The field radiated by an acoustic monopole in the presence of an infinite membrane, or plate, is studied, with emphasis on the case when fluid loading effects are small and when a free wave in the surface has supersonic phase speed relative to the fluid. Coupling between fluid and surface is then specified by a Mach angle θM and by a fluid loading parameter ε, with ε [Lt ] 1. Asymptotic expressions for the field are derived which are uniform in the observation angle θ, measured from the surface. Previous descriptions have suggested the formation of a strong two-dimensional beaming effect along the surface of the Mach cone θ = θM. Here it is shown that this effect is a spurious consequence of nonuniform asymptotics. A beam is indeed formed, and persists without attenuation or distortion to large distances k0R ∼ ε−2. However, the beam amplitude is small compared with that of the three-dimensional reflected field, while at distances k0R [Gt ] ε−2 only the reflected wave survives. Some interesting features of the reflexion coefficient and of the field near to the membrane are also discussed. In particular, it is shown that the pressure field generated by a subsonic surface wave is also confined to a conical zone, the transition across the generators of the cone being described by Fresnel functions of a familiar kind.

Two-dimensional frequency-wave-number spectra [Fcy ](kx, ω) and [Fcy ](kz, ω) of the longitudinal velocity component are presented for the sublayer in fully developed turbulent pipe flow, at Reynolds numbers between 10600 and 46400. All of these sublayer spectra apparently scale by introducing dimensionless quantities based on a chara cteristic length scale ν/UT and a characteristic time scale ν/UT2.

Representative convection velocities have been obtained from the [Fcy ](kx ω) spectra. The characteristic convection velocity in the sublayer is independent of wave-number and is the same at all positions in the layer cx ≃ 8·0UT. This result has led to the conclusion that sublayer turbulence is wave-like.

Existing visualization data seem to indicate that the sublayer waves are also relatively periodic at least at low values of Reynolds number. Characteristic dimensions of the sublayer waves are λ+x ≃ 630, and λz+ = 135. Results of the visualization studies of Fage & Townend (1932) and of Runstadler, Kline & Reynolds (1963) and Kline et al. (1967) do not appear to conflict with a wave model for the sublayer.

All of the existing measurements of the sublayer have been for relatively low Reynolds numbers. Some of the present results for positions just outside the sublayer suggest that at Reynolds numbers greater than 30000, the structure and properties will change substantially from those observed to date. In particular the streaky structure which is commonly regarded as being characteristic of the sublayer will probably not be detected at sufficiently high Reynolds numbers.

For a viscous incompressible fluid the low Reynolds number description of the flow generated by a three-dimensional point source of oscillating strength situated on a wall is approximately quasi-steady in the neighbourhood of the singularity. This quasi-steady solution contains a number of unacceptable features, the principal one being that it is not a uniformly valid approximation within a small region surrounding the source point. In addition to this the vorticity in this region is predicted to be zero everywhere on the wall except at the singular point where it is infinite, which does not seem to be a physically reasonable distribution. When account is taken of the finite radius of the hole through which the fluid is driven and the finite width of the wall, the above difficulties are resolved yielding results that are quite realistic and informative.

The suggestion made by the authors in a previous paper (Hurle & Jakeman 1969) that the Soret effect could give rise to overstable solutions of the thermosolutal Rayleigh–Jeffreys problem is investigated theoretically and experimentally.

Oscillatory instability is shown to occur in initially homogeneous layers of water-methanol mixtures when they are heated from below. This instability triggers a finite-amplitude steady mode. The magnitude and sign of the Soret coefficient was changed by varying the composition of the mixture; as predicted, overstable modes were observed when the sign of the coefficient was such as to produce a stabilizing contribution to the density gradient. The observed critical Rayleigh numbers and temporal frequencies are consistent with theory.

The transient process by which an incompressible dissipative rotating stratified fluid adjusts to a small change in the rotation rate of its container is examined theoretically. The aim is to clarify the effects of the imposed density stratification and of the boundary condition specified for the density perturbation on the behaviour of the fluid, particularly during the time span when the adjustment is performed in a homogeneous fluid. For a weakly stratified fluid in a cylinder, it is shown how these two factors govern the nature and intensity of boundary layers on the vertical wall which close the secondary meridional circulation generated by Ekman layers along the horizontal boundaries. For a more strongly stratified fluid, the usefulness and importance of potential vorticity conservation in determining the quasi-steady motion is verified, and a calculation for a spherical container demonstrates some new features that arise only when the container boundaries are not normal or parallel to the rotation axis. It is shown that experimental results of Holton (1965) are in less good agreement with predictions of the linear theory than had been previously indicated.

The flow in a two-dimensional laminar separation bubble is analyzed by means of finite-difference solutions to the Navier-Stokes equations for incompressible flow. The study was motivated by the need to analyze high-Reynolds-number flow fields having viscous regions in which the boundary-layer assumptions are questionable. The approach adopted in the present study is to analyze the flow in the immediate vicinity of the separation bubble using the Navier-Stokes equations. It is assumed that the resulting solutions can then be patched to the remainder of the flow field, which is analyzed using boundary-layer theory and inviscid-flow analysis. Some of the difficulties associated with patching the numerical solutions to the remainder of the flow field are discussed, and a suggestion for treating boundary conditions is made which would permit a separation bubble to be computed from the Navier-Stokes equations using boundary conditions from inviscid and boundary-layer solutions without accounting for interaction between individual flow regions. Numerical solutions are presented for separation bubbles having Reynolds numbers (based on momentum thickness) of the order of 50. In these numerical solutions, separation was found to occur without any evidence of the singular behaviour at separation found in solutions to the boundary-layer equations. The numerical solutions indicate that predictions of separation by boundary-layer theory are not reliable for this range of Reynolds number. The accuracy and validity of the numerical solutions are briefly examined. Included in this examination are comparisons between the Howarth solution of the boundary-layer equations for a linearly retarded freestream velocity and the corresponding numerical solutions of the Navier-Stokes equations for various Reynolds numbers.

An experimental investigation was conducted in a circular pipe to examine the influence of a transverse magnetic field on the structure of turbulent shear flow of a conducting fluid (mercury). In the present paper, part 1, mean velocity profiles, turbulence intensity profiles, velocity fluctuation spectra, axial pressure drop profiles, and skin friction data are presented which quantitatively exhibit the Hartmann effect and damping of the velocity fluctuations over a broad range of Reynolds numbers and magnetic fields. The results of heat transfer experiments will be reported by the authors in the following paper, part 2.

The conventional hot-wire static calibration procedure for the measurement of absolute turbulence intensities with constant-temperature hot-wire anemometers is investigated and serious errors are found. An alternative calibration procedure is developed which involves shaking the wire at low frequencies in a uniform flow. A series of tests indicate that this dynamic calibration method is more accurate and consistent than the conventional procedure.

A method for verifying various calibration procedures is demonstrated. This method involves the measurement of velocity perturbations in a series of Karman vortex streets. The velocity perturbation amplitude is held fixed, but the frequency varies from one vortex street to another. This method also acts as a direct check of the hot-wire system frequency response.

The linear hydrodynamic stability analysis of liquid pools heated from below combining surface tension and buoyancy effects as presented by Nield (1964) is confirmed by experiment for a series of silicone oils. The experimental method used is an adaptation of the Schmidt–Milverton technique, in which the stability limit is located by the change of slope in the plot of heat flux versus temperature drop across the liquid pool.

The effect of blowing through a porous rotating disk on the flow induced by this disk is studied. For strong blowing the flow is almost wholly inviscid. First-order viscous effects are encountered only in a thin layer at some distance from the disk. The results of an asymptotic analysis are compared with numerical integrations of the full equations and complete agreement is found.

Proudman (1956) and Stewartson (1966) analyzed the dynamical properties of a fluid occupying the space between two concentric rotating spheres when the angular velocities of the spheres are slightly different, in other words, when the motion relative to a reference frame rotating with one of the spheres is due to an imposed azimuthal velocity which is symmetric about the equator. The consequences of forcing motion across the equator are explored here. Whereas the flow inside the cylinder [Cscr ] circumscribing the inner sphere and having generators parallel to the axis of rotation is similar to that which results when the driving is symmetric, the flow outside [Cscr ] is quite different. The Ekman layer on the outer sphere persists outside [Cscr ] - its dynamics is modified in the vicinity of the equator - and is instrumental in transferring fluid from one hemisphere to the other. The divergence of this Ekman layer causes slow, axial motion in the inviscid region outside [Cscr ]. On [Cscr ], two shear layers of thickness O(R−2/7) and O(R−1/3) (where R is the Reynolds number, assumed large) remove discontinuities in the flow field and return fluid from one hemisphere to the other (rather than one Ekman layer to the other as is the case when the driving is azimuthal).

A comparison of laboratory experiments in a shallow-water tank driven by an oscillating piston and numerical solutions of the Korteweg-de Vries (KdV) equation show that the latter can accurately describe slightly dissipative wavepropagation for Ursell numbers (h1L2/h03) up to 800. This is an input-output experiment, where the initial condition for the KdV equation is obtained from upstream (station 1) data. At a downstream location, the number of crests and troughs and their phases (or relative locations within a period) agree quantitatively with numerical solutions. The crest-to-trough amplitudes disagree somewhat, as they are more sensitive to dissipative forces. This work firmly establishes the soliton concept as necessary for treating the propagation of shallow-water waves of moderate amplitude in a low-dissipation environment.