| This thesis is divided into three parts. In Part I a mechanism by which air bubbles may be entrapped in a liquid is considered. A number of processes in which air is entrained in a flow appear to involve the formation of a thin air film between a relatively fast liquid stream and a region of slow recirculation. Eventually, the film breaks into bubbles. Here, the possible causes for the breakup of the film are investigated. The linear stability of a vertical film of a viscous gas bounded by liquid in uniform motion on one side, and by liquid at rest on the other side, is studied. Instabilities are found that are controlled by two basic mechanisms. One is due to the velocity jump across the film and can be related to the usual Kelvin-Helmholtz instability. The second one is controlled by the viscosity jump across the air-liquid interfaces.;In Part II a method to determine steady, irrotational, two-dimensional free surface flows of an inviscid fluid in the presence of gravity, is described in detail. This method which is based on conformal mapping techniques and collocation, is applied to the case of supercritical flows produced by a line sink or source in a layer of fluid of finite depth. Limiting solutions characterized by a pair of points of stagnation at the free surface are calculated. In addition, near-limiting flows with a velocity slightly different from zero at the uppermost points of the free surface are computed. These results complete the set of solutions previously known.;Finally, in Part III a linear analysis of the effects of compressibility on the stability of two superposed isentropic fluids is presented. The results of the analysis are illustrated with several numerical examples. It is found that, in the present conditions, compressibility has a stabilizing effect at small wavelengths and a destabilizing effect at long wavelengths. The magnitude of these effects is however small in most circumstances. A physical basis for the interpretation of the results is also described in qualitative terms. |
