It is shown how a simple property of the spherical vortex model can be used to investigate the dynamics of a buoyant, expanding thermal. No details of the vortex motion are required, only the fact that the flow round the buoyant region is potential. The main result is a demonstration that there is a relation between the two constants C and α arising in the dimensional analysis (where in the usual notation w = C (Δr) ½) and r = αz), which have up till now been measured separately and treated as independent. The analysis has been extended to spheroidal thermals by calculating the virtual mass for the appropriate outline, and it has also been generalized to include thermals in which the total buoyancy is increasing with time.

Using these risults, and an earlier experimental verification that the mean angles of spread are nearly the same under various conditions of stability, it is suggested that the whole of the mean behaviour of a thermal can be calculated in two nearly independent steps. first, the density difference or Δ as a function of height may be calculated using purely kinematic equations of conservation. Secondly, the velocity is obtained from the local values of Δ and radius r, using a mean value of C, since this has now also been shown to vary little over a wide range of conditions.

A solution is obtained for steady, moderately sheared, three-dimensional flow past a wire grid of arbitrary resistance distribution which is placed normal to the axis of a duct of arbitrary but constant cross-section. The formulation presented is an extension of those given by Owen & Zienkiewicz (1957) and Elder (1959) for weakly shared, two-dimensional flow past wire grids. Unlike these earlier formulations, however, in the present study the equations of motion are solved without placing restrictions on the magnitude of variation of resistance across the grid. The resulting solution, taking account of streamline deflexions, is verified experimentally for moderately sheared flow past three grids constructed to produce three widely differing velocity distributions in a water tunnel of circular cross-section.

In this paper the equations for Alfvén waves are examined and conditions necessary for the occurrence of resonance are determined. An experiment using liquid sodium inside a torus is described. Waves were generated by means of alternating current supplied to a coil around the torus. A strong resonance was observed at the fundamental frequency, and a weak resonance at three times this frequency. At the fundamental resonance the alternating magnetic field attained magnitudes more than 9 times the magnitude of the field that would have been generated in free space by the exciting current. The results were in good agreement with prediction.

The stability of viscous flow between rotating cylinders with an axial flow has been investigated theoretically by Goldstein (1937), Chandrasekhar (1960, 1962), and Di Prima (1960); and experimentally by Cornish (1933), Fage (1938), Kaye & Elgar (1957), Donnelly & Fultz (1960) and Snyder (1962a). As was pointed out by Di Prima (1960) there were a number of discrepancies in the early work of the 1930's which were clarified in part by the papers of the 1960's. In turn, there appear to be certain small detailed differences in the more recent papers. In part it is these differences with which the present paper is concerned. In addition, the results of the previous theoretical investigations which are limited to the case in which the cylinders rotate in the same direction, are extended to the case of counter rotation.

Using identical equipment, an attempt was made to reproduce the unexpected flow reversals obtained by Sibulkin (1962) in his study of the vortex motion associated with draining a liquid from a vessel through an orifice in its bottom. Reversal of the initial direction of rotation was found only for counter-clockwise filling with large initial heads and settling times, unless during settling or draining of the vessel a shock was applied to the system, in which case the tendency to reversal was generally more pronounced with clockwise filling. Re-reversal of the motion was also observed in a number of cases. An alternative explanation is proposed, based on a consideration of the surface waves generated by a shock.

The Rayleigh stability equation of inviscid linearized stability theory was integrated numerically for amplified disturbances of the hyperbolic-tangent velocity profile. The evaluation of the eigenvalues and eigenfunctions is followed by a discussion of the streamline pattern of the disturbed flow. Here no qualitative distinction is found between an amplified and the neutral disturbance. But considering the vorticity distribution of the disturbed flow it is shown that in the case of amplified disturbances two concentrations of vorticity occur within a disturbance wavelength, while in the neutral case only one maximum of vorticity exists. The results are discussed with respect to the instability mechanism of free boundary-layer flow.

Further consideration is given to the stability of the flow of an idealized elasticoviscous liquid contained in the narrow channel between two rotating coaxial cylinders. The work of Part 1 (Thomas & Walters 1964) is extended to include highly elastic liquids. To facilitate this, use is made of the orthogonal functions used by Reid (1958) in his discussion of the associated Dean-type stability problem. It is shown that the critical Taylor number Tc decreases steadily as the amount of elasticity in the liquid increases, until a transition is reached after which the roots of the determinantal equation which determines the Taylor number T as a function of the wave-number ε become complex. It is concluded that the principle of exchange of stabilities may not hold for highly elastic liquids.

The problem of small angle depressions in a liquid surface due to an impinging two-dimensional potential jet is considered. Using conformal mapping methods and finite Hilbert transforms, the problem is formulated as a non-linear singular integral equation. The integral equation is approximated by a set of non-linear algebraic equations which are solved numerically by a method of repeated linear corrections. In addition, an asymptotic solution (for low jet velocity) is derived.

From the numerical solutions of the integral equation, the liquid-surface profiles and the free streamlines of the jet are calculated for four cases. These results verify the appearance of lips on the liquid surface which have been observed experimentally by others.

The travelling-wave plasma converter is analyzed allowing for the compressible nature of the fluid. The study is restricted to conditions for which the magnetic Reynolds number is small. Steady and time-varying flow conditions are investigated using small perturbation theory. Relations for optimum conversion effectiveness are established and the effects of variable electrical conductivity are investigated. Conditions for electromechanical resonance are derived and it is shown that the conversion process introduces a damping effect.

The flow in the noise-producing region of a circular jet is found to be dominated by a group of large eddies, containing nearly a quarter of the turbulent shear stress in the quasi-plane region of the shear layer: their contribution to the shear stress decreases as the effects of axisymmetry become noticeable at more than about two diameters downstream of the nozzle. These large eddies appear to be almost entirely responsible for the irrotational fluctuations near the nozzle, which, for this and other reasons, are larger relative to the reference dynamic pressure than in other shear flows. As a consequence of this, the convection velocity near the high- and low-velocity edges of the flow is biased towards the mean velocity in the high-intensity region. The dominance of the large eddies therefore explains the measurements of near-field pressure fluctuations by Franklin & Foxwell (1958), and of convection velocity by Davies, Barratt & Fisher (1963) and the present authors. The strength of these large eddies, compared with those in the boundary layer or wake, is remarkable.

The large eddies appear to be mixing-jets similar to those found by Grant (1958) in the wake, but with their projection in the (y, z)-plane inclined at about 45° to the y (radial) axis instead of lying along the y-axis as in the wake.

It is suggested that the augmentation of these large eddies by artificial means could be used to increase the mixing rate and permit the reduction of jet noise by means of acceptably short ejector shrouds.

The medium-scale motion is found to be far from isotropic in scales, although the two scales associated with a given vorticity component are more nearly equal. This phenomenon is also noticeable in the wake.

It is found that the departure from self-preservation, which starts when the shear layer thickness is no longer small compared with the nozzle radius, does not grossly affect the region of high turbulence intensity and maximum noise production until this region itself is no longer small compared with the radius. The maximum shear stress seven diameters downstream of the exit is still 70% of its value near the exit, and the non-dimensional mean velocity gradient is practically unchanged.

Under the assumption that the local acceleration and inertial terms are to be neglected in the equation of motion, a comparison is made between the unsteadystate movement of a suspension of particles and the same problem in reversed (or negative) time. The formalized discussion confirms Bretherton's (1962) conclusion that, if in a steady unidirectional shear flow at small Reynolds number a rotationally symmetric particle twice assumes a position with its axis of rotation in the plane perpendicular to the flow, its orbit must be periodic. The reversibility phenomena observed by S. G. Mason (1963) in dilute and concentrated suspensions are explained as well.

Let D0 be the Stokes drag on an axially symmetric body moving parallel to its axis with velocity U0 through an unbounded fluid. The drag D experienced by the same body oscillating with velocity U = U0eiσt along its axis in the unbounded fluid is given by the expression $\frac{D}{D_0} = \left \{{1 +{\frac {d_0}{6 \surd{(2)} \pi \mu a U_0}}(1+i)M+O(M^2)}\right \}e^{i \sigma t},$ where a is any characteristic particle dimension and $M^2 = a^2 \sigma \rho |\mu$ is a dimensionaless number. The part of this drag formula which gives the energy dissipation is calculated for bodies of various shapes.