A study was made of the laminar-turbulent transition of a wake behind a thin flat plate which was placed parallel to a uniform flow at subsonic speeds. Experimental results on the nature of the velocity fluctuations have made it possible to classify the transition region into three subregions: the linear region, the non-linear region and the three-dimensional region.

In the linear region there is found a sinusoidal velocity fluctuation which is antisymmetrical with respect to the centre-line of the wake. The frequency of fluctuation is proportional to the $\frac {2}{3}$ power of the free-stream velocity, and the amplitude increases exponentially in the direction of flow. The behaviour of small disturbances in the linear region was investigated in detail by inducing velocity fluctuation with an external excitation—actually sound from a loudspeaker. Solutions of the equation of a small disturbance superposed on the laminar flow were obtained numerically and compared with the experimental results. The agreement between the two was satisfactory.

When the amplitude of fluctuation exceeds a certain value, the growth rate deviates from being exponential due to non-linear effects. Although velocity fluctuations in the non-linear region are still sinusoidal and two-dimensional, the experimental results on the distributions of amplitude and phase indicate that the flow pattern may be described by the model of a double row of vortices. This configuration lasts until three-dimensional distortion takes place in the final subregion, the three-dimensional region, in which the fluctuation loses regularity and gradually develops into turbulence without being accompanied by abrupt breakdown or turbulent bursts.

The behaviour of a natural convection plume above a line fire is studied both theoretically and experimentally. In the theoretical treatment, a turbulent plume above a steady two-dimensional finite source of heated fluid in a uniform ambient fluid is investigated. By the use of the lateral entrainment assumption, a quadrature solution has been obtained for each of two separate ranges of a source Froude number, F < 1 or F > 1. In neither of these cases can the finite width line source be accurately represented by an equivalent mathematical line source at a lower level. Only the special case, F = 1, can be so represented and its solution is discussed.

In the experimental treatment, hot gases, resulting from the burning of a liquid fuel in a long channel burner, are driven upwards by buoyancy and gradually cooled down by the entrainment of ambient air. The average temperature along lines parallel to the channel burner was measured by a piece of resistance wire. For the case of a non-luminous diffusion flame, the effective radiation loss to the surroundings was assumed to be negligible, and,by a comparison of the energy flux supplied from the fuel and the energy flux contained in the plume, the characteristic turbulence entrainment coefficient is determined. By the alternate use of either an absorbing or a reflecting surface for the table-top surrounding a luminous flame, a measurement was made of the energy radiated from the flame that was intercepted by the fire surroundings and subsequently returned to the buoyancy plume by heating the ingested air. These measurements agree with estimates computed from such data as are available. The experimental results relating to the behaviour of the convection plume agree closely with the theoretical predictions in all cases.

Isolated masses of a dense aqueous solution (i.e. thermals) were released at the surface of a freshwater layer overlying one of salt water. While the whole of a thermal remained in the upper layer, the equations $z = n_1r, \; z^2 = k_1t$, with $k_1 = C_1 n_1^{\frac {3}{2}}(Mg| \rho)^{\frac {1}{2}}$, were obeyed, where z is the distance travelled, 2r the width of the thermal, t the elapsed time, M the mass excess (the difference between the masses contained within and displaced by the thermal while in the upper layer), and ρ the density of the displaced fluid. n1 was constant for any one thermal, but varied between thermals over the range 1·9 to 7·5. C1 had roughly the same value (0·73) for all thermals.

The behaviour after the leading extremity of the thermal (the ‘front’) entered the lower layer depended on the value of the parameter S = Vρ/M, where Δρ is the density difference between the upper and lower layers and V is the volume of the thermal when the widest part is at the level of the discontinuity. It was found that Y = 0 if S = β (‘weak’ thermals), and Y = 0·95−½S if 0·1 < S [les ] β (‘strong’ thermals), where Y is the fraction of the mass of the substance released which penetrated indefinitely into the lower layer. The constant β was approximately equal to 1.90.

In weak thermals, the equation z − s = a1(t − ts)2 was obeyed while the front was in the lower layer, until the cluminating point z = s was reached at t = ts. The acceleration a1 was always negative, and constant for any one thermal, but varied between thermals. Also for weak thermals, $x = C_2 V^{\frac {1}{3}}|S$, where x is the distance from the interface to the culminating point and C2 is a constant. C2 was approximately equal to 3·5. For strong thermals, the distance travelled while the front was in the lower layer obeyed the equation z2 = k2t. The origins of z and t usually differed from those found in the upper layer, and generally k2 ≠ k1.

The effect of combustion or heating on a slightly non-uniform flow in a tube of constant radius is explored by examining a simplified model, in which a density decrease occurs across a plane actuator-disk normal to the axis of the tube. The flow is considered to be steady, axi-symmetric, incompressible and inviscid and to originate at an injector-plate which is situated upstream of the disk. This paper analyses and discusses the effects caused by the density decrease when the velocity of flow through the injector-plate has a fractional non-uniformity ue, when there is a curvature θe, of the injector-plate, and when the density decrease has a fractional non-uniformity δ2. It is shown that the non-uniformity of the flow far downstream of the disk caused by the disturbances ue and θe is diminished by the density decrease; while that due to the disturbances δ2 is increased, unless the density decrease occurs close to the injector-plate. The distance separating the injector-plate and actuator-disk is found to be an important parameter. When this distance is small, compared to the radius of the tube, and the density decrease is severe, a small disturbance ue, θe or δ2 may set up a pressure variation at the injector-plate of many times the inlet dynamic pressure of the flow. It is conjectured that this pressure variation could affect the uniformity of velocity and composition of the flow through the injector-plate, and thus cause the disturbances ue and δ2 to grow or diminish.

Local solutions are found for the inviscid shear flow past an acute corner (of included angle [les ] ½π on the side of the fluid) on an otherwise arbitrary boundary. Unlike irrotational ‘corner flows’, these solutions are determinate locally, provided that the vorticity is known. Under certain circumstances the existence of a corner eddy may be inferred.

The power specturm of a passive scalar contaminant undergoing a first-order chemical reaction and isotropic turbulent mixing is deduced for three different spectral ranges: (i) the inertial-convective range; (ii) the viscous-convective and viscous-diffusive ranges for very large Schmidt number; (iii) the inertial-diffusive range for very small Schmidt number. The analysis is restricted to stationary, locally isotropic fields, and to systems so dilute that the heat of reaction has no effect on the reaction rate.

A theory is developed for the incompressible flow of a fluid with high electrical conductivity about thin cylinders (airfoils) in non-uniform motion. A uniform magnetic field is applied parallel to the free stream and solutions are obtained subject to the restriction of small perturbations. The effects of viscosity are included, for the most part, only through the use of the Kutta condition, where applicable, for lifting airfoils. The validity and range of applicability of the infinite-conductivity assumption are determined on the basis of an order-of-magnitude analysis; the general character of the flow is discussed at length.

The flow-field for infinite conductivity is changed from the non-magnetic case only through the new transport speed of vorticity; the forces on the airfoil are changed due to surface currents. For the case of the Alfvén speed less than the free-stream speed, the airfoil lift and pitching moment are given in integral form for general unsteady-airfoil motion and are given in closed form for harmonic ocsillations. The forces at moderate frequencies may be larger than in the corresponding non-magnetic case. The response to a unit-step change in the downwash is studied and the asymptotic form of the lift is obtained for small and large time.

For the case of the Alfvén speed greater than the free-stream speed, vorticity and current are shed from both the leading and trailing edges. Therefore the extension of the usual Kutta condition is not obvious. It is shown that if finite viscosity and / or conductivity tend to remove the trailing-edge singularity, the flow is unstable and no steady flow can be obtained.

1. The diffusion terms in the mean velocity and temperature equations of turbulent flow are analysed to decide when variations of fluid properties can produce appreciable errors.

2. A theoretical demonstration is given that in the mean-flow continuity equation for a gas the error in assuming constant density is small if the flow is turbulent, even when the temperature variations are large.

3. Separate discussion is given of the case of local heat sources in turbulence, as large errors can occur there.

The flow about a spinning sphere moving in a viscous fluid is calculated for small values of the Reynolds number. With this solution the force and torque on the sphere are computed. It is found that in addition to the drag force determined by Stokes, the sphere experiences a force FL orthogonal to its direction of motion. This force is given by ${\bf F}_L = \pi a^3 \rho \Omega \times {\bf V}[1 + O(R)]$ .

Here a is the radius of the sphere, Ω is its angular velocity, V is its velocity, ρ is the fluid density and R is the Reynolds number, $R = \rho \mu ^{-1} Va$. For small values of R, the transverse force is independent of the viscosity μ. This force is in such a direction as to account for the curving of a pitched baseball, the long range of a spinning golf ball, etc. It is used as a basis for the discussion of the flow of a suspension of spheres through a tube.

The calculation involves the Stokes and Oseen expansions. A representation of solutions of the Oseen equations in terms of two scalar functions is also presented.

The shedding of vorticity from the edges of a plate, which is accelerated normal to itself from rest in still air, is investigated experimentally by means of a new flow-visualization technique using spark-lighted shadowgraphs and heated air, benzene or other vapours to introduce sufficient changes in density along the surface of discontinuity.

The photographs show small-scale undulations and the formation of a number of centres of vorticity along the well known big-scale vortex sheets which roll up along their edges.

A recent study of a laminar jet in a rotating spherical shell of fluid is extended to the case of a turbulent planetary jet at the equator of a rotating, stratified atmosphere or ocean. General forms of the velocity, density and pressure functions of both the mean motion and the turbulence are derived by a dimensional analysis applied to the mean and perturbation equations. The horizontal and vertical dimensions are estimated, based on the three characteristic constants of the problem, which are the momentum transfer, the stability and a rotation parameter. The estimates are in good agreement with the dimensions of the Cromwell current, i.e. the equatorial undercurrent of the Pacific Ocean.

To the first order of approximation, the mean axial velocity in the theory is independent of distance along the jet axis. The mean horizontal transverse velocity component is much smaller and decreases upstream. The mean vertical velocity is extremely small, also decreasing upstream. The two horizontal velocity components of the turbulence are of the same order and, in the undercurrent, are about one-fourth the mean axial velocity. The vertical turbulent component is much smaller. Finally, it is shown that the eddy-viscosity concept is inappropriate for this problem because at least one of the eddy coefficients would have to be negative.