This paper examines the energy conversion mechanisms which govern the emission of low frequency sound from an axisymmetric jet pipe of arbitrary nozzle contraction ratio in the case of low Mach number nozzle flow. The incident acoustic energy which escapes from the nozzle is partitioned between two distinct disturbances in the exterior fluid. The first of these is the free-space radiation, whose directivity is equivalent to that produced by monopole and dipole sources. Second, essentially incompressible vortex waves are excited by the shedding of vorticity from the nozzle lip, and may be associated with the large-scale instabilities of the jet. Two linearized theoretical models are discussed. One of these is an exact linear theory in which the boundary of the jet is treated as an unstable vortex sheet. The second assumes that the finite width of the mean shear layer of the real jet cannot be neglected. The analytical results are shown to compare favourably with recent attenuation measurements.

Thermoelectric currents in the presence of magnetic fields can cause pumping or stirring of liquid-metal coolants in nuclear reactors or stirring of molten metal in industrial metallurgy. The interaction between the thermal and magnetohydrodynamic fields is a mutual one owing to alterations in the thermal convection and to the Peltier and Thomson effects (although these are usually small). This paper sets up the equations of magnetohydrodynamics and thermal convection when coupled by thermoelectricity and solves some illustrative problems in which the thermal field is known ab initio. Examples where the effects are due to either continuous or discontinuous variation of material composition are included. Practical magnitudes are discussed for the case of a fusion-reactor blanket, where the effects are potentially important owing to the unusual thermoelectric power of lithium.

Submerged resonant ducts offer an approach to the design of wave-energy extraction devices consistent with the need for maximum seaworthiness. This paper gives a full account of one type of analysis of these systems, based upon two-dimensional wave hydrodynamics and linearized duct dynamics. The mathematical analyses are given in detail in § 2 while § 1 describes as concisely as possible (i) the assumptions underlying each analysis, (ii) its results and their implications for design, and (iii) any available experimental comparisons.

One theoretical prediction, unexpected when it was first made but since confirmed by experiment (Knott & Flower 1979), is that the effective pressure fluctuations to which a resonant duct responds can be substantially greater than those that would be present at the level of the duct mouth if the duct were absent. Other important predictions are concerned with added mass, radiation damping and the conditions for optimum energy extraction, calculated below for a wide variety of mouth design configurations and internal duct geometries. Broad tentative conclusions from the analyses are given at the end of § 1.

The instabilities of two-dimensional convection rolls in a horizontal fluid layer heated from below are investigated in the case when the Prandtl number is seven or lower. Two new mechanisms of instability are described theoretically as well as experimentally. The knot instability causes the transition to spoke-pattern convection at higher Rayleigh numbers while the skewed varicose instability accomplishes a change to larger horizontal wavelengths of the convection rolls. Both instabilities disappear in the limits of small and large Prandtl number. Although the experimental methods fail in realizing closely the infinitely conducting boundaries assumed in the theory, the observations agree in all qualitative aspects with the theoretical predictions.

A problem of major practical interest is the variation with x and t of the statistical properties of Γ(x, t), the distribution of concentration of a contaminant in a cloud containing a finite quantity Q of contaminant, released in a specified way at t = 0 over a volume of order L30. Of particular relevance is the case of relative diffusion (when x is measured throughout each realization relative to the centre of mass of the cloud), when important properties are L(t), the linear dimension of the cloud, C(x, t), the ensemble mean concentration, $\overline{c^2}({\bf x}, t)$, the variance of the concentration, and p(y, t), the distance-neighbour function. Much fundamental work has led to a knowledge of the way L varies with t, but not of the way the other properties vary. Hitherto therefore, prediction of such variation has normally used unjustifiable empirical concepts such as eddy diffusivities, but this is ultimately unsatisfactory, practically as well as theoretically. Hence the exact equations have been used to obtain a quite new description of the structure of a dispersing cloud, which it is hoped will serve as a basis for future practical work.

When κ = 0 (where κ is the molecular diffusivity) the magnitude of p(y, t) is of order Q/L3 for most y, but of order Q/L30 when |y| is very small. By a variety of arguments it is shown that these facts can be explained (for many, if not all, flows) only if the distributions of C and $\overline{c^2}$, as well as that of p, have a core-bulk structure. In the bulk of the cloud C and $\overline{c^2}$ have magnitudes of order Q/L3 and Q2/L30L3 respectively, but there is a core region of thickness decreasing to zero surrounding the centre of mass within which they have much greater magnitudes. In one case, examined in some detail, the magnitudes in the core are of order Q/L30 and Q2/L60.

It is then shown that the core and bulk exist even in the real case when κ ≠ 0. In the real case the core thickness no longer tends to zero but to a constant of order λc, the conduction cut-off length. As a consequence almost entirely of molecular diffusion acting in the core region, the magnitudes of C and $\overline{c^2}$ in both the core and the bulk decay to zero in a way which depends on the details of the fine-scale structure of the velocity field. Several examples of the decay are discussed.

A general linear theory is presented to describe oscillatory flows of gases and liquids in a tube of circular cross-section, including the effects of radial and tangential pressure gradients as well as the temperature. The basic equations are solved by separation of variables. The resulting eigenvalue equation is extensively discussed whereby the splitting of the eigenvalues into ‘bands’ is obtained in a natural way. A systematic analysis of a number of simplified cases leads to analytic approximations for the eigenvalues over an extended domain of parameter variation (frequency, friction) so that a complete survey of all the eigenvalues is established. Then the problem of satisfying simultaneously arbitrary end-conditions for all flow variables with the obtained bands of eigenfunctions is formulated in a way to allow the application of Galerkin's method. Finally the theory is applied to a few examples of ‘end-layers’ and radial resonance, which cannot be treated by previous theories.