The vorticity transport equation is solved for radial incompressible flow between disks by a finite-difference method with discretization based on the method of Allen & Southwell. The solution permits detailed characterization of the flow for the Reynolds number range investigated, 1 ≤ Re ≤ 300. Above Re = 60 separation is observed with the bubble size increasing rapidly with Re. The streamwise and transverse pressure and velocity gradients are examined to interpret the observed phenomena.

Experiments on the interaction between solitary shallow-water waves propagating in the same direction have been performed in a rectangular channel. Two methods were devised to compensate for the dissipation of the waves in order to compare results with Hirota's (1971) solution for the collision of solitons described by the Kortewegde Vries equation. Both qualitative and quantitative agreement with theory is obtained using the proposed corrections for wave damping.

The structure of the Stewartson E¼-layer (E being the Ekman number) in a compressible gas contained in a rapidly rotating cylinder is investigated for the case in which the end plates of the cylinder are thermally insulated. It was found by Matsuda & Hashimoto (1976) that the E¼-layer could not have a relevant structure in the ordinary configuration in which the E¼-layer meets the end plates through its Ekman extension of thickness E½. In this paper the E¼ × E¼ square region, in addition to the Ekman extension, is considered. The heat generation due to the radial fluid motions in the Ekman extension causes the temperature fields in the E¼ × E¼ square region through which heat is conducted to the side wall of the cylinder. Numerical calculations were made to obtain the temperature fields, which are shown in several figures.

The Stewartson E½- and E¼-layers in a rapidly rotating compressible fluid are considered within the framework of linearized equations and the boundary-layer method. The fluid is contained in a cylinder made of a thermally insulated side wall and conducting top and bottom end plates. The end plates and the side wall rotate with slightly different angular velocities. The case of an incompressible fluid was discussed by Stewartson, who found that the flow is restricted to the side-wall boundary layers. In the case of a compressible fluid, however, the solutions are strongly dependent upon the thermal boundary conditions assumed on the side wall. In particular, if the wall is insulated the fluid in the inner core is dragged along too since it is coupled strongly to the flow in the side-wall Stewartson layers. The critical parameter governing the solutions is found to be $(\gamma -1) PrG_0 E^{-\frac{1}{3}}/4\gamma$, where γ is the ratio of specific heats, Pr the Prandtl number, G0 the square of the rotational Mach number and E the Ekman number.

This paper contains a simple and entirely conventional application of lifting-line theory to a close-hauled, high aspect ratio sail, set upright on a flat water surface. In seeking an optimum spanwise loading distribution however, an unconventional criterion is used, which leads to an unexpected result.

By seeking to maximize the forward thrust for a given rolling moment, rather than maximizing the lift-drag ratio, an optimum loading distribution is obtained which departs dramatically from elliptic loading. It offers the prospect of a significant improvement in extreme yacht performance if the associated mechanical and control problems can ever be solved.

The equations for the viscous flow between two coaxial infinite disks, one stationary and the other rotating, are solved numerically. The effects of applying a uniform suction through the rotating disk are determined. Initially, the fluid and disks are at rest. The angular velocity of one disk and the amount of suction through it are gradually increased to specific values and then held constant. At large Reynolds numbers R, the equilibrium flow approaches an asymptotic state in which thin boundary layers exist near both disks and an interior core rotates with nearly constant angular velocity. We present graphs of the equilibrium flow functions for R = 104 and various values of the suction parameter a (0 ≤ a ≤ 2). When a = 0, the core rotation rate ωc is 0·3131 times that of the disk. Fluid near the rotating disk is thrown centrifugally outwards. As a increases, ωc increases and the centrifugal outflow decreases. When a > 1·3494, the core rotation rate exceeds that of the disk and the radial flow near the rotating disk is directed inwards. We also present accurate tabular results for two flows of special interest: (i) the flow between a stationary and a rotating disk with no suction (a = 0) and (ii) Bödewadt flow. The latter can be obtained by suitable scaling of the boundary-layer solution near the stationary disk for any a ≥ 0. Since several solutions to the steady-state equations of motion have been reported, the question arises as to whether other solutions to the time-dependent equations of motion with zero initial conditions can be found. We exhibit a rotational start-up scheme which leads to an equilibrium solution in which the interior fluid rotates in a direction opposite to that of the disk.

An experimental investigation was carried out of the development of steady, laminar, incompressible flow of a Newtonian fluid in the entry region of a curved pipe for the entry condition of uniform motion. Two semicircular pipes of radius ratios 1/20 and 1/7 were investigated, covering a Dean number range from 138 to 679. The axial velocity and the component of secondary velocity parallel to the plane of curvature of the pipe were measured using laser anemometry. It was observed that, in the upstream region where the boundary layers are thin compared with the pipe radius, the axial velocity within the irrotational core first develops to form a vortex-like flow. In the downstream region, characterized by viscous layers of thickness comparable with the pipe radius, there appears to be three-dimensional separation at the inner wall. There is also an indication of an additional vortex structure embedded within the Dean-type secondary motion. The experimental axial velocity profiles are compared with those constructed from the theoretical analyses of Singh and Yao & Berger. The quantitative agreement between theory and experiment is found to be poor; however, some of the features observed in the experiment are in qualitative agreement with the theoretical solution of Yao & Berger.

The steady supersonic flow of a vibrationally relaxing gas past a cone is studied using numerical methods. Near the tip of the cone the flow is obtained by means of a coordinate expansion and built on to this is a characteristic network used to obtain the remainder of the flow. Of particular interest is the development of the frozen shock at the tip into a relaxation-dominated wave at distances large compared with the width of the wave. The numerical results are presented in a concise similarity form which will permit accurate extrapolation to very weak waves in atmospheric air.

The response of surface gravity waves with profile ζ to forcing by the atmospheric pressure p(a) is studied. It is shown that not only the usually considered cross-spectrum 〈p(a)ζ〉 is responsible for wave growth. All higher-order spectra 〈p(a)ζ1,…,ζn〉 also lead to wave growth linear in ε = ρ(a)/ρ,ρ(a) and ρ being the density of air and water respectively. The bispectral contribution is investigated in detail and is calculated for three models of the bispectrum. The results indicate that bispectral contributions are not negligible and may account for typically 30-50%, and possibly more, of the usually considered cross-spectral contribution. The bispectral growth mechanism contains the fluctuating-stress mechanism discussed by Longuet-Higgins (1969) as a special case. As a byproduct new information on the symmetry properties of the hydrodynamic coupling off the dispersion shell is obtained.

Measurements of the statistical property called the ‘rescaled range’ in grid-generated turbulence exhibit a Hurst coefficient H = 0·5 for 43 < UT/M < 1850, where M/U is a characteristic time scale associated with the grid size M and mean velocity U. Theory predicts that H = 0·5 for independence of two observations separated by a time interval T, and the deviation from H = 0·5 is referred to as the ‘Hurst phenomenon’. The rescaled range obtained for grid turbulence contains an initial region UT/M < 43 of large H, approaching 1·0, corresponding approximately to the usual region of a finite non-zero autocorrelation of turbulent velocity fluctuations. For UT/M > 1850 the rescaled range breaks from H = 0·5 and rises at a significantly faster rate, H = 0·7-0·8, implying a long-term dependence or possibly non-stationarity at long times. The measured autocorrelations remain indistinguishable from zero for UT/M > 20. The break in the trend H = 0·5 is probably caused by motions on scales comparable to characteristic time scales of the wind-tunnel circulation. Rescaled-range analysis is a powerful statistical tool for determining the time scale separating the grid turbulence from the background wind-tunnel motions.

It is well known that the vortices shed from a circular cylinder lock on in frequency to the vibrations when the cylinder is forced to vibrate or is naturally excited to sufficient amplitudes by flow-induced forces. This paper presents a model for a universal wake Strouhal number, valid in the subcritical range of Reynolds numbers, for both forced and vortex-excited oscillations in the locking-on regime. The Strouhal numbers thus obtained are constant at St* = 0·178 over the range of wake Reynolds numbers Re* = 700-5 × 104. This value is in good agreement with the results obtained by Roshko (1954a) and Bearman (1967) for stationary circular cylinders and other bluff bodies in the same range of Reynolds numbers. A correspondence between the amplification of the cylinder base pressure, drag and vortex circulation is demonstrated over a wide range of frequencies and for vibration amplitudes up to a full cylinder diameter (peak to peak). The fraction ε of the shed vorticity in the individual vortices is found to be dependent upon the base-pressure parameter K = (1 − Cpb)½. Consequently, ε is also a function of the amplitude and frequency of the vibrations in the locking-on regime.