The introduction to Part 1 (Lighthill 1957) proposed a paper in three parts, in the nature of a broad introductory discussion of the dynamics of a pure dissociating gas, which might act as a source of ideas for later, more comprehensive investigations. Part 1 treated ‘equilibrium flow’, Part 2 was to treat transport properties under ‘quasi-equilibrium’ conditions, and Part 3 flows in which large departures from equilibrium occur. When Part 1 was submitted for publication, much of Part 2 had already been written. At this moment, however, the author suddenly became obliged to abandon the project for two years, in order that his contributions to two collective works, Laminar Boundary Layers and Incompressible Aerodynamics, could be produced in time to avoid serious delay in the appearance of the contributions of other authors.

This paper attempts to explain theoretically the observed results that (1) the cells in steady convection approach a hexagonal form, and (2) the occurrence of ascent or descent in the middle of the cell depends on how the kinematical viscosity varies with temperature. The theory is based on non-linear equations and, of course, a variable coefficient of viscosity.

It is found that, due to the variation of viscosity with temperature, the non-linear terms contain a second-order term which is destabilizing. This second-order term regulates the development and leads to a final motion composed of regular hexagons with ascent or descent in the middle of the cell according as the viscosity decreases or increases with temperature.

The influence of a variable viscosity on Rayleigh's result concerning the initiation of convection is obtained as a by-product.

This paper considers the problem of the propagation of a shock wave down a non-uniform tube. Linearized solutions to the problem (Chester 1954) do not hold when the velocity behind the shock is near or at the sonic speed. By retaining appropriate non-linear terms of the flow equations, a solution is obtained which holds for all conditions behind the shock, and reduces to the linearized solution for conditions away from sonic.

The behaviour of supersonic or subsonic flow entering regions of expanding or contracting area changes is discussed. It is found that subsidiary shocks may be formed; these can be located and described using the present solution. Explicit solutions are given for the cases of supersonic or subsonic flow entering a region of linearly expanding or contracting area. The point of shock formation as well as the path of the subsidiary shock is obtained for the case in which the area contracts.

Reverse-flow relations are used to provide convenient expressions for the aerodynamic forces which act on a general wing-fuselage combination in supersonic flow. The drag, lift, spanwise and chordwise lift distributions, and wing moments are treated. Consideration is given to available methods and results, including tables, which apply to the wing-fuselage interference problem, and reverse-flow relations are then employed to effect desirable changes in the detining force expressions by introducing wings or fuselages in the reverse flow. It is shown that the aerodynamic forces can be determined from a solution for the pressure on only the fuselage surface within the domain of dependence of the wing, this region being selected on the basis of relative ease of computation. In some cases the simplification achieved is quite substantial. Certain results in the literature arise naturally as special cases. The reverse-flow theorem is re-examined in the light of the procedure considered, and it is found to be inapplicable in one respect. The difficulty is circumvented by constructing an acceptable configuration which is equipollent to the prescribed one. It appears that the method given is applicable in other linear hyperbolic problems in mathematical physics when bulk or gross information is required and a suitable reciprocity relation can be constructed.

An exact solution is presented in this paper for the problem of laminar convective flow under a pressure gradient along a vertical pipe, the walls of which are heated or cooled uniformly; the solution is based on the assumption that velocity and buoyancy profiles far from the pipe entrance do not change with height, and entry-lengt effects are ignored. Two different types of behaviour are found accordingly as the pressure gradient and buoyancy forces act together or in opposition near the centre of the pipe.

When an upflow is heated (or a downflow cooled) the velocity near the walls is increased relatively and that near the axis decreased until, for sufficiently large Rayleigh numbers, definite velocity and thermal boundary layers are formed.

In the case of cooled upflow (or heated downflow) there is an increase in the velocity across the whole profile for small Rayleigh numbers. As the Rayleigh number is increased the velocity and buoyancy increase, slowly at first and then rapidly, and the solution ‘runs away’ at a Rayleigh number of about 33. For higher Rayleigh numbers, laminar Poiseuille flow of an increasingly complicated profile is theoretically possible, but is unlikely to be found in practise.

This paper is concerned with the spherically symmetric collapse of an empty cavity in water. The effects of viscosity and surface tension are neglected, but the compressibility of the water is allowed for and a suitable equation of state for the water assumed. The object of this is to clarify the effect of compressibility on the flow by considering it in isolation and thus to describe the formation of a pressure pulse by the collapse and its subsequent propagation.

The exact flow equations are integrated numerically and it is found that very high flow speeds develop in the neighbourhood of the collapse point. The radius of the cavity is found to be proportional to (-t)n for small t, where t = 0 is the instant of collapse, and n is some positive number less than unity.

The flow in the neighbourhood of the collapse point can be described by means of a similarity solution, and the value of n is determined by regularity properties of the similarity solution (the value of n depends on the equation of state assumed for the water). The similarity theory, which is valid only at very high pressures and velocities, can be continued beyond the instant of collapse to describe the formation of a shock wave after the collapse is completed, and the initial propagation of this shock.

This paper describes a theory for a piston-operated compressor in which shock waves are used to heat the gas being compressed. Detailed calculations are given showing the use of such a compressor to heat air for use in a hypersonic wind tunnel. The effect of real gas properties on the compression process is included in this discussion.

It is shown that the dispersion of a substance, with molecular diffusivity κ, in a stationary, homogeneous, turbulent velocity field can be formulated in terms of a ‘substance auto-correlation function’, this being a generalization of the well-known Lagrangian correlation between the velocity of a fluid particle at different times. It is found that the interaction between the molecular diffusion and the turbulent motion reduces the dispersion from the value it would have if the processes of molecular and turbulent diffusion were independent and additive. The conflict, between the results obtained in this paper and previous results which implied that the interaction increases the dispersion, is resolved. The ratio, of the contributions to the dispersion from the interaction term and the turbulent diffusion term, is obtained for comparatively large times by the use of intuitive arguments, and is found to be inversely proportional to the Prandtl number and a Reynolds number of the turbulence.

The plane, steady, laminar vortex flow of a viscous, heat-conducting perfect gas is treated. Simple relations are obtained for the flow quantities in the irrotational vortex, for arbitrary Prandtl numbers. When the Prandtl number is ½, the irrotational vortex is also isentropic. When the temperature dependence of the viscosity coefficient is taken into account, the vortex flow is rotational. An exact solution for the rotational vortex is obtained which is suitable for numerical evaluation by successive approximations. Distributions of velocity, temperature, pressure, density, and stagnation temperature through the rotational vortex are given for a typical case.

In a previous paper (1953b) it was shown theoretically that just below the boundary layer at the surface of a free wave the mass-transport gradient should be exactly twice that given by Stokes's irrotational theory. The present paper describes careful experiments which confirm the higher value of the gradient.

The results have an implication for any oscillatory boundary layer at the free surface of a fluid; such a boundary layer must generate a second-order mean vorticity which diffuses inwards into the interior of the fluid.

This paper considers the slow motion of a sphere, permanently and uniformly magnetized in one direction, in a viscous electrically conducting medium. The line of the magnetic poles is assumed to be parallel to the direction of the motion of the sphere. The velocity and pressure fields are calculated by two iterations. The distortion of the magnetic field is also calculated. An expression is obtained for total drag due to the viscous, pressure and magnetic forces.