Adiabatic disturbances propagating as transverse waves in an inviscid fluid rotating as a Rankine vortex about the axis of its cylindrical container are considered. The propagation of the first mode of the first two harmonic waves has been investigated. Relative to a fixed co-ordinate system, for each harmonic, there are three waves. Two waves are rotating in the same direction as the fluid, one faster and the other slower than the core of the fluid, and one wave rotates in the opposite direction. The latter is stable and relative to the core of the rotating fluid it is the fastest wave. Relative to the container, the other two waves are speeded up by rotation. However, relative to the rotating core, the angular velocity of the fast wave decreases when the fluid is speeded up, and when it is zero the wave breaks down. As the region of potential flow decreases the angular velocity of the slow wave increases and its amplitude decreases, and in the limit of vanishing potential flow, the wave rotates as fast as the fluid and its amplitude tends to zero.

An analysis of a hydrostatic thrust bearing with electrically conducting compressible lubricant under an axial-current-induced pinch is presented. It is shown that the load capacity of the bearing can be increased by the pinch effect and the magnitude of the pinch effect depends on the mass flow rate. It is also shown that a load proportional to the square of the axial current can be sustained even when there is no flow or external pressurization.

Disintegration processes occurring with charged liquid jets of distilled water have been examined. High-speed photographic techniques were used to determine the effect of charging on disintegration of the jet, the size distribution of the drops formed, and the velocities of the drops. At relatively small currents, the jet remains undisplaced while the drops formed acquire components of velocity perpendicular to the jet axis. At sufficiently large currents, the jet develops kink or longitudinal instabilities which can cause the jet to be appreciably displaced, and the drops may have relatively large components of velocity perpendicular to the jet axis. The size distributions of the drops formed are significantly different from those resulting in the absence of electrification. Mean drop size decreases with increased charging in all cases. Drop speeds increase with increased charging as a result of both increased electrical repulsion and reduction in size.

The stability of non-Newtonian jets was investigated. A linearized stability analysis shows that a liquid column of a viscoelastic fluid exhibits more rapid growth of axisymmetric wave disturbances than a Newtonian fluid of the same zero shear viscosity. This result is independent of the form of constitutive equation chosen. Experiments in weakly elastic fluids confirm this expectation, whereas data on fluids with more pronounced elastic properties indicate that non-linear phenomena are dominating. The disturbances appear as a series of droplets connected by random lengths of threads, which thin with distance and eventually lead to jet breakup. Even in dilute viscoelastic solutions, jet breakup does not occur by the growth of clearly defined waves.

The stability and time-dependent deflexions of a thin flexible cylinder with zero bending rigidity set in a viscous stream are examined. The cylinder is fixed at one end and free at the other. Modal shapes are found based on solutions to linearized equations resulting from small deflexion assumptions; the dependence of cylinder motion upon the aerodynamic, elastic and physical size characteristics of the cylinder is exhibited. It is found that the cylinder motion is always unstable and that cylinder amplitude increases without bound as time is increased.

In the design of dielectrophoretic liquid orientation and expulsion systems for zero-gravity environments, maximum electromechanical effect of an imposed electric field is obtained by concentrating the field gradients in the neighbourhood of liquid interfaces. In typical configurations, the electric field gradient plays the role of an electromechanical wall, with a stiffness and inertia represented dynamically by electrohydrodynamic surface waves. As an orientation system rotates, the liquid motions are characterized by these waves as they couple to inertial bulk oscillations and centrifugal surface waves resulting from the rotation. A study is made of configurations typified by an equilibrium in which a circular cylindrical column of inviscid liquid undergoes rigid body rotation. The equilibrium is made possible, even though the cylindrical interface is bounded from outside only by its vapour, because the interface is stressed by an essentially tangential axial electric field intensity, with a strong gradient in the radial direction. Dispersion equations are developed for the electrohydrodynamic centrifugal waves of small amplitude. Conditions for incipience of instability and the frequencies of normal modes of oscillation are given. Experimental observations, which demonstrate the destabilizing influence of the rotation and the effect of rotation and electric field intensity on the normal mode frequencies, are in satisfactory agreement with the theory.

Direct measurements of the energy transfer spectrum in locally isotropic grid turbulence have been used to determine the extent of validity for grid turbulence of the dynamical equation for the three-dimensional energy spectrum in isotropic turbulence. The extent of applicability of the isotropic energy balance is consistent with the usual local isotropy criterion based on energy spectra alone.

The present results are in general agreement with some previous measurements by Uberoi, who determined the transfer spectrum assuming the strict validity of the isotropic dynamical equation. The measured energy transfer spectra are quantitatively similar to those calculated by Kraichnan using the direct-interaction approximation.

It does not seem to be possible to prove analytically that an incompressible, inviscid free shear layer is less unstable with respect to spatially growing three-dimensional disturbances than to two-dimensional ones. For this reason a numerical calculation for the special case of the hyperbolic tangent velocity profile was performed. It was found that even for spatially growing disturbances the amplification of three-dimensional disturbances is smaller than for two-dimensional ones.

Collapsing cylindrical metallic shells have been used to compress magnetic fluxes and generate megagauss magnetic fields. Such shells experience large, rapidly growing accelerations and their symmetry can be completely destroyed by Rayleigh-Taylor instabilities. This paper presents a theoretical study of the Rayleigh-Taylor instability for radially accelerated incompressible cylindrical shells submitted to the pressure of much lighter media. Low-amplitude flute perturbations are considered and Fourier-analyzed in the azimuthal angle. A fourth-order linear differential system with time-dependent coefficients is derived, which determines the two interface-displacements. Stability criteria are discussed. When the perturbation wavelength is much greater or much smaller than the shell thickness, the differential system splits into two independent differential equations and results are greatly simplified; analytical solutions are available for some cases.

The case of axial field compression (A.F.C.) is discussed as an application. Numerical solutions give the time behaviour of all possible initially given disturbances. The initial perturbations, which are able to reach the axis during their development and which are consequently dangerous in magnetic field compression experiments, have been calculated. Results are consistent with the few experimental data available. They show that the degree of symmetry of cylindrical devices has to be extremely good in order to get successful compressions.

Finally, non-linear and compressibility effects have been taken into account for some A.F.C. cases, solving the full non-linear fluid equations numerically.

The problem considered is that of two-dimensional viscous flow in a straight channel. The steady Navier-Stokes equations are linearized on the assumption of small disturbance from the fully developed flow, leading to an eigenvalue equation resembling the Orr-Sommerfeld equation. This is solved in the limiting cases of small and large Reynolds number R, and an approximate method is proposed for moderate R. The main results are (i) the dominant mode of the disturbance velocity (i.e. that which persists longest) is antisymmetrical; (ii) for large R there are two sequences of eigenvalues. Both sequences are asymptotically real as R → ∞. The members of the first sequence are O(1) as R → ∞ and are complex for all finite R. The members of the second sequence are O(R−1) and the imaginary part is O(R−N) for all N. It is the eigenvalues of the second sequence which will dominate the flow at large R.

Upper bounds on the torque are derived for a fluid that is contained between two concentric rotating cylinders. Absolute upper bounds are obtained by requiring that the fluid satisfy the boundary conditions and the dissipation integral. Improved bounds are then found by requiring that the fluid satisfy continuity conditions. These bounds are in qualitative agreement with the data in that they reflect the asymptotic parameter dependence in the range of experimental data.

The study of sink flow turbulent boundary layers is of particular relevance to the problem of laminarization. The reason lies in the fact that the acceleration parameter which principally determines when a turbulent boundary layer will begin to revert towards laminar is, in these flows, constant from station to station. The paper presents theoretical solutions to this class of boundary layer by making use of the Prandtl mixing-length formula to relate the turbulent shear stress to the mean velocity gradient. Near the wall the Van Driest recommendation for mixing length is adopted and the Van Driest function, A+, is chosen such that the skin friction coefficient does not exceed a certain maximum value.

The predicted solutions, which are in good agreement with available experimental data, display a plausible shift from the turbulent towards the laminar solution as the acceleration parameter is increased.

We consider here the flow due to the oscillation of a slender oblate spheroid in a non-homogeneous, rotating fluid confined between two parallel planes which are perpendicular to the (vertical) axis of rotation. The direction of oscillation of the spheroid is perpendicular to the axis of rotation. By solving a set of dual integrals the steady-state solution is obtained in the two cases when the plates are at an infinite distance from the body and when they are at a large but finite distance. The singular or discontinuous surfaces observed in the case of homogeneous fluid are absent here. Also, the steady-state velocity is no longer independent of the distance along the axis of rotation. The velocity has now a vertical gradient, an important feature in the case of stratified fluid. It is also found that the presence of the plane boundaries increases the force on the body.

A fluid swirling through an axisymmetrically deformed tube is considered, ignoring viscosity and compressibility. For a tube of radius R, having a longitudinal wall deformation of wave number k, the flow near the wall is blocked, if the Rossby number assumes one of the critical values (λ2n + k2R2)−½, where n is any positive integer, and λn is the nth zero of the Bessel function J1(λ). Rossby number is defined as W/2Rω, in which W and ω are the uniform axial and angular velocities in an undeformed tube. For a convergent-divergent nozzle, the critical Rossby numbers have the same form, with kR = 0. The flow exhibits radically different patterns when each critical Rossby number is crossed.