The presence of the edge of a half plane in a turbulent fluid results in a large increase in the noise generated by that fluid at low Mach numbers. The parameter which is important is the product $2k\overline{r}_0$, where $\overline{r}_0$ is the distance of the centre of an eddy from the edge. Eddies which satisfy the inequality $2k\overline{r}_0\ll 1$ have the sound output of the quadrupoles associated with the fluid motion in a plane normal to the edge increased by the factor $(k\overline{r}_0)^{-3}$. There is no enhancement of the sound from the longitudinal quadrupoles with axes parallel to the edge: the rr, θr and θθ quadrupoles are the dominant sound sources. The far field sound intensity induced by these sources depends upon the fifth power of a typical fluid velocity. The intensity has a directional dependence on cos2 ½θ if the half plane is rigid and sin2 ½θ if it is a pressure release surface, θ = 0 being a direction in the half plane.

If the eddies are far from the edge so that $(k\overline{r}_0)^{\frac{1}{2}} \gg 1$ then the farfield sound has the same features as would be predicted by geometrical acoustics. The edge does not produce any significant sound amplification.

An analysis is presented for the interaction of capillary and gravity waves in a liquid layer of finite depth. The method of multiple scales is used to obtain a third-order expansion uniformly valid for all times. Although this expansion is valid for a wide range of wave-numbers, it breaks down at two critical wave-numbers if the liquid depth is larger than √3/kc, kc = (ρg/T)½, where g is the gravitational acceleration, and ρ and T are the liquid density and surface tension, respectively. For a deep liquid, the singularities are at kc/√2 and kc/√3 respectively, as found by Wilton (1915), and Pierson & Fife (1961).

A second-order expansion valid for wave-numbers near the first critical value (corresponding to a wavelength of 2·44 cm in deep water) is obtained. This expansion shows that two different wave profiles could exist at or near the first critical wave-number. One of these profiles is gravity-like while the other is capillary-like.

The two-dimensional flow of an incompressible viscous fluid past a circular cylinder, symmetrically placed in a uniform shear field, is considered both theoretically and experimentally for small values of the shear Reynolds number. A series of angular rotational speeds is covered, each giving rise to a fundamentally different flow pattern. It is shown first that the Stokes solution to this problem is not entirely consistent everywhere with the linear shear boundary condition which presumably exists far from the body. Using the method of inner and outer expansions, this solution is then improved by properly taking into account the first-order effects of the inertia terms, but, surprisingly, the streamline structure in the outer region is still found to depart from that of the uniform shear sufficiently far away from the object.

In spite of the somewhat bizarre nature of the theoretical solution far from the cylinder, experimental studies clearly show, however, that it accurately represents the actual flow within the inner region over a wide range of cylinder rotation rates.

Heat transfer from a cylinder placed symmetrically in a constant shear field is considered experimentally for low values of the shear Reynolds number, but for Péclet numbers Pe as large as 2000. With the cylinder held stationary, the experimentally obtained Nusselt number Nu is found to be in excellent agreement with the theoretically derived asymptotic expression, $Nu = 1.641 Pe^{\frac{1}{3}} (Pe \rightarrow \infty)$, for Péclet numbers in excess of 100. In contrast, with the cylinder rotating at a speed corresponding to zero torque, the Nusselt number becomes effectively independent of the Péclet number for Pe > 70. This surprising behaviour, predicted theoretically by Frankel & Acrivos (1968), results from the presence of a region consisting entirely of closed streamlines which surrounds the freely rotating cylinder.

The objective of the paper is to formulate a physically realistic definition of shock impedance. The definition obtained, expression (15), is consistent with the acoustic limit, with the Polachek & Seeger result for head-on shock incidence, and with the various reflexion limits. It seems to be applicable to all known regular and irregular refractions, with the possible exception of a refraction containing a Guderley patch. It is shown that one result of increasing impedance mismatch is to produce precursor and postcursor waves. It is thought the impedance mismatch caused by the jets of supersonic aircraft might be used to reduce the sonic boom overpressure.

Any slight tilt or tide on the fluid in a rotating cylinder causes periodic motions, whose radiation pressures in the viscous boundary layers force mean differential rotations of the fluid, which are found numerically. At certain fluid depths, even very small tilts can cause shears large enough for perturbations to overcome Ekman friction, causing turbulence. An experiment confirms the theory.

Convective instability of a ferromagnetic fluid is predicted for a fluid layer heated from below in the presence of a uniform vertical magnetic field. Convection is caused by a spatial variation in magnetization which is induced when the magnetization of the fluid is a function of temperature and a temperature gradient is established across the layer. A linearized convective instability analysis predicts the critical temperature gradient when only the magnetic mechanism is important, as well as when both the magnetic and buoyancy mechanisms are operative. The magnetic mechanism predominates over the buoyancy mechanism in fluid layers about 1 mm thick. For a fluid layer contained between two free boundaries which are constrained flat, the exact solution is derived for some parameter values and oscillatory instability cannot occur. For rigid boundaries, approximate solutions for stationary instability are derived by the Galerkin method for a wide range of parameter values. It is shown that in this case the Galerkin method yields an eigenvalue which is stationary to small changes in the trial functions, because the Galerkin method is equivalent to an adjoint variational principle.

The stability of parallel shear flow of an inviscid compressible fluid is investigated by a linear analysis. The extension of the Rayleigh stability criterion and Howard's semi-circle theorem to compressible flows, obtained by Lees & Lin (1946) and Eckart (1963) respectively, are each rederived by a different approach. It is then shown that a subsonic neutral solution of the stability equation may be found when the basic flow is represented by the hyperbolic-tangent velocity profile. With the aid of this solution, the unstable eigenvalues, eigenfunctions and Reynolds stress are determined by numerical methods. A brief discussion of the results follows.

The stability of a horizontal layer of fluid heated from above or below is examined for the case of a time-dependent buoyancy force which is generated by shaking the fluid layer, thus causing a sinusoidal modulation of the gravitational field. A linearized stability analysis is performed to show that gravity modulation can significantly affect the stability limits of the system. In this analysis, much emphasis is placed on qualitative results obtained by an approximate solution, which permits a rather complete stability analysis. A useful mechanical analogy is developed by considering the effects of gravity modulation on a simple pendulum. Finally, some effects of finite amplitude flows are considered and discussed.

Recent theoretical results for the turbulent flow of polymer solutions in round tubes have been extended to deduce the similarity laws for the boundary-layer flow of drag-reducing polymer solutions. The analysis shows directly how the drag reduction depends on the elastic properties of the fluid and thereby defines the levels of elasticity necessary to achieve significant reductions in drag.

Calculations employing available physical property measurements of highly elastic (0·1%) and moderately elastic (0·01%) polymer solutions indicate that, for boundary layers on large objects, drag reduction may not occur at polymer concentrations that are economically attractive. For example, at a Reynolds number of 109 the reduction in drag is predicted to be 60% and 10% for the concentrated and dilute polymer solutions respectively. Some savings in polymer however, may be realized by special injection techniques or fluid systems with specially tailored properties.

In this paper the problem of interaction of an oblique blast wave encountering a small bend along a plane wall is studied for the case when relative outflow from the reflected shock is supersonic. A theoretical solution is developed completely with the help of conformal transformations and complex variable techniques. Numerical results showing the pressure distribution along the wall have been obtained for two incident shock strengths.

The problem considered is that of a strong shock propagating from a point energy source into a cold exponential atmosphere with radiative heat transfer in the flow behind the shock. The radiation mean free path is taken to be small compared to the shock radius, so that the shock may be treated as discontinuous and the radiative heat flux represented by the Rosseland diffusion approximation. The solution obtained is an approximate one based upon the ‘local radiality’ assumption and integral method previously utilized by Laumbach & Probstein for the case of adiabatic flow. The ‘thin shock’ concepts, which underlie the integral method, are extended to the present case of a radiating flow enabling an approximate integral of the differential energy equation to be obtained. A radiation parameter is developed, which provides an index as to when the effects of radiation may be neglected and the flow taken to be adiabatic. The physical interpretation of this parameter is that of the ratio of a characteristic radiation energy flux to a characteristic kinetic energy flux. When the value of this parameter is less than about 0·1, radiation effects may be neglected. It is shown that, when the radiation mean free path varies as a power of the temperature (Tn), where $n = -\frac{17}{6}$, the infinity of solutions for various polar angles can be transformed into two distinct solutions thereby essentially eliminating the parametric dependence on the polar angle and the atmospheric scale height. For fixed values of the radiation parameter the dependence on the explosion energy and the atmospheric density at the point of explosion is also eliminated. The results presented are for the mean free path–temperature variation indicated, but the technique of solution does not have this restriction, though for other temperature dependences some of the scaling advantages are sacrificed. The solution demonstrates the existence of an independence principle in which the flow becomes isothermal and independent of the detailed radiation mechanism when the radiation parameter becomes large. The limiting results of the present analysis for a uniform density atmosphere correspond quite, well with the exact solutions of Elliott & Korobeinikov. The radiating far field behaviour of the descending shock is shown to approach that for adiabatic flow, and, consequently, the asymptotic adiabatic solution obtained by Raizer is an appropriate limit to the present solution. However, the asymptotic results for the ascending shock show that the radiating flow does not approach an adiabatic one but rather an isothermal one.