On the stability of some flows of an ideal fluid with free surfaces

The stability of 4 types of 2-dimensional free-surface flows of an ideal fluid was investigated when subjected to small perturbations. The perturbations of a hollow vortex flow bounded by cylindrical walls were neutrally stable; the propagation of these perturbations is compared to the propagation of gravity waves in H2O. The impinging of a jet on a plate of finite width was also a stable configuration. A series of orifice flows had stable perturbations with the exception of an isolated unstable perturbation in flow through a Borda mouthpiece. The existence of unstable perturbations is indicated in the case of equal and opposite jets. The basic flow potential for a hollow vortex bounded by parallel plane walls is expressed in terms involving elliptical functions; the complexity of the equations made a solution intractable. The method of attack gave the upper bounds on Rl (lambda) rather than a 1-dimensional continuum of permissible eigenvalues and corresponding eigenfunctions.