At sufficiently high temperature the oxygen and nitrogen molecules in air dissociate into atoms. Energy is required for this decomposition and, furthermore, if the temperature is not uniform, concentration gradients are formed and energy is transferred by the consequent interdiffusion of atoms and molecules. In this paper, a simple model of a gas is formulated to illustrate the effect of these processes on heat transfer in three situations: (1) in a layer of gas at rest between two walls at different temperature, (2) in Couette flow, and (3) in a laminar boundary layer on a flat plate.

In the model, the law for the rate of reaction (dissociation and recombination) is of an especially simple form with the speed of reaction characterized by a single parameter. When the parameter becomes large, the gas approaches chemical equilibrium; at the other extreme, no reaction occurs within the gas.

Two chemical conditions of the walls are considered, one being that the walls are catalytic (the surface reaction rate is assumed sufficiently high to hold the gas at the wall in chemical equilibrium), and the other that the walls have no effect on the reaction, i.e. they are non-catalytic.

The most important of the simplifications made are: (a) The reaction rate law is put in a form in which the equilibrium concentration of atoms varies linearly with temperature. Thus, there is only one temperature at which the gas is undissociated instead of the actual range of temperature. (b) In problems (1) and (2), μ, κ, and ρD are taken to be constant. (c) In problem (3) the Lewis number is assumed to be unity. (d) Only binary mixtures of atoms and molecules are considered (so that ionization and more complex dissociation processes are not covered). (e) Coupling of irreversible flows, such as that causing thermal diffusion, is neglected. (f) Only problems in which the pressure is constant are considered.

The approximate Tricomi equation relevant to sonic speed of two-dimensional small-distrubance flow is solved by separation of variables, where these are certain stipulated functions of the Cartesian velocity perturbations. The symmetric flow patterns obtained from this solution are shown to correspond to those about half-bodies, whose ordinates vary as xn where 0·4 &\les n,<1, and x is the distance along the plane of symmetry. The surface pressures on such bodies are deduced.

In particular, the body whose ordinates vary as $x^{2|5}$ has a sonic surface velocity, except at the nose, where an edge-force which causes a drag force is shown to exist. On the assumption that a free-stream breakaway (at sonic velocity) occurs at the shoulder of a body, this solution thereby yields the flow about an aerofoil of the same shape having a flat base. This bluff-nosed section has only a little more than half the drag of a wedge on the same chord and base.

This paper describes an experimental investigation of the form of the large scale motions in turbulent flow. These motions have been found to be more ordered than has usually been supposed and their origin and dynamics are discussed in terms of physical models of typical eddies.

Nine components of the double velocity correlation tensor have been measured at a number of positions in the wake of a circular cylinder and in a ‘flat plate’ boundary layer. These have been supplemented by measurements of correlations with separations in directions other than the axial ones. In the wake, the correlations at large values of the separation are explained in terms of two types of large scale motion. One of these is a pair of vortices, side by side and rotating in opposite directions with axes aligned approximately normal to the plane of the wake. The other typical motion is a series of jets in which turbulent fluid is projected outward from the core of the wake. It is suggested that these are the result of an instability of the turbulent shear stress. A qualitative explanation of the apparent structural equilibrium of the wake is given in terms of this instability. The vortex pair eddies were not found in the boundary layer but there is evidence of jets much like those in the wake.

Correlations measured in grid turbulence have been found to be highly anisotropic and consistent with the presence of vortex pair eddies. When a plane strain was applied to grid turbulence, the effect on the correlations suggested the presence of a stress instability similar to that postulated for the wake.

A hydromagnetic shock tube has been used to obtain an approximate measurement of the time to reach equilibrium ionization behind shock waves of Mach number 11 to 17, moving into air at a pressure of about 1 mm of mercury. This ionization time decreases with increasing Mach number. Experimental results are presented as a graph of the ionization time vs Mach number. The principal source of error in the measurements is the attenuation of the shock and the results indicate a lower limit for the ionization time in air.

A theoretical treatment is presented for the slow flow of a viscous fluid through a cylindrical container within which a small spherical particle is confined. The sphere is situated in an arbitrary position within the cylinder and moves at constant velocity parallel to the walls. Approximate expressions are derived which give the frictional drag, rotational couple, and permanent pressure drop caused by the presence of this obstacle in the original Poiseuillian field of flow. The primary parameters involved are the ratio of sphere to cylinder radius and fractional distance of the particle from the longitudinal axis of the cylinder. With appropriate modifications, the results are also applicable to a sphere settling in a quiescent fluid. This yields the necessary boundary corrections to Stokes law arising in connection with devices such as the falling ball viscometer when the sphere is eccentrically located.

This paper considers the stabilizing effect of density stratification on the horizontal shear layer between two parallel streams of uniform velocities. A simple continuous velocity distribution, $U = V\; \rm {tanh}(y|d)$, is used to represent the laminar shear layer. The density of the fluid is assumed to vary as exp (-βy), y being the vertical coordinate, with a small total change in density across the shear layer. The fluid is unbounded, and is assumed to be inviscid, incompressible and under the action of gravity.

By the methods of hydrodynamic stability theory, it is shown that a disturbance of small amplitude and wave-number α is neutrally stable if the Richardson number, defined as $J = g\beta d^2|V^2$, has the value $\alpha ^2 d^2 (1 - \alpha^2 d^2)$, and the form of the neutral disturbance is obtained. It follows that the critical Richardson number is $\frac{1}{4}$, so that the flow is stable if $J\;\; \textgreater \;\; \frac{1}{4}$. The relation between these results and Goldstein's derivation of the same critical Richardson number for a flow with discontinuous velocity and density gradients is discussed.