The paper examines the results of an experiment which was designed to elucidate the manner in which wave characteristics, strut geometry and aspect ratio influence the angles at which struts ventilate. The experiment was conducted using small-scale models in a towing tank which allowed the wave parameters to be varied independently. The results indicate which parameters of a seaway are most hazardous to the operation of a hydrofoil ship in high seas and suggest design features which may extend the capability range of such craft.

The propagation of an internal wave in an ocean which is stratified in both temperature and salinity is considered. It is shown how the effects of viscosity, heat conduction and solute diffusion attenuate a cross-wave from an oscillatory disturbance. Under certain conditions there is no wave solution even though the oscillatory frequency is less than the Brunt–Väisälä frequency and the fluid is stably stratified.

An exact analytic solution is derived for the perturbation of a magnetic field while exposed to an immersed, axisymmetric, azimuthal, steady current source of arbitrary distribution in the presence of a slender, electrically conducting, independently permeated, compressible jet threading the axis of symmetry, subject to an equilibrium pressure balance. A further influence is the enclosure of the magnetic field by a coaxial cylindrical wall. The steady-state result invariably exhibits an infinite discrete superposition of axially decaying terms. In addition, there arise two admissible alternatives involving a fluid parameter λ (dependent on the flow speed, sound speed and both Alfvén speeds pertaining to the jet) together with a scale parameter χ(0) (equal to twice the ratio of the cross-sectional area of the jet to that of its externally enveloping field). Provided that λ exceeds χ(0), each element constituting the current distribution induces a stationary-wave contribution confined, as a consequence of an applied radiation condition, to the upstream domain, corresponding to an upstream-directed group velocity. However, if λ is exceeded by χ(0), this upstream wave is replaced by another decaying term, acting on both sides of every current constituent, like all other decaying terms.

The outer region of a turbulent boundary layer along a flat plate was photographed and analysed; in addition, limited observations of the wall area were also made. The technique involved suspending very small solid particles in water and photographing their motion with a high-speed camera moving with the flow.

The single most important event observed in the outer region was fluid motion which in the convected view of the travelling camera appeared as a transverse vortex. This was a large-scale motion transported downstream almost parallel to the wall with an average velocity slightly smaller than the local mean. It appeared to be the result of an instability interaction between accelerated and decelerated fluid, and it is believed to be closely associated with the wall-region ejections. The transverse vortex was part of a deterministic sequence of events; although these events occurred randomly in space and time. The first of these events was a decelerated flow exhibiting velocities considerably smaller than the local mean. It was immediately followed by an accelerated flow. Both these events extended from near the wall to the far outer region. Their interaction resulted in the formation of one or more transverse vortices. While the transverse vortex was transported downstream, small-scale fluid elements, originating in the wall area of the decelerated flow, were ejected outwards (ejection event). After travelling some distance outwards the ejected elements interacted with the oncoming accelerated fluid in the wall region and were subsequently swept downstream (sweep event). The sequence of events closed with two large-scale motions.

Estimated positive and negative contributions to the instantaneous Reynolds stress during the events were many times higher than the local mean values.

An aspect of the laminar far wake behind a symmetrical two-dimensional body placed in a uniform shear flow is described theoretically by means of the Oseen type of successive approximation, in which the shear is regarded as a small perturbation on a uniform stream. The expression for the stream function is determined up to the third approximation both in and outside the wake region, and the region in which the results of the perturbation analysis are valid is also determined. The stream function is found to contain four constants which cannot be determined from the boundary conditions for the far wake. The analysis also shows that the spreading of the wake is greater towards the side of smaller velocity than the side of larger velocity, the asymmetrical feature of the velocity defect becoming more evident as the distance from the obstacle is increased: the point which shows the maximum velocity defect shifts to the low-velocity side.

An analysis is presented of the motion of a turbulent thermal in an unstratified environment. Although based upon the entrainment hypothesis introduced by G. I. Taylor (see Morton, Taylor & Turner 1956), the analysis differs from previous work in that it is not limited to small density differences between the thermal and its surroundings. Also, the influence of the virtual mass of the unsteadily moving fluid, ignored by previous investigators, is included and shown to be of significance for any density difference.

Calculations of the temporal variations of size, velocity and density are presented in non-dimensional form for thermals with initial density ratios covering the practically attainable range. It is shown a posteriori that losses of momentum and buoyancy to a wake are probably of negligible influence in any real case.

An experimental investigation of the flow development of an axisymmetric jet exhausting into a moving air stream is made for two values of the ratio of jet velocity to external air velocity. The u-component turbulence intensity and Reynolds shear stress measurements together with the dissipation length scales inferred from measured u-component spectra suggest that the turbulence similarity assumptions are incorrect for the present flow situation. A discussion of the turbulence structure of the flow indicates that self-preservation does not apply for this situation and that the flow far downstream depends strongly on the complete past history.

The properties of infinitesimal disturbances to Poiseuille flow in a circular pipe have been found for a wide range of wavenumbers through recent numerical work (Salwen & Grosch 1972; Garg & Rouleau 1972). These studies did not, however, find the least-damped disturbances. In this paper, the properties of disturbances are found in a limiting case. These disturbances are thought to have decay rates which are equal to or very close to the smallest value possible for any given large value of the Reynolds number R. For disturbances which decay in time, the limiting disturbances can be found analytically. They have the property that the axial wavenumber α tends to zero as R → ∞. The smallest decay rate -βi is given by \[ -\beta_iR = j^2_{1,1}\approx 14.7, \] where j1,1 is the first zero of the Bessel function J1. Two modes have this decay rate. One is axisymmetric with motion only in the azimuthal direction, and the other has azimuthal wavenumber n = 1. For disturbances which decay in space, the limiting solutions can be found by numerically evaluating power series. They have the property that the frequency β tends to zero as R tends to infinity. The smallest decay rate αi for these disturbances is given by αiR ≈ 21·4, corresponding to an axisymmetric mode with motion only in the azimuthal direction. A mode with azimuthal wavenumber n = 1 has a slightly larger decay rate given by αiR ≈ 28·7.

Convection in water above ice penetrates into the stably stratified region above the density maximum at 4 °C. Two-dimensional penetrative convection in a Boussinesq fluid confined between free boundaries has been studied in a series of numerical experiments. These included cases with a constant temperature at both boundaries as well as cases with a fixed average flux at the lower boundary. Steady convection occurs at Rayleigh numbers below the critical value predicted by linear theory. At high Rayleigh numbers, resonant coupling between convection and gravitational modes in the stable layer excites finite amplitude oscillations. The problem can be described by a simplified model which allows for distortion of the mean temperature profile and balances the convected and conducted flux. This model explains the finite amplitude instability and predicts the Nusselt number as a function of Rayleigh number. These predictions are in excellent agreement with the computed results.

A plane harmonic sound wave is considered to be incident upon a rigid plane screen that contains a periodic rectangular array of circular or elliptical apertures, and a characterization is sought for the reflexion and transmission coefficients of the scattered waves when the relationships aperture dimension [Lt ] spacing [Lt ] wavelength apply. The problem is analysed with the help of an integral equation over a single aperture and, as a consequence of the determination of the leading terms in its asymptotic solution, some prior results for more general (that is, irregular) aperture spacing are confirmed and specific features of the interaction in the periodic arrangement are established. Similar formulations are devised and given attention for the related problems in which (i) the screen is backed by a rigid infinite plane and (ii) the apertures contain rigid pistons capable of executing normal displacements compatible with an assigned and common impedance. A section is devoted to the solution, based on expansion of its kernel, for an integral equation of the first kind with a plane circular or elliptical domain.

Experiments using a wind tunnel and a flow visualization technique in a towing tank were conducted to investigate the mechanism of vortex shedding from bevelled trailing edges. These reveal an important difference between the wake structures generated by heaving and steady motion. The suppression of vortex-excited vibration by means of bevelled trailing edges is attributed to the intermittency and rapid decay of the vortex trail resulting from an asymmetric circulation distribution in the vortex formation region.

The two-dimensional wave pattern produced in a homogeneous rotating fluid by a forcing effect oscillating with a frequency σ′0 and travelling with a uniform speed U along a line inclined to the axis of rotation at an arbitrary angle α is studied following Lighthill's technique. It is shown how the far field changes with α and σ′0.

For all σ′0 < 2Ω, except for σ′0 = 2Ω sin α (Ω being the angular velocity of the fluid), the forcing effect excites two systems of waves. When σ′0 → 2Ω sin α one of these systems spreads out, influencing the upstream side while the other shrinks in the downstream direction. This upstream influence is to the left or to the right of the line of motion of the forcing effect (the forcing line) according as σ′0 − 2Ω sin α[lg ] 0 and increases as σ′0 − 2Ω sin α decreases. For σ′0 > 2Ω there is only a single system propagating downstream. As α varies these systems undergo a kind of rotation retaining the main features. α ≠ 0 or ½π makes the pattern asymmetric about the forcing line while a non-zero σ′0 splits the steady-case identical wave systems into two, which are otherwise coincident.

When σ′0 = 2Ω sin α the forcing effect excites straight unattenuated waves of fixed frequency travelling both ahead and behind in a ‘column’ parallel to the forcing line and enclosing it. Also there are two other systems, which propagate without penetrating into an upstream wedge. It is shown that this ‘column’ is the counterpart of the ‘Taylor column’.

An experimental investigation has been carried out to determine the behaviour of three-dimensional disturbances in laminar natural convection flow adjacent to a flat vertical surface with uniform heat flux input. A controlled two-dimensional disturbance, with a superimposed transverse variation, was introduced into the boundary region by a vibrating ribbon. The downstream propagation and amplification of these disturbances were studied in detail. Of principal interest was their nonlinear interaction with the base flow and any secondary mean flows that might arise therefrom. Measurements of the transverse mean velocity component indicate a double longitudinal vortex system. These results also show a distortion of the longitudinal base velocity profile which rapidly increases downstream. An alternate spanwise steepening and flattening of the profile is found to result. These mean flow modifications are found to be in good general agreement with existing theoretical and experimental studies of such flows. Our results are also compared with those obtained for forced flow. Several very important differences and similarities are indicated.

The object is to predict the nature of small-amplitude long-period oscillations of a homogeneous rotating fluid over a ‘sea bed’ that is nowhere level. Analytically, we are limited to special choices of bottom topography, such as sinusoidal corrugations or an undulating continental slope, so long as the topographic restoring effect equals or exceeds that due to planetary curvature (the beta-effect). (Very slight topographic features, on the other hand, provide weak, resonant interactions between Rossby waves.)

Integral properties of the equations, and computer experiments reported elsewhere, verify the following results found in the analytical models: typical frequencies of oscillation are [lsim ]fδ, where f is the Coriolis frequency and δ measures the fractional height of the bottom bumps; an initially imposed flow pattern of large scale will rapidly shrink in scale over severe roughness (even the simplest analytical model shows this rapid change in spatial structure with time); and energy propagation can be severely reduced by roughness of the medium, the energy velocity being of order fδa, where a is the horizontal topographic scale (although in an exceptional case, the sinusoidal bottom, the group velocity remains finite for vanishingly small values of a).

We examine the hydromagnetic stability of a radially stratified fluid rotating between two coaxial cylinders, with particular emphasis on the case when the angular velocity greatly exceeds both buoyant and Alfvén frequencies. If the magnetic field is predominantly azimuthal instabilities then have an essentially non-axisymmetric and wavelike character. Various bounds on their phase speeds and growth rates are derived, including a ‘quadrant’ theorem analogous to Howard's semicircle theorem for Kelvin–Helmholtz instability. Their strong tendency to propagate against the basic rotation (i.e. ‘westward’), previously noted by the author in the study of a more simplified (homogeneous) model, seems relatively insensitive to the generation mechanism (e.g. unstable gradient of magnetic field, angular velocity or density), but a number of counterexamples show that this constraint need not apply if the magnetic field displays significant spatial variations of direction as well as magnitude and that eastward-propagating amplifying modes are then possible.

The fully viscous hydrodynamic stability equations for a round laminar vertical jet have been numerically solved using the proper boundary-layer base-flow velocity profile and for both symmetric and asymmetric disturbances. The symmetric mode is found to be unconditionally stable. The first asymmetric mode is found to be unstable and characteristics are compared with previous calculations. The computed critical Reynolds number for this mode is 9·4, which agrees with the calculations of Burridge (1968). Disturbance amplitude-ratio contours are also calculated and related to the convection of disturbances in the flow.

The effect of thermal buoyancy on jet stability is assessed by solving the fully viscous equations, coupled through buoyancy, and using a buoyancy-perturbed jet flow. A Prandtl number σ of 6·7 is used, and positive thermal buoyancy is found to have a destabilizing effect. Stability characteristics for the limiting case of buoyancy, a purely thermal point-source plume, are determined for a Prandtl number of 2.

Finally, an experiment was performed using water jets in water (σ ≈ 4·52–5·89) and a new method of jet production is described. The effect of varying amounts of thermal buoyancy on the laminar length of a jet undergoing naturally occurring transition was determined experimentally. These experiments confirm the calculated destabilizing effect of buoyancy. An empirical correlation is presented for the laminar length of a jet. Also, the effect of both symmetric and asymmetric artificially induced disturbances was determined experimentally. The disturbance amplitude ratio at which transition to turbulence takes place is found to be much less than for buoyant flows adjacent to a wall. The effects of frequency and amplitude of the artificial disturbances were experimentally determined and the trends are found to be consistent with the results of small disturbance theory.

The principal new result is that positive thermal buoyancy destabilizes jet flow, and consequently calls into question earlier experimental studies wherein jet flows were observed by density differences. Another new result is the calculation. of amplitude-ratio contours for a non-buoyant jet and the quantitative description of jet stability in terms of these contours along paths of constant physical frequency. A comparison of the non-buoyant theory with experimental jets containing varying amounts of thermal buoyancy indicates that transition did not occur at a well-defined value of the amplitude ratio. Perhaps experiments with truly non-buoyant jets and/or more detailed buoyant calculations could explain this remaining question.

The steady two-dimensional problem of reflexion of an oblique partly dispersed plane shock wave from a plane wall is studied analytically. Viscosity, diffusion and heat conduction are neglected. The thermodynamic state of the gas is assumed to be determined by the instantaneous values of the specific entropy s, pressure p and a finite number of internal state variables. Results for the flow field behind the reflected shock are obtained by a perturbation method which is based on the assumption that the influence of relaxation is relatively weak.