A critical review is given of theories dealing with viscous effects in shock tubes for cases in which the boundary layer is thin compared with the diameter. In particular an examination of the radial variation of flow quantities is used to show that the approach of Mirels (1957) is based on firmer ground than that of Trimpi & Cohen (1955). It is also shown that the small perturbation theories of these and other authors lead to an equation for running time identical in form to that derived by Roshko (1960) from an asymptotic analysis of boundarylayer leakage through the interface.

The flow of an incompressible elastico-viscous fluid between two parallel, infinite disks is investigated when one disk is held at rest and the other performs rotary oscillations about their common axis. It is found that the purely periodic primary motion has associated with it a secondary steady velocity distribution, as well as a secondary periodic motion with twice the frequency of the primary. The steady component of the secondary flow is discussed in detail.

A remarkably stable type of revolving hollow water jet was generated in a vertical pipe, fixed in the base of a large tank, by first establishing Borda free flow, in which the jet springs clear of the pipe wall. Swirl was then imparted to the oncoming water, and an air core formed in the jet which was of varicose shape with alternate swellings and contractions of both its inner and outer surfaces. The observed wavelengths are compared with the theory, in which inertia and surface tension but not viscosity and gravity are taken into account.

Experiments are described in which a spinning tube was initially filled with water and closed at both ends; when the water had acquired uniform angular velocity the tube was suddenly opened at one end and hence emptied by centrifugal action, so that a cavity progressed along it towards the far end. The velocity of the cavity was found to be steady and proportional to the speed of rotation over the range tested, which confirmed the supposition that gravity and viscosity had insignificant effects on the cavity motion. Contrary to expectation, since the cavity velocity seemed to be too large for it to occur, the ‘Taylor phenomenon’ was observed in the liquid ahead of the cavity; that is, the motion generated by the invasion of the cavity extended over a continually lengthening region beyond it.

The theoretical discussion in § 4 explains several features of the experiments satisfactorily, although the complete analytical problem has so far proved insoluble.

A dispersion relation is set up for transverse waves in a plasma with an ellipsoidal velocity distribution. It is shown that the most unstable wave has its wavenormal parallel to the shortest axis of the ellipsoid and its vector potential parallel or anti-parallel to the longest axis. The maximum possible amplification rate is then calculated. Ellipsoidal velocity distributions arise in any flow with an anisotropic pressure tensor. If the resulting instability leads to a microscopic redistribution of particle velocities, then the effective transport coefficients of the plasma are changed. In Particular it is shown that the effective viscosity is decreased, and becomes dependent on the local gradient of the macroscopic velocity.

This paper concerns an investigation of turbulence in the density stratified shear flow of a specially designed wind tunnel in which the density gradient is created by differential heating of the air. The first three sections of the paper consist of a description of the apparatus and of the mean temperature and velocity gradients in the tunnel, together with a discussion of a method of measuring low wind speeds based on the periodic shedding of vortices by a circular cylinder. In the remaining sections details of the experimentally determined structure of the turbulence of the flow and of its eddy conductivity and viscosity are presented and their dependence on the over-all gradient form of Richardson number, $[g \partial T | \partial z]|[T(\partial U| \partial z)^2]$, considered.

In this paper flow-visualization techniques are used to study the flow instability which occurs at the orifice in the free convection open thermosyphon. The influence of the shape of the orifice on the measured heat transfer of the system is also studied under both laminar and turbulent conditions. The dominant mode of penetration of the hot stream by the cold fluid entering at the base of the reservoir is found to instigate a mixing region at the orifice. In turbulent flow this spreads into and eventually fills the tube as the Rayleigh number is increased. In such circumstances a sharp-edged orifice appears to give better overall heat transfer than a rounded orifice.

The viscometer investigations of Donnelly & Ozima (1962) on the stability of flow between rotating cylinders in the presence of a magnetic field have been extended by making careful torque measurements in the subcritical range using improved mercury. The results show that a small difference in stability can be observed with conducting cylinders as compared with insulating cylinders. The results also suggest that a heretofore unnoticed instability begins well before the instability studied earlier. This relatively weak instability accounts for some of the anomalous effective viscosity observed by Donnelly & Ozima.

The uniqueness condition that was utilized by the author (Concus 1962) is considered. The condition, which excludes certain fluid depths, is shown to be physically unacceptable because it is essentially impossible to satisfy in practice. The resulting in validation of the perturbation method is discussed, and a revision is presented, which invokes the presence of viscosity and allows retention of the previously obtained solutions. The revision may also be applied to the work of other authors who utilized the same method to solve other standing-wave problems.

Large-amplitude atmospheric flows past mountain ridges are investigated. The flows are assumed to be steady and two-dimensional. Diffusive and viscous effects are neglected but static compressibility is taken into account.

The larger part of the investigation is devoted to the study of waves in the lee of mountain ridges. The major contribution consists in the treatment of the large-amplitude motion. The flows are governed by an equation which turns out to be linear for certain upstream conditions. These conditions impose some restrictions on the wind profile and stratification of the entropy and specific energy far upstream. However, flow patterns representing realistic upstream conditions have been obtained.

A comparison between a compressible flow and an incompressible flow with equivalent upstream conditions is included.

The position of the region of transition to turbulence and the manner in which turbulence develops are investigated using a hot-wire anemometer to study the character of the flow in the wake of a circular cylinder. In the range of Reynolds numbers greater than 200 in which turbulent motion is developed, the region of transition to turbulence moves towards the cylinder with increasing Reynolds number. The manner of transition to turbulence appears to undergo a basic change as the region of transition moves from the periodic wake into the region of flow immediately behind the cylinder where the separated layers have not rolled into vortices, that is, as the Reynolds number increases from Roshko's transition range to his irregular range. When transition occurs in the periodic wake it is a result of distortion due to large-scale three-dimensional effects. Turbulence, when it develops in the separated layers, is preceded by two-dimensional Tollmien-Schlichting waves which eventually degenerate to turbulence by the action of small-scale three-dimensionalities.

A body floting on the free surface of water is given a small vertical displacement from its equilibrium position and is then held fixed. When the fluid has again come to rest the body is released. The subsequent damped motion is investigated when viscosity and surface tension are neglected and the equations of motion are linearized. The method applies to bodies of arbitrary shape in two or three dimensions, and is described in detail here for the heaving motion of a horizontal half-immersed circular cylinder of radius a.

The forced periodic motion of such a cylinder has been studied in earlier papers. In particular, the hydrodynamic forces exerted by the fluid on the body can be described by a dimensionless coefficient, $\Lambda(\omega (a|g)^{\frac{1}{2}})$, where ω is the (real) angular frequency. The function ∧ can be found by convergent infinite processes, but not explicitly, and the difficulties of the problem are due to this. The free motion of the cylinder is solved in the present paper by Fourier methods. The motion is regarded as the superposition of simple harmonic motions, and the displacement y(t) is thus obtained in the form of a Fourier integral $y_0(\tau (a|g)^{\frac{1}{2}})= -{\frac {1}{8}}iy_0(0) \int ^\infty_{-\infty}{\frac {u(1+ \Lambda (u))\; e^{-iu \tau }du} {1- \frac{1}{4}\pi u^2(1+ \Lambda(u))}}.$

It is seen that the integrand involves the force coefficient ∧ and is thus not strictly an explicit expression. The asymptotic behaviour for large times can be found explicitly when the depth is infinite: $y_0(t) \sim -\frac{4}{\pi}y_0(0) {\frac {a}{gt^2}}.$

A damped harmonic behaviour had been expected. The slow monotonic decay occurs because the function $\Lambda (\omega(a|g)^{\frac {1}{2}})$, when continued into the complex ω-plane, can be shown to be many-valued near ω = 0. No physical interpretation has yet been found for this property. The free motion of a cylinder set in motion by an applied force is also treated, with similar results.

Reasons are given why there are no rapidly oscillatory terms in the asymptotic expression. For finite constant depth the function $\Lambda (\omega(a|g)^{\frac {1}{2}})$ is single-valued near ω = 0, and the asymptotic expression for this case is not yet known.