This paper concerns the boundary layer on a semi-infinite flat plate in a uniform stream of conducting fluid, with magnetic field in the stream direction. It is found that when β, the square of the ratio of the Alfvén speed to the undisturbed fluid speed, is slightly less than unity, two solutions of the Greenspan-Carrier equations governing the motion exist for ε(= σμν) less than unity.

At present, solutions for natural convection problems involving discontinuous changes in wall temperature do not exist. This paper reports results of an extensive experimental investigation of the particular case of a vertical flat plate with a step-change in wall temperature. Temperature profiles and local heat transfer coefficients determined with a Mach-Zehnder Interferometer are presented for a wide range of the pertinent parameters. The flow field associated with this problem was studied by means of a series of Tellurium dye experiments in water. Photographs are presented showing representative flow patterns, and the stability of the flow is considered as a function of the ratio of the excess temperature below a discontinuity to the excess temperature above.

The classical Kelvin-Helmholtz problem of the instability of the vortex sheet between two uniform streams is extended to allow for non-uniformity in the streams. A small-wavelength approximation shows that the most unstable disturbances have a growth rate proportional to the greatest discontinuity of velocity at the vortex sheet. The solution for all wavelengths is found for two cases when the variation in the stream velocity is small compared with the stream velocity itself. One of these cases indicates that a transverse variation in the stream velocity can increase the instability for long wavelengths, but only to a small extent.

Free-surface oscillations of a liquid relative to an equilibrium state of uniform rotation about the vertical of an axisymmetric container are considered for small $\alpha = \omega ^2a|g$, where ω is the angular velocity of rotation and a the cylinder radius. A variational approximation is used to obtain explicit results, with an error of O(α2), for axisymmetric gravity and inertial waves in a flat-bottomed circular cylinder; these results are found to be in agreement with observations reported by Fultz (1962). The first-order (in ω) effects of rotation on asymmetric waves in a circular cylinder also are determined.

A kinematic model of the flow around and into a buoyant ‘thermal’ is discussed in some detail, and compared with existing laboratory observations. The basic assumption is that the flow is instantaneously the same as it is for Hill's spherical vortex of fixed size moving through a frictionless fluid. The equations describing the motion of a particle have been modified to allow for an expansion in radius proportional to the distance travelled, and a numerical integration of these time-dependent equations has been performed in order to find particle trajectories, with respect to both the instantaneous boundary of the spherical vortex and axes at rest. It is shown that for the expanding vortex there is no quantity corresponding to the ‘drift distance’ or the total forward displacement of particles in the flow round a sphere of constant size; particles in the wake of an expanding vortex have a finite forward velocity at large times.

The model gives very close agreement with the observed behaviour of particles entering a turbulent buoyant thermal, except that in the laboratory measurements the region containing the turbulent fluid resembles an oblate spheroid rather than a sphere. The thin mixing layer over the front and the addition of fluid over a broad region at the rear of a thermal, as well as the detailed particle trajectories, can all be explained as consequences of this mean velocity distribution.

A general reverse-flow relation is obtained within the framework of second-order (in surface deflexion) supersonic flow theory. From this it is shown that the second-order increment in the drag of an arbitrary quasi-cylindrical body can be expressed as surface and volume integrals of the first-order solutions corresponding to forward and reverse flow past the body. Analogous results are obtained for second-order transverse forces and moments on an arbitrary quasi-planar wing, where the first-order reverse flow must correspond to certain zero-thickness wings. Other similar results are possible. Thus, second-order aerodynamic forces on bodies may be obtained from first-order solutions by quadrature. It is also shown that the reverse-flow integral relation can yield the pressure distribution on the surface by inversion of an integral equation constructed therefrom. It is thought that these results should be particularly useful for the Machnumber range between that of linearized theory and that of full hypersonic small-disturbance theory.

The problem of supersonic flow over an inclined flat-plate delta wing with supersonic edges is solved to second order in incidence. This solution for surface pressure is uniform and fully analytic. The approach utilizes a reverse-flow integral method previously developed for second-order problems. This method is augmented by a number of techniques appropriate to its framework. The simplification over standard techniques achieved by using these reverse-flow methods is quite substantial and makes the problem tractable.

Reverse-flow procedures give a volume-surface integral relation that connects the second-order forward flow over the body of interest with the linearized reverse-flow over a related body. A singular integral equation is generated from the integral relation by introducing the edge sweep of the reverse-flow wing as a free parameter. An inversion is available which gives the second-order solution on the surface of the wing. The solution is then made uniformly valid using techniques previously developed.

The steady distribution function for homogeneous turbulence is studied starting from Liouville's equation, modified by the introduction of an instantaneously fluctuating external force, which acts as a random source of energy. A new technique for solving Liouville's equation is presented giving a systematic development of the concepts of turbulent diffusion and turbulent viscosity. It amounts to a consistent generalization of the random phase approximation. When the rate of input of energy into the kth Fourier component uk has a power form h|k|−α, the functional form of the mean value 〈 uku−k 〉 can be determined exactly in the limit of large Reynolds number; it is $Ah^{\frac{2}{3}}|\bf K|^ {-{\frac {1}{3}}(5+2 \alpha)}$. Liouville's equation proves an inadequate basis for the steady time-dependent mean $\langle u_k(t)u_{-k}(t^ \prime) \rangle $ and a more general equation is derived. The new equation can be solved in a similar way and shows that the time-dependent correlation starts like a Gaussian in time, then passes through an exponentially decaying state, then eventually has a power dependence $|t-t^\prime|- \gamma^ {|k|}$.

The influence of radiation on the propagation of small disturbances is investigated by considering a signalling problem and obtaining approximate limiting solutions. It is found that, for small time, the main disturbance travels at the isentropic speed of sound. For some intermediate time, the main disturbance travels at the isothermal speed of sound. For long time, the disturbance travels at the isentropic speed of sound. The decay and diffusion of these waves are also determined.

The results of measurements of far-field sound emitted from jets are reported. The narrow-band power spectral density of the sound in the far field was measured for three jet diameters, three Mach numbers, and five angular positions. The intensity distribution of mean-square pressure fluctuation in the far field in several wide frequency ranges were also measured. The similarity relations found from the experiments are reported.

A detailed equation is proposed for the force exerted on a sphere that accelerates rectilinearly in an otherwise still fluid. In addition to the buoyant force, the fluid exerts forces that depend on (a) the velocity of the sphere, (b) the acceleration of the sphere and (c) the history of the motion. The equation reduces to the known theoretical solution for low velocity and large acceleration.

The proposed equation was tested and found most satisfactory for a particular case in which the velocity was not small, viz. the case of simple harmonic motion along a straight line. The acceleration (added mass) and history coefficients in the equation were evaluated experimentally. They were found to depend on the ratio of the convective acceleration to the local acceleration as measured by the parameter V2/aD, in which V, a and D are the velocity, acceleration and diameter of the sphere, respectively. The Reynolds numbers varied from 0 to 62 during the tests.

The vertical constant-speed motion of a constant-strength point source towards a horizontal free boundary is analysed. A procedure based on expansions in even powers of the Froude number is employed. The asymptotic expansion of the potential is found to satisfy a simple differential equation, which, when integrated, yields an image-type solution valid for all Froude numbers. Froude-number effects are contained in a distribution of sources along the vertical line from the image of the submerged source with respect to the undisturbed free surface upward to infinity. The solution is valid for arbitrary values of the density ratio across the free surface.