In the mixing of a jet with a cross-stream, it is found that in the near field, defined as the region of the flow from the jet exit to a distance of a few diameters downstream of this exit, a considerable amount of dynamical adjustment takes place. This near-field region characterizes the subsequent behaviour and development of the jet, its wake and the cross-stream in the vicinity of this mixing region. The rapid evolution of the flow gives rise to a pair of bound vortices attached to the lee side of the jet boundary, to fast development of the turbulent and mean vorticity, to a vortex-shedding system, and to the largest rates of entrainment of cross-stream flow into the jet. Furthermore, it is found that the geometrical configuration of the boundaries at the jet exit plays an important role in the mixing and development processes.An intrinsic method is proposed for the delineation of the flow boundaries between the jet and the cross-stream. Calculations of mass, momentum and vorticity fluxes have been made. The vorticity flux gives evidence of the rapid stretching and tilting of the vorticity vector field in the near-field region.

The connection between the dipole moment function (dipole moment as a function of internuclear distance), M(u), and its matrix elements has been studied for the one-dimensional model of a diatomic molecule. It is shown that M(u) is completely determined by a single row or column of the matrix 〈v | M(u) | v′〉, but that the diagonal matrix elements do not completely determine M(u). Attention is given to the problem of approximating M(u) when a finite number of matrix elements are known. The usual method (called by us the ``polynomial approximation'') is compared with a new approximation scheme which we call the ``wave function approximation.'' These methods are equivalent for a harmonic oscillator, but not in general. Estimates of the errors of the two methods are obtained in the case where the anharmonicity of the potential is small. The ``wave-function expansion'' of M(u) which is developed and used to carry out the calculations is a new way of relating matrix elements to M(u) which makes it much easier to calculate the dipole moment function from its matrix elements. This method has been used to obtain explicit formulas relating the dipole moment function to its matrix elements for the harmonic oscillator and for the Morse oscillator.

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The shedding of atmospheric vortex streets from mountain peaks has been simulated in the wakes of several shapes of circular cones and one combination of two such cones placed in the uniform, unstratified flow of a wind tunnel. Conditions for vortex shedding are more favorable the steeper the slopes of the peaks. From the laboratory measurements and with the assumption of Reynolds number independence, predictions are made of the periodicities of vortex shedding from six volcanic peaks whose periodicities of vortex shedding have been determined by others from satellite photographs of wake clouds. The predicted periods agree with the measured periods in three cases and are significantly smaller in three cases. For the latter cases it is concluded that stratification has so altered the atmospheric flow that either the Strouhal number has been lowered or the barrier effect of the topographic obstacle has been considerably enhanced. It is also concluded that stratification sufficient to reduce turbulence is necessary for the existence of an extended atmospheric vortex street.