The investigation by Hayes (1964a) of the behaviour of a constant-density inviscid rotational flow in the neighbourhood of a stagnation point on a plane wall has been extended to include the effects of viscosity. The principal effect is the manner in which the singularity in vorticity discovered by Hayes is removed. A solution of only the boundary-layer equatiosn indicates the vorticity decays algebraically from the wall. Application of the method of matched asymptotic expansions, however, shows that the difference between boundary layer and outer vorticity, when carried out to second order in the outer flow, does not contribute to an algebraic decay. These results suggest that an infinite number of higher-order outer terms are generated which match the algebraic terms thereby yielding the conventional exponential decay. Numerical results are presented which also support this conclusion. The main contribution of the wall shear stress in the immediate neighbourhood of the stagnation point is shown to come from the external lateral vorticity.

The flow in a pipe of circular cross-section which is coiled in a circle is studied, the pressure gradient along the pipe varying sinusoidally in time with frequency . The radius of the pipe a is assumed small in relation to the radius of curvature of its axis R. Of special interest is the secondary flow generated by centrifugal effects in the plane of the cross-section of the pipe, and an asymptotic theory is developed for small values of the parameter = (2/a2), where is the kinematic viscosity of the fluid. The secondary flow is found to be governed by a Reynolds number , where is a typical velocity along the axis of the pipe, and asymptotic theories are developed for both small and large values of this parameter. For sufficiently small values of it is found that the secondary flow in the interior of the pipe is in the opposite sense to that predicted for a steady pressure gradient, and this is verified qualitatively by an experiment described at the end of the paper.

An extension of the StuartWatson technique for examination of the non-linear hydrodynamic instability of time-dependent flows is proposed. An example in Bnard convection is used to illustrate the method. Extensions to more general problems are indicated.

This paper is the report of an experimental study of heat transfer from fine horizontal wires of various lengths to fluids having various Prandtl numbers. Transport characteristics were determined for the full spectrum of processes from natural, through mixed, to forced convection. The experimental results are compared with those of past analysis and with correlations. The very high level of accuracy and reproducibility of the data makes possible the detection of very small effects. The influence of cylinder length on transport is shown for both of the asymptotic rgimes of natural and of forced convection. Transport in the mixed-convection rgime is determined and limits of that rgime are estimated.

Measurements are presented of the wave-number/frequency and wave-number/phase velocity spectrum of wall pressure for a two-dimensional turbulent boundary layer in zero pressure gradient, obtained from a Fourier transform of experimental filtered spatial correlations. This method allows the results to be corrected for acoustic disturbances in the wind tunnel, and for finite transducer size. An empirical form for the pressure field is proposed, based on the measurements, and is used to predict a frequency spectrum correction for transducer size which agrees well with measured values.

The stability of a two-fluid vortex is studied as a step towards understanding the separation and containment problems in a gaseous-core nuclear rocket. In particular, the linear hydrodynamic stability of two incompressible, immiscible, viscous fluids occupying separate annular regions of a cylindrical Couette apparatus is considered. Neglecting surface tension and gravity, a conservative assumption, the governing equations for arbitrary jumps in fluid properties are derived and numerical solutions to the resultant eigenvalue problems obtained. Results are presented for the effect on neutral stability of density and viscosity jumps, varying gap widths, and differing fluid-fluid interfacial positions. The solutions are limited, however, to the case of stably stratified fluids and a stationary outer cylinder.

Two separate modes (multiple eigenvalues) have been discovered for all cases in which two fluids, differing in any property, are present. A rationale is presented for this phenomenon as well as for most of the other observed results.

While most results are believed to be manifestations of the Taylor cylindrical Couette instability phenomenon, evidence is presented for the existence of additional hidden eigenvalues attributable to the classical KelvinHelmholtz and/or the recently reported Yih viscosity-stratification instability phenomena.

The hydrodynamic theory of the resonant cylinder (Gans 1970) is extended to include the effects of a magnetic field parallel to the rotation axis. The linear response is modified by a change in boundary-layer suction and a change in the resonant length. These effects are of equal importance. The theory is valid for small container conductivity and for amplitudes such that the cube of the amplitude is less than the dimensionless precession rate. The importance of container conductivity is assessed. The free modes of the system are given in an appendix. These modes move both east and west.

Experimental apparatus capable of producing magnetic Reynolds numbers of the order of 20 for indefinite lengths of time is described. The apparatus was used to assess the linear theory, though not designed for this purpose. Experiments beyond the range of linear theory are described. The results show finite amplitude effects similar to those previously observed in precessing spheroids in the absence of magnetic effects (Malkus 1968). Additional structure attributable to magnetic effects is observed.

A linear theory is developed for the spin-up of a compressible fluid, stratified by a spherical gravity field. Numerical results are obtained for the case of strong stratification (BruntVisl frequency N much greater than the rotation frequency 0). The interior flow is solved in terms of a set of angular eigenfunctions which have been obtained numerically. The principal result is that the spin-up is limited to a layer adjacent to the spherical boundary, the thickness of the layer being of the order of L(0/N), where L is the radius of the boundary. The solution is qualitatively similar to that found by Holton (1965), Walin (1969), and Sakurai (1969a, b) for a stratified fluid in a cylinder. The thickness of the spin-up layer diminishes with latitude , the variation being described roughly by the formula L0| sin |/N. For the case of slow continuous spin-up, the Ekman suction velocity has been calculated, and the results show that || = 24 is the dividing angle between suction (|| > 24) and blowing (|| < 24).

When a layer of particles moves through a viscous liquid it experiences forces which tend to disrupt the layer into clusters of particles separated by open channels. A theoretical description of this process is presented and a viscous instability is predicted. The spatial growth of the instability is approximated by ez, where where a is the particle radius and d is the average distance between particles. This result implies that any initial irregularity in a uniform particle distribution will be amplified by viscous forces alone. Significant amplification will occur when the particle has drifted a small multiple of the separation distance, if this separation is not much greater than the particle diameter. Thus, any initially uniform particle layer will form clusters as it drifts through a viscous fluid. The distance in which this clustering occurs will be unaffected by changes in the particle velocity, as long as the Reynolds number remains small. The preferred form of irregularity will consist of small clusters separated by individual particles which trail some distance behind. Experimental verification of these conclusions is presented.

The axial and radial gradients of the tangential velocity distribution are calculated from prescribed secondary flow functions on the basis of a zero-order approximation to the momentum equations developed by Lewellen. It is shown that secondary flow functions may be devised which meet pertinent physical requirements and which at the same time lead to realistic tangential velocity gradients.

The total-temperature distribution in both the axial and radial directions is calculated from such secondary flow functions and corresponding tangential velocity results on the basis of an approximate turbulent energy equation. The method employed for the solution of this equation stresses the equivalence of the vortex tube to counter-current systems with transverse diffusion such as distillation columns and heat exchangers.

An availability function is derived that permits the evaluation of vortex tube performance on the basis of velocity data.

Turbulent diffusivities resulting from the quantitative use of the tangential velocity approximation are shown to agree with those derived from the total-temperature calculations.

The steady-state flow in a rotating container is examined when the container is deformed into an ellipsoidal figure which is fixed in inertial space. The analysis is carried out for a fluid of small viscosity, and to the second order in Rossby number. Results show a vortex existing along the rotation axis, this being an interior manifestation of non-linear boundary-layer effects. These effects are a direct consequence of the forced oscillation being at twice the rotational frequency. The configuration is chosen to suggest the effects of gravitational body tides on the dynamics of the core of the earth. This problem is related to the similar problem of a precessing spheroid, and an experiment is described which tests the present theory and confirms previous experimental data from precessing spheroids.

A discussion is given of the current state of knowledge of vortex streets behind circular cylinders in the Reynolds number range 50 to 160. This was prompted by Gaster's (1969) report that he could not find the transition at a Reynolds number of about 90 observed by Tritton (1959) and Berger (1964a). A further brief experiment confirming the existence of the transition is described Reasons for rejecting Gaster's interpretation are advanced. Possible (mutually alternative) explanations of the discrepant observations are suggested.