Measurements have been made of the mean and fluctuating pressure distributions on long circular cylinders, having smooth and rough surfaces, at Reynolds numbers of 1·11 × 105 and 2·35 × 105 in both uniform and turbulent streams. The presence of free-stream turbulence a t these Reynolds numbers was found to suppress coherent vortex shedding on the smooth cylinder and give rise to a complex pressure field in which the mean pressure distribution was almost independent of Reynolds number over the small range of Reynolds numbers tested. The pressure distributions on the rough cylinder were found to be completely different in uniform and turbulent streams; the presence of turbulence gave rise to an increase in the level of vortex shedding energy, and produced mean pressure distributions similar to those obtained on smooth cylinders at Reynolds numbers of the order of 107.

Experiments have been carried out to examine the spectrum of internal gravity waves excited in a stratified incompressible fluid during stabilization following the buoyant rise of a miscible fluid. The rise time of the buoyant fluid to its stabilization height in the stratified fluid was observed to be about 0.85 of the Brunt-Väisälä period for the stratified fluid. The motion of specific fluid elements in the wave field was observed using neutrally buoyant marker particles, and the particle trajectories were found to be in close accord with theoretical predictions. Observations on the internal waves generated by the forced oscillation of a spherical body suspended in the stratified medium showed the wave pattern to be well behaved and similar to that described by Mowbray & Rarity. However, the gravity wave field generated by the motion of the buoyant fluid was observed to be inhomogeneous and transient in nature. Wave periods from one to four times the Brunt-Väisälä period were clearly observed and at later times it appeared that the motion tended towards vertical oscillations a t the Brunt- Väisälä frequency.

An infinitely long circular cylinder is fixed with its generators horizontal so that it is half-immersed, with its axis lying in the free surface of water. A regular train of water waves is incident on the cylinder from an arbitrary horizontal direction, and is partly reflected and partly transmitted under the cylinder. In the present paper we are concerned with the vertical component of the wave acting on the cylinder. It is assumed that the fluid is inviscid, that the fluid motion is irrotational, and that the depth of water is infinite. The equations of motion are linearized, and surface tension is neglected.

We shall find it convenient to use the fact that the required vertical force component can be inferred from the solution of a related problem, which we shall call the generalized heaving problem. In this latter problem a certain normal velocity is prescribed on the cylinder so that water waves which travel obliquely outwards are generated. There are no waves incident from infinity. When the prescribed velocity has the same phase everywhere on the cylinder the waves travel normally outwards, and in this case the generalized heaving problem reduces to the ordinary heaving problem, on which much information is already available. The generalized problem is solved here by a method which is a generalization of the known method (Ursell 1949) for ordinary heaving (when the wave crests are parallel to the cylinder axis). Generalized-added-mass coefficients and generalized-wave-making parameters for generalized heaving are computed for a range of wavenumbers and angles of travel, and are extended to larger wave-numbers by means of asymptotic analysis. Reciprocity relations (the Haskind relations) are then used to obtain the vertical force component in the original transmission problem from the wave-making parameters of the generalized heaving problem.

If the air in a resonance tube half-filled with water is driven at an acoustic resonant frequency, surface waves of much lower frequency may also be excited. Experiments on this phenomenon are reported and compared with the theory of spatial resonance.

Experimental investigations of the heat transfer by combined free and forced convection to water in a horizontal tube with a uniform heat flux have revealed many interesting features of the transition from laminar to turbulent flow. Fluctuations in fluid temperature and overall pressure drop variations facilitated the study of the transition regime.

The first phase of the experiments studied the extreme cases of combined forced- and free-convection transition regimes. For forced convection without heat transfer (isothermal flow) the results compared well with the existing data, predicting a transitional Reynolds number of about 2300. For free convection with no flow, the records of temperature fluctuations during transient heating indicated the transition regime.

In the second phase, extensive measurements were made for the combined forced- and free-convection case. A plot of the Reynolds number against the Rayleigh number Rag enabled the present results (L/D = 150) to be compared with those of Petukhov & Polyakov (for X/D ratios 40 and 100).X = length from the start of flow; L = effective length of heated test section; D = inner diameter of tube. The results show that beyond transition two types of turbulence - hydrodynamic and thermal- can be distinguished depending on whether the fluctuations are pre- dominantly in velocity or in temperature. For large vaIues of Re and Ruq, these two regions merge into turbulent, combined free and forced convection.

In the transition regime two types of flow are encountered: unstable flow characterized by pulses and a stable flow with stable fluctuations. While a curve in the plot of heat input vs. flow velocity demarcates the two regimes, the main features of transition are described by means of an intermittency factor defined as the ratio of thermal fluctuation at any point to a corresponding magnitude of thermal fluctuation on the demarcating curve.

The iso-intermittency lines drawn in the transition envelope assist in describing the structure of transition. The concentration of these lines at the central area of the envelope indicates the region of maximum coupling between thermal and hydrodynamic effects.

A qualitative study of inlet turbulence confirmed the prediction of Mori et al. for air. The results presented here along with those of Mori et al. and Petukhov & Polyakov indicate that thermally induced secondary flows attenuate the fluctuations in low inlet turbulence flows, while they restabilize the flow as the inlet turbulence is increased. Also, the effect of inlet turbulence on transition to an unstable flow regime was studied. In general, an increase in the inlet turbulence brought about an increase in the critical Rayleigh number.

The paper describes a hydrodynamic stability analysis of the flow in an alluvial channel in which dunes have developed along the bed. The purpose is to develop a mathematical model describing the three-dimensional flow leading to instability of an originally straight channel. The model offers an explanation of the fact that some channels tend to meander, others to braid.

The pattern and propagation of hydromagnetic Rossby waves excited by travelling forcing effects on a rotating spherical shell of incompressible, inviscid, perfectly conducting fluid are studied using Lighthill's technique. The basic magnetic field H0, is assumed to be uniform and acting in the ‘beta-plane’ in an arbitrary direction. The two situations when the forcing effects travel along and perpendicular to H0, are considered.

The steady forcing effects travelling in the direction of an eastward or west-ward H0, excite two types of wave systems. The first consists of uiiattenuated signals directly behind or ahead of the forcing effect. The other system consists of semicircular waves travelling in all directions or waves travelling in a limited wedge.

When the forcing effect moves eastward, perpendicular to an H0, acting northward, the waves excited in the steady case are confined to certain wedges and trail behind with cusp-shaped wave crests. The magnetic field increases the semi-angle of the wedges, so that the region of disturbance is expanded. An oscillatory forcing effect generates various systems of waves. If the frequency of oscillation exceeds a certain critical frequency, excitement of waves in all directions is possible. The situation with a westward-moving forcing effect is also discussed. The effect of large rotation is to reduce the length of the waves.

An inviscid model of two-dimensional vortex shedding behind a square-based section is developed. The model uses a discrete-vortex approximation for the free shear layers. The motion of the shear layers is computed from the velocities of the discrete vortices, which in turn are derived through a Schwartz-Christoffel transformation of the section. The flow round the body is impulsively started from rest and initially develops symmetrically. The introduction of a small asymmetric disturbance results in asymmetric interaction of the shear layers amplifying into steady vortex-shedding motion.

The model is shown to predict the form of vortex shedding, the Strouhal number and some other flow quantities to a good degree of agreement with experimental results.

Finite amplitude, impulsively started spin-up and spin-down is analysed for axially symmetric flow of a viscous, incompressible, electrically conducting fluid confined between infinite, flat, parallel, insulating boundaries. A uniform axial magnetic field is present in the initial state, but is subsequently distorted by fluid motions. The method of matched asymptotic expansions reduces the problem to a first-order, ordinary, nonlinear, integro-differential equation for the transient development of the interior angular velocity on the time scale of spin- up, as driven by quasi-steady nonlinear Ekman-Hartmann boundary layers. This two-parameter equation is solved analytically in certain limits and numeric-ally in general. The solutions show that nonlinear non-magnetic spin-up and spin-down take longer than for linearized flow, spin-down occurring more rapidly in the early stages but requiring more time for completion than spin-up. A magnetic field promotes both spin-up and spin-down, but a weak field is relatively ineffective for spin-down yet very effective for spin-up. A strong magnetic field dominates nonlinear processes and gives identical spin-up and spin-down times, which coincide with that found from linear hydromagnetic theory.

Howard's technique for examining the stability characteristics of a two-dimensional, inviscid, heterogeneous shear flow in the vicinity of a neutral curve is considered. Examples are presented for which erroneous conclusions would be obtained by a direct interpretation of the results of this technique. Examples for which instability would be deduced for a stable region; an example for which stability would be deduced for an unstable region; and an example for which the technique breaks down altogether are discussed.

The last example is plane Couette flow between two rigid walls, which is shown to be destabilized by the addition of stable stratification. This example thus proves that the existence of a relative extremum in the basic vorticityprofile is not a necessary condition for the instability of an inviscid, heterogeneous shear flow.

It has been conjectured for many years that plane Couette flow is stable to infinitesimal disturbances although this has never been proved. In this paper we use a, combination of asymptotic analysis and numerical computation to examine the associated Orr-Sommerfeld differential problem in a systematic manner. We obtain new evidence that the conjecture is, in all probability, correct. In particular we find that, at a fixed large value of the Reynolds number R, as in an experiment, if a disturbance of wavenumber α has a damping rate - αci then – ci has a minimum value of order R−½ when α is of order R½. We believe that this result may be an essential prerequisite to an understanding of the stability of plane Couette flow to finite-amplitude disturbances.

Davies-Jones & Gilman (1971) reported in this Journal on a linear stability analysis and second-order initial-tendency calculation for thermal convection in a thin rotating annulus heated uniformly from below. The present work gives extensive numerical calculations for an annulus model with realistic laboratory boundary conditions which extends the previous work into the finite amplitude range. The model allows the mode with the longitudinal wavenumber predicted to occur at the onset of instability to grow to a finite amplitude and induce secondary axisymmetric differential rotation and meridional circulation through its Reynolds and thermal stresses, these circulations in turn modifying the forcing cells. No higher harmonics are allowed. The Boussinesq equations for the fundamental mode and secondary circulations are solved on a staggered finite-difference grid in the annulus cross-section, mostly following the scheme laid out by Williams (1969).

Stationary convection is studied for Taylor numbers T < 3 × 103. The profile predicted for the mean circulations in the earlier analysis, that of fast rotation in the outer half, slow rotation in the inner half of the annulus (except at very high Prandtl number), together with a four-celled meridional circulation, is confirmed. For a given Taylor number T, the differential-rotation energy peaks relative to the cell energy at a modest Prandtl number P somewhat less than unity, and its production is driven mostly by the Reynolds stresses in the cells. Meridional circulation is driven by potential-energy conversion at high P and by Reynolds stresses at low P, but retains the same form for all P with increased amplitude relative to the cells at low P. For Rayleigh numbers R a given percentage above the critical value Rc the differential-rotation energy increases like T, while the meridional circulation remains nearly constant. For given P and T differential-rotation relative energy peaks at modest R/R, while the meridional circulation continues to increase. The induced differential rotation tends to distort the cell boundaries from tilted straight lines produced by Coriolis forces into S shapes qualitatively like the profile of differential rotation itself.

One example of nonlinear overstable convection is given. The induced differential rotation has time-independent and oscillatory parts. The redistribution of momentum is carried out by periodically reversing horizontal and vertical Reynolds stresses.

The diffraction of a Kelvin wave by a transverse (to a straight coastline) discontinuity in depth is considered. A Fourier-integral formulation leads to a singular integral equation that may be solved exactly; however, the integrals in this solution are intractable without further approximation. An expansion to third order in a depth-change parameter yields results that are generally adequate for tidal problems (such as that posed by the Mendocino fracture zone) but are inadequate for the double-Kelvin-wave regime. Approximations are developed for a continuous change of depth that is either small or gradual, and the diffracted Kelvin wave along the coastline is found to have an amplitude that is inversely proportional to the square root of the depth and a phase that is given by the integral of the wavenumber.