The viscous hypersonic flow past an axisymmetric blunt body is analysed based upon the Navier-Stokes equations. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number, P, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach number, M, and the free-stream Reynolds number based on the body nose radius, R, go to infinity, and ε = (γ − 1)/(γ + 1), where γ is the ratio of the specific heats, and δ = 1/(γ − 1) M2 go to zero.

When the angular amplitude of oscillation of a sphere in an infinite mass of elastico-viscous fluid is fairly small, so that velocity and stress components may be expanded as power series in this amplitude, the purely periodic primary motion has associated with it a secondary flow which has a steady component as well as a component of double the primary frequency. An expression for the stream function of the steady secondary flow is obtained for all possible frequencies and the results are illustrated by considering in detail a particular fluid. It is shown that the streamline projections on a plane containing the axis of rotation are strongly dependent on the parameters measuring the elasticity of the fluid and on the frequency. The circulatory secondary flow can be in the opposite sense to that in a Newtonian fluid, in either the whole or part of the elastico-viscous fluid.

A theoretical analysis is given of the unsteady flow of a liquid within a cylinder of finite length started suddenly so as to spin about its axis. It is found that a secondary flow, caused by the end walls of the cylindrical container, has a strong effect on the generation of spin in the liquid. In the vicinity of the end walls the fluid motion is characterized by a boundary-layer flow, which can be either laminar or turbulent. The fluid within the boundary layers rotates faster than that at a large distance from the end walls, and therefore is thrown, by centrifugal forces, radially outwards. The radial outflow in the boundary layer creates a slow secondary motion within the spinning liquid. Due to the secondary flow, the transport of angular momentum from the walls to the interior is accomplished by convection rather than diffusion. A treatment is given for both laminar and turbulent end-wall boundary layers. The theoretical results are compared with experimental observations and good agreement is found.

A compact cluster of 3 to 6 rigid equal spheres is falling under gravity in a viscous liquid. The small effects of intertia on a horizontal regular polygonal configuration are that the polygon expands as it falls and small perturbations from this configuration die out, although when the polygon is large enough it becomes weakly unstable. This is an extension of the analysis of Hocking (1964, which was applied to the experiments of Jayaweera, Mason & Slack (1964).

The problem of the flow near a stagnation point when the main stream outside the boundary layer fluctuates in magnitude but not in direction about a steady mean is discussed. The velocity distribution is found in the two limiting cases of small and large values of the frequency of the oscillation. The corresponding two approximate solutions give similar results in an overlapping range of frequency.

The problem of defining an effective velocity of convection for turbulent fluctuations in a shear flow is considered, and the definitions adopted by various workers are discussed. An experiment in the shear layer of a circular jet has shown that the usual definitions, based on peaks of the space-time correlations of the fluctuations, yield convection velocities whose magnitudes depend on the value of space or time separation chosen. An alternative approach shows that, by considering the turbulent field as a superposition of harmonic travelling waves, a wave-number/velocity spectrum can be defined that lends itself to the definition of a wave-number-dependent convection velocity and an overall convection velocity, both of which have real physical significance. An experimental technique is described for obtaining the spectrum, and results are presented for one position in the shear layer of the jet.

The effect of compressibility is included here in a study of wakes created in two-dimensional, steady, aligned-fields, magnetogasdynamic flow past obstacles. The gas is assumed to be viscous, resistive, and thermally conducting. With the Oseen type of approximation as well as the magnetogasdynamic boundary-layer approximation, a great simplification in the formulation of wakes results. The boundary-layer equations, although linearized, still retain the coupling between the velocity, the magnetic, and the temperature fields. The solution of the magnetogasdynamic wake, in general, is a superposition of three individual-wake components, each satisfying a diffusion type of equation. Only one of them is capable of extending upstream. Hence the wake picture is generally characterized by a conventional downstream wake with also the possibility of the existence of an upstream one.

To be sure, the general features of the magnetogasdynamic wakes in aligned-fields flows are similar to those of an incompressible fluid; however, the flow now, instead of just being subalfvénic, must be subcritical for the upstream wake to occur. That is, the flow condition corresponding to the occurrence of the upstream wake is such that the sum of the square of the Mach number M∞ and the square of the Alfvén number A∞ is less than unity. Evidently it is the mechanism of magneto-sonic-wave propagation that modifies the transition of wakes from the Alfvénic point A∞ = 1 (for an incompressible fluid) to the subcritical are $A^2_\infty + M^2_\infty = 1$ in the Taniuti-Resler diagram.

The classical problem of the motion of a one-dimensional unsteady shock generated by a piston moving with velocity vp = ctn is extended to take into account thermal radiation effects by the similarity method of Taylor and Sedov. Gray gas and local thermodynamic equilibrium are assumed and a modification of the Schuster-Schwarzschild differential equation for the heat flux is adopted. The optical thickness is not restricted to be thin or thick, and the absorption coefficient is assumed to vary with the density and temperature. Numerical results indicate that the pressure and velocity are not affected much by the radiation, but the density, temperature and radiant heat flux are changed considerably.

The mathematical basis for resonance is investigated using a model equation describing one-dimensional dispersive waves interacting weakly through a quadratic term. If suitable time-invariant boundary conditions are imposed, possible oscillations of infinitesimal amplitude are restricted to a discrete set of wave-numbers. An asymptotic expansion valid for small amplitude shows that oscillations of different wave-number interact primarily in independent resonant trios. Energy is redistributed between members of a trio over a characteristic time inversely proportional to the amplitude of the oscillations in a periodic manner. The period depends on the initial conditions but is in general finite. Cubic interactions through resonant quartets are also discussed. The methods used are valid for a fairly wide class of equations describing weakly non-linear dispersive waves, but the expansion procedure used here fails for a continuous spectrum.

When a smooth jet of water falls vertically on to a horizontal plane, it spreads out radially in a thin layer bounded by a circular hydraulic jump, outside which the depth is much greater. The motion in the layer is studied here by means of boundary-layer theory, both for laminar and for turbulent flow, and relations are obtained for the radius of the hydraulic jump. These relations are compared with experimental results. The analogous problems of two-dimensional flow are also treated.

The heat transfer in a radial liquid jet is investigated. In the region where a similarity solution of the momentum equation is available solutions of the energy equation describing the effects of viscous dissipation, initial heating and wall heating are obtained in closed form. Two examples illustrating the work are discussed. In the second of these an approximate method, based on the heat flux equation, is used to describe the initial development of the thermal boundary layer.

An experimental investigation of the fluid dynamic forces on spheres suspended in a Poiseuille flow was performed. Small spheres of polystyrene, nylon, and Lucite, having diameters ranging from 0.061 in. to 0.126 in. were suspended in Poiseuille flows in a 0.419 in. diameter tube. Variations in particle size and density, the fluid properties, and the angle of inclination of the tube, resulted in a sphere Reynolds number (based on particle diameter and approach velocity) ranging from 80 to 250. The results are presented as curves which include the coefficients of lift and drag, and the dimensionless rotation speed plotted versus Reynolds number and a dimensionless shear parameter.