnett equation gives better agreement, especially with respect to the asymmetry of the profiles.

The measured N2 profiles agree on the whole with the shock-tube measurements of other investigators but show substantial deviations from the low density wind-tunnel experiments of Robben & Talbot (1966b) for higher Mach numbers. Bird's ‘energy sink model’ (1971) is in agreement with the measured density profiles for a realistic interaction law and a suitable rotational collision number. Rotational relaxation in nitrogen is found to be very fast for all Mach numbers. Consequently the coupling between rotational and translational relaxation is very strong.

We examine a rapidly rotating flow that exhibits periodic vortex detachment. Specifically, the rotation/symmetry axis of a fluid-filled cylinder is set perpendicular to gravity. A free buoyant cylindrical float placed within the container is acted upon by both centrifugal and gravitational forces, the competition of which causes fluid motion and, in certain parameter ranges, flow instability. The motion is determined, a criterion for separation is advanced, preliminary experiments and data are described and the relationship of this phenomenon to other examples of vortex shedding in rotating fluids is discussed.

This paper presents a procedure whereby three-dimensional inviscid flow through a highly loaded turbomachinery cascade of lifting lines can be treated by methods corresponding to classical aerodynamic theory. In contrast to earlier linearized (thin airfoil) three-dimensional theory, the present study allows analysis of the flow corresponding to the large turning and/or large pressure ratios induced by practical rotors or stators. For the sake of simplicity, the present paper is limited to incompressible flow through a highly loaded rectilinear cascade and to the design problem, i.e. given blade loading. Formulae are derived for both the mean and the three-dimensional components of the flow; in particular, the velocities at the blades induced by the trailing vorticity associated with nonuniform blade circulation are determined.

Jets from notched nozzles are investigated by schlieren photography and pressure traverses. It is demonstrated that the dominant feature of the flow which determines the structure far downstream is the trailing vortices shed from the swept edges of the notches.

The large negative Soret coefficient of 1N-LiI gives rise in a Rayleigh-Bénard experiment to a density distribution which is observed to stabilize the fluid layer for values of the Rayleigh number as large as 196 times the value of 1708 for the onset of convection in a pure fluid. The Soret transport also affects the convective heat flux. A power law relating heat flux and temperature difference is found with the same exponent as is found in pure fluids but with a lower value of the multiplicative constant. The Rayleigh number at the onset of power-law behaviour depends on the Soret coefficient. Three types of oscillation are seen: transient oscillations at onset, low frequency fluctuations at low Rayleigh number, and higher frequency oscillations similar to those observed in pure water. The intermediate state found after onset in NaCl solutions is not found in LiI.

Nonlinear corrections to Stokes's linear edge-wave solution are obtained by means of perturbation expansions in the amplitude. The shallow-water formulation is considered first, but even for small beach angles β the behaviour in the deep water offshore becomes important and this formulation is limited. In the full formulation, amplitude dependence is required in the dispersion relation and in the exponents for the exponential decay away from the shore. There is a non-uniformity in the results as β → ½π, which is corrected by a special perturbation expansion.

Analytic solutions are obtained for non-equilibrium dissociating flow of an inviscid Lighthill-Freeman gas after a curved shock, by dividing the flow into a thin reacting layer near the shock and a frozen region further downstream. The method of matched asymptotic expansions is used, with the product of shock curvature and reaction length as the small parameter. In particular, the solution gives expressions for the reacting-layer thickness, the frozen dissociation level, effective shock values of the frozen flow and the maximum density on a stream-line as functions of free-stream, gas and shock parameters. Numerical examples are presented and the results are compared with experiments.

This paper examines the problem of a pulsating compact body moving with constant velocity. This problem is usually incorrectly treated as a convected monopole. The analysis here shows that the motion of such a ‘real’ source introduces additional coupled multipoles, whose combined effects generate previously unexpected convective features. The amplification obtained is not the monopole convective amplification (1 — Mr)−2. It is found to depend on the virtual mass tensor of the body, the minimum effect being (1 — Mr)−3. There is also amplification in the direction perpendicular to the flight path (unless the motion is parallel to a principal axis of the virtual mass tensor).

The field produced by oscillation of a convected compact body of constant geometry is also investigated. Again, this problem is often misrepresented as a moving dipole. Here it is shown that the effect of convection on such a real source is surprising and complicated. It cannot be described completely by Doppler factors, and there is amplification in the direction perpendicular to the source motion.

These two model problems serve as a warning that the effect of flight on real sources cannot be anticipated until such real sources are correctly modelled, and that also the influence of source motion is likely to be much greater than has so far been anticipated.

In this paper we develop a uniformly valid, second-order theory for calculating the unsteady incompressible flow that occurs when an airfoil is subjected to a convected sinusoidal gust. Explicit formulae for the airfoil response functions (i.e. fluctuating lift) are given. The theory accounts for the effect of the distortion of the gust by the steady-state potential flow around the airfoil, and this effect is found to have an important influence on the response functions. A number of results relevant to the general theory of the scattering of vorticity waves by solid objects are also presented.

Preliminary measurements have been made of the debouching of homogeneous fluid from a broad source at its equilibrium depth into a linearly stratified tank of salt water. With c the velocity of the nose of the intrusion, h its half-thickness near the source, N the environmental buoyancy frequency and v the kinematic viscosity of the fluid, it is shown for 100 [lsim ] Re ≡ 2ch/ν [lsim ] 500 that the intrusion becomes practically steady under an inertia-buoyancy balance. The internal Froude number Fr = c/Nh is shown to be of order unity. Forward-propagating disturbances and the ends of the tank are inferred to play an important part in the flow.

The two-dimensional theory of lunate-tail propulsion is extended to motions of arbitrary amplitude, regular or irregular, so that an accurate comparison may be made with the actual lunate-tail propulsion of scombroid fishes and cetacean mammals. There is no restriction at all on the amplitude of motion but the tail's angle of attack relative to its instantaneous path through the water is assumed to remain small. The theory is applied to the regular finite amplitude motion of a thin aerofoil with a rounded leading edge to take advantage of the suction force and a sharp trailing edge to ensure smooth tangential flow past the rear tip. This can represent the vertical motions of the horizontal lunate tails of large aspect ratio with which cetacean mammals propel themselves or the horizontal undulations of the vertical lunate tails of certain fast fishes. The dependence of the thrust, the hydromechanical propulsive efficiency and the energy wasted in churning up the eddying wake on the reduced frequency, the angle of attack and the amplitude of motion is exhibited.

Nonlinear effects are considered for shallow-water edge waves on beaches with a general depth distribution. The case of uniform depth away from the shoreline is considered in detail. It is shown that the results obtained are in qualitative agreement with those obtained by Whitham (1976) using the full nonlinear theory for a beach of constant slope.

The present investigation is oriented towards a better understanding of the turbulent structure in the core region of fully developed and completely wall-bounded flows. In view of the already existing results concerning the bursting process in boundary layers (which are semi-bounded flows), an amplitude analysis of the Reynolds shear stress fluctuation u1u2, sorted into four quadrants of the u1, u2 plane, was carried out in a turbulent pipe flow. For the wall side of the core region, in which the correlation coefficient u1u2/u’1u’2 does not change appreciably with the distance from the wall, the structure of the Reynolds stress is found to be similar to that obtained in boundary layers: bursts, i.e. ejections of low speed fluid, make the dominant contribution to the Reynolds stress; the regions of violent Reynolds stress are small fractions of the overall flow; and the mean time interval between bursts is found to be almost constant across the flow. For the core region, the large cross-stream evolution of the correlation coefficient u1u2/u’1u’2 is associated with a new structure of the Reynolds stress induced by the completely wall-bounded nature of the flow. Very large amplitudes of u1u2 are still observed, but two distinct burst-like patterns are now identified and related to ejections originating from the two opposite halves of the flow. In addition to this interaction, a focusing effect caused by the circular section of the pipe is observed. As a result of these two effects, the mean time interval between the bursts decreases significantly in the core region and reaches a minimum on the pipe axis. Investigation of specific space-time velocity correlations reveals the possible existence of rotating structures similar to those observed at the outer edge of turbulent boundary layers. These coherent motions are found to have a scale noticeably larger than that of the bursts.

The frequencies of the first four sloshing internal wave modes in two superposed fluid layers contained in a circular channel are calculated for two positions of the free surface and for various ratios of the depths of the two layers. Flow patterns are given for the first four sloshing modes for the case in which the fluids occupy a semicircular space and the depth of the upper layer is one-quarter of the radius.

It is hoped that the results obtained will provide a guide for estimating the frequencies of sloshing internal wave modes in long lakes.

The source function describing the energy transfer between the components of the internal wave spectrum due to nonlinear interactions is derived from the Lagrangian of the fluid motion and evaluated numerically for the spectral models of Garrett & Munk (1972a, 1975). The characteristic time scales of the transfer are found to be typically of the order of some days, so that nonlinear interactions will play an important role in the energy balance of the wave field. Thus implications of the nonlinear transfer within the spectrum for generation and dissipation processes are considered.

Numerical solutions for the flow field about cones with nose angles of up to 30° at angles of attack up to 50° for a range of Reynolds numbers and wall temperature ratios are presented. The solutions obtained permit interaction between the inviscid region and the boundary layer on the body through the displacement-thickness effect. The solutions are valid throughout the flow field except in the region adjacent to the leeward line of symmetry. Comparisons are made with experimental results and other numerical solutions. Detailed flow structure and the variation of surface conditions with cone angle, incidence, Reynolds number and wall temperature are indicated. The numerical methods used for the inviscid flow equations are Telenin's method and the method of characteristics, while a modified form of the method of integral relations is applied to the boundary-layer equations.