The transmission of sound out of a semi-infinite circular jet pipe in the presence of subsonic flow from the pipe is investigated. An unstable cylindrical vortex layer attached to the edge of the pipe is considered across which differences in mean subsonic flow, density and temperature are included. A solution satisfying the Kutta condition and causality is found which possesses an instability wave term that dominates within a region of approximately 45° to the downstream jet axis. It is shown that when an exterior flow is imposed the noise level increases upstream whilst the instability wave weakens downstream. The stable part of the solution is shown to agree very well with some recent experimental results.

This paper presents a new experimental time-domain technique for the evaluation of the large-scale structure in a turbulent flow. The technique is demonstrated by hot-wire anemometry for a circular jet flow at a moderate Reynolds number of 104, and the large-scale structure identified is compared successfully with smoke flow-visualization observations. The temporal and spatial relationships of the separate large-scale flow events have been derived, and this information enabled the evaluation of the nonlinear spatial development of the large-scale flow structure.

It is now well established that coherent structures exist in turbulent shear flows. It should be possible to recognize these in the turbulence signals and to program a computer to extract and ensemble average the corresponding portions of the signals in order to obtain the characteristics of the structures. In this work only the u-signal patterns are recognized, using several simple criteria; simultaneously, however, the v or w signals as well as uv or uw are also processed. It is found that simple signal shapes describe the turbulence structures on the average. The u-signal pattern consists of a gradual deceleration from a local maximum followed by a strong acceleration. This pattern is found in over 65% of the total sample in the region of high Reynolds-stress production. The v signal is found to be approximately 180° out of phase with the u signal. These signal shapes can be easily associated with the coherent structures that have been observed visually. Their details have been enhanced by quadrant truncating. These results are compared with randomly generated signals processed by the same method.

Earlier ideas are combined to produce a systematic approach both to forming the bulk equations of motion of a dilute suspension and to calculating the overall hydrodynamic interactions between the suspended particles. Equations governing averaged field quantities are derived by taking ensemble averages of the conservation laws and constitutive relations. The bulk equations thus produced contain a term in which the averaging is performed holding one particle fixed. If now the same prescription is applied to fields averaged with one particle fixed, equations are produced containing a term averaged with two particles fixed, and so on up an infinite hierarchy. The hierarchy can be truncated in an asymptotic analysis for small particle concentrations.

This approach to the mechanics of suspensions is illustrated by applying it to three problems which have already been well studied by different methods. The problems concern the first effects of hydrodynamic interactions on the bulk stress and sedimentation velocity of a free suspension, and on the permeability of a fixed bed. Earlier results are recovered in a new light. Multiparticle effects, which before have occurred as divergent sums, are seen to arise because the suspension described by the averaged equations assumes a viscosity and density different from the solvent, or in the case of the fixed bed because the suspension starts behaving as a porous medium instead of as a Newtonian solvent. A close connexion is thus revealed between the averaged-equation description of the interactions and a self-consistent-field model.

The motions of a floating torus oscillating in response to incident waves are analysed under the assumptions that the incident wavelength is comparable with the radius of the body section and small compared with the larger radius of the torus. This problem serves to illustrate certain features of the strip theory for ship motions, but the axisymmetric geometry and absence of body ends greatly simplify the analysis. Matched asymptotic expansions are used, with the inner solution close to the body section composed of suitable radiation and scattering problems for the two-dimensional circular cylinder. Resonant standing-wave modes in the internal basin have a singular effect upon the hydrodynamic forces acting on the body, and its response to incident waves.

Using the Fourier components of the velocity potential at the surface in an iterative perturbation theory, the author derives expressions for the modal frequency shifts and modal decay rates in a spectrum of in viscid gravity–capillary surface waves. The expressions differ from those calculated by the perturbation methods of Hasselmann (1962) and Valenzuela & Laing (1972), which are based on expanding the velocity potential about the equilibrium fluid level z = 0. This difference is shown to be due to the failure of the z = 0 perturbation method to converge rapidly enough to produce lowest-order corrections that are smaller than unperturbed quantities. A physical explanation for this failure is given.

In this paper we examine how the unsteady flow field radiated from an oscillating body is altered from the result of acoustic theory as the direct consequence of disturbances propagating through the non-uniform flow produced by the presence of the body. Taking the specific example of an oscillating airfoil placed in supersonic flow and having the contour of a parabolic arc, we derive a closed-form representation for the unsteady flow field in terms of the confluent hypergeometric function. The analytical expression reveals explicitly that, though the body shape has a negligible effect in the near field, it inextricably affects the unsteady flow at a large distance, both in its amplitude and phase, and substantially modifies the results of acoustic theory. In addition, we display the relation of this solution to the ‘fundamental solution’ and the other salient physical features connected with disturbances propagating through non-uniform flow. The present results recover Whitham's rule in the limit of zero frequency of oscillation and also include, as another special case, the unsteady solution for a wedge obtained by Carrier and Van Dyke.

In this paper we formulate the aerodynamic sound problem for a relaxing medium in a rather general way, independent of the details of the relaxation process. The medium is characterized by an appropriate relaxation time τ0 and by a frozen (af0) and an equilibrium (ae0) sound speed. The equation describing aerodynamic sound in such a medium is the familiar one describing acoustic waves in a non-equilibrium medium but subjected to aerodynamic sound sources expressed in terms of a frozen and an equilibrium form of the Lighthill stress tensor. The far-field result for both compact and non-compact sources in the frequency range ω [Gt ] τ0−1 can be expressed as the ratio of far-field densities for the relaxing and non-relaxing propagation medium: \[ \frac{\rho}{\rho_L} = \exp\left[-\left(1-\frac{a^2_{e_0}}{a^2_{f_0}}\right)\frac{x}{2a_{f0}\tau_0}\right], \] where x is the observation distance and the subscript L stands for ‘Lighthill’. The result for the main radiated aerodynamic sound, which comes from sources in the range ω [Lt ] τ0−1, essentially propagates in a manner described by the lower-order equilibrium waves, the diffusive effects from the higher-order waves being small, and the result for compact sources is a restatement of Lighthill's result in terms of the equilibrium propagation speed with the source region identically in equilibrium. For non-compact sources the propagation is still given by ae0 but the source region is now understood to encompass relaxation effects, the details of which are left unspecified.

A numerical proceure is introduced to solve the one-dimensional equations of gasdynamics for a cylindrically or spherically symmetric flow. The method consists of a judicious combination of Glimm's method and operator splitting. The method is applied to the problem of a converging cylindrical shock.