Wind, blowing over a water surface, induces a thin layer of high vorticity in which the wind stress is supported by molecular viscosity; the magnitude of the surface drift, the velocity difference across the layer, being of the order of 3% of the wind speed. When long waves move across the surface, there is a nonlinear augmentation of the surface drift near the long-wave crests, so that short waves, superimposed on the longer ones, experience an augmented drift in these regions. This is shown to reduce the maximum amplitude that the short waves can attain when they are at the point of incipient breaking.

Theoretical estimates of the reduction are compared with measurements in wind-wave tanks by the authors and by Mitsuyasu (1966) in which long mechanically generated waves are superimposed on short wind-generated waves. The reductions measured in the energy density of the short waves by increasing the slope of the longer ones at constant wind speed are generally consistent with the predictions of the theory in a variety of cases.

Two attempts were made to develop a three-dimensional laminar boundary layer in the flow over a flat plate in a curved duct, establishing a negligible streamwise pressure gradient and, at the same time, an appreciable crosswise pressure gradient.

A first series of measurements was undertaken keeping the free-stream velocity at about 30 ft/s; the boundary layer was expected to be laminar, but appears to have been transitional. As was to be expected, the cross-flow in the boundary layer decreased gradually as the flow became progressively more turbulent.

In a second experiment, at a lower free-stream velocity of approximately 10 ft/s, the boundary layer was laminar. Its streamwise profile resembled closely the Blasius form, but the cross-flow near the edge of the boundary layer appears to have exceeded that predicted theoretically. However, there was a substantial experimental scatter in the measurements of the yaw angle, which in laminar boundary layers is difficult to obtain accurately.

Inertialess incompressible flow through a rapidly rotating, variable-area conduit of circular cross-section is treated. For the practical case of an expansion (or contraction) placed between two pipes, the flow is strongly asymmetrical and involves regions of weak reverse flow in the expansion and downstream pipe, while the disturbance to the fully developed pipe flows persists for large, O(E−½) distances upstream and downstream, where E is the (small) Ekman number. The flow in the two pipes depends only on the ratio of their radii and is independent of the shape and length of the expansion. The startling implication of the disturbance's persistence is that, in practice, fully developed flow will almost never be realized in rapidly rotating pipes.

The pressure field due to a large circular capped air bubble rising in water has been determined experimentally. The results verify the Davies & Taylor cap boundary condition and the frontal pressure field is well approximated by that due to irrotational flow around an oval body.

The pressure field extends axially as far as ten bubble half-widths below the bubble floor. Immediately below the floor the pressure is constant for about two-thirds of a bubble height. The wake is closed and contains symmetric pressure minima. For the bubbles studied, turbulence, as well as the diffusion of vorticity, probably controls the momentum distribution and energy dissipation in the wake.

A general characteristic of rapidly rotating fluids is that accurate experimental measurements can only be made of the main (azimuthal) flow. The secondary flow is then usually deduced from theory, although this is often incomplete in the boundary regions where the secondary flow is of most interest.

In this paper we consider the case of source-sink flow between the porous walls of a rapidly rotating annular container and numerically integrate the full equations of motion in order to determine the complete structure of the secondary flow. The results are compared with the (approximate) analytic studies of Hide (1968) and Bennetts & Hocking (1973) to show the differences between the two approaches.

A defect of many previous numerical papers has been the inability to check the solution in the nonlinear case. To overcome this, new experimental measurements of the azimuthal velocity profile for a Rossby number of 0·238 have been obtained and these are compared with the numerical results.

The detailed flow fields associated with instability in axisymmetric jets are realized by numerical integration of the time-dependent Navier-Stokes equations.

The mechanism of amplification of small disturbances is shown to be two-dimensional for a thin boundary layer profile and conclusions regarding three-dimensionality which have been inferred from recent models of axisymmetrical systems are clarified.

The computed flow field is shown to be dominated by the large-scale vortex ring structure which has been observed experimentally. Although the wavelength of vortex shedding is found to be slightly variable owing to the randomness of the initial perturbation, the results are shown to agree closely with experiment.

The stability of Couette flow of stratified salt solutions is investigated in an apparatus with both the inner and outer cylinders rotating. The ratio of the radius of the inner cylinder to that of the outer cylinder is 0·2. The flow is visualized by means of shadowgraph and dye-trace methods. Compared with homogeneous fluids, the effect of the stabilizing density gradient is to increase the critical speed of the inner cylinder and to decrease the critical wavelength for a given angular speed of the outer cylinder. When the cylinders are rotating in the same direction, in the critical state, the instabilities appear along the inner cylinder in a spiral wave form which is itself not very stable. With counterrotating cylinders, the instabilities appear as regularly spaced vortices which, for the most part, are neither symmetric Taylor vortices nor simple spirals. In addition, these vortices rotate as a whole at a speed generally smaller than that of the inner cylinder. From shadowgraph observations, stability curves are constructed for three density gradients. The critical wavelength and the rotational periods of the vortices are also determined.

A Mach-Zehnder interferometer was used to stud two-dimensional Bénard convection cells. The experiments were performed with distilled water and sea water in the region where density is a linear function of temperature. Two-dimensional convection rolls were formed with Rayleigh numbers as great as 23400. Reversal in the temperature profile was obtained for R/Rc ≥ 3·8, and an overshoot of about 6% was observed at R/Rc = 9·2 and 13·8. This agrees with the values predicted theoretically by Veronis (1966) for stress-free boundaries and Royal (1969) for rigid boundaries. This disagrees with the experimental results of Gille (1967), who reports an overshoot of only 1 ½% at R/Rc = 16. Many of the other results agree with those of other experimenters, such as the relation between the cell height-to-width ratio and Rayleigh number, the relation between the Nusselt number and Rayleigh number, and the value of the critical Rayleigh number.

This paper considers the dispersion of a cloud of passive contaminant released from an instantaneous source in the steady two-dimensional laminar flow near the forward stagnation point on a bluff body. The body is replaced by its tangent plane y = 0 with x measuring distance along the plane. Far away from y = 0 the flow is irrotational with velocity potential ½l(x2 – y2), where l is a positive constant. When the boundary layer is ignored the equation governing the distribution of concentration can be solved exactly. Consequences of this solution are that for large times the centre of mass moves parallel to the body at a speed proportional to exp (lt) while the cloud spreads out along the body symmetrically about the centre of mass with the magnitude of the spread also proportional to exp (lt). However, this solution is unrealistic because most of the contaminant is confined to a layer adjoining the body of thickness of order (k/l)½, where k is the molecular diffusivity, and this layer normally lies within the boundary layer, which is of thickness of order (v/l)½, where v is the kinematic viscosity. An approximate analysis, based on ideas similar to those supporting the Pohlhausen method in boundary-layer theory, suggests that when the boundary layer is taken into account the conclusions above remain true provided that exp (lt) is replaced by exp (βlt), where β is a constant depending on v/k. Calculations give values of β ranging from 0·73 when v/k = 0·5 to 0·10 when v/k = 103.

A layer of viscous incompressible fluid is confined between two horizontal plates which rotate rapidly in their own plane with a constant angular velocity. A hemisphere has its plane face joined to the lower plate and when a uniform flow is forced past such an obstacle, a Taylor column bounded by thin detached vertical shear layers forms. The linear theory for this problem, wherein the Rossby number ε is set equal to zero on the assumption that the flow is slow, is examined in detail. The nonlinear modifications of the shear layers are then investigated for the case when ε ∼ E½, where E is the Ekman number. In particular, it is shown that provided that the Rossby number is large enough separation occurs in the free shear layers. The extension of the theory to flow past arbitrary spheroids is indicated.

The theory initiated by Lighthill (1952) to describe the sound radiated by turbulence embedded in an uniform fluid at rest is here extended to the case where the turbulence exists on the edge of a uniformly moving stream. An exact analogy is developed between the distant real sound field and that which would be radiated by a particular quadrupole distribution adjacent to a vortex sheet positioned in the linearly disturbed flow. The equivalent sources in this analogy are quadrupoles identical in strength with those in Lighthill's model, but the quadrupoles are now shown to convect with the fluid-particle velocity. There is no amplifying effect of shear. The particular case of a plane shear layer is worked out in detail for sound waves of scale large in comparison with the shear-layer thickness.

A downstream zone of silence is predicted as is the formation of highly directional beams associated with the interference of sound radiated directly and sound reflected from the fluid interface. A distinct structure results in which the variation of sound with flow velocity, density and angle is not easily accounted for by simple power-law scaling. Finally a comparison is made with some features of jet noise; the modelling of the high frequency jet noise problem by a single shear layer yields some features consistent with experiment.

The objective of this paper is to describe approximately the coupled steady-state processes of light propagation and induced laminar incompressible fluid flow in the case of natural convection.

For the case of a homogeneous fluid and under the assumptions that light energy is instantaneously transformed into heat and that the induced velocities are not too large, it is reasonable to use the boundary-layer equations to describe the induced natural flow. These equations are augmented by the conservation of energy equation. The velocity, temperature and intensity functions are expected to exhibit similarity properties.

A high-intensity light beam with a given rotationally symmetric Gaussian initial intensity distribution is propagating vertically upwards into a fluid initially at rest. The fluid characteristics are assumed to be constant. A stream function is introduced to satisfy the conservation of mass equation. The conservation of momentum equation leads to conditions on the unknown functions involved in the stream function. Additional conditions follow from the conservation of energy equation, which involves the local light intensity as a driving term.

Under the assumptions made, self-defocusing (thermal blooming) will occur. The main results are an exponential increase of the boundary-layer thickness and an exponential decrease of temperature and of light intensity due to the blooming effect in addition to the exponential decrease due to absorption.