Accession Number : AD0000484


Title :   ON THE STABILITY OF SOME FLOWS OF AN IDEAL FLUID WITH FREE SURFACES


Corporate Author : BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS


Personal Author(s) : FOX, J L ; MORGAN, G W


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/000484.pdf


Report Date : Dec 1952


Pagination or Media Count : 140


Abstract : 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.


Descriptors :   *FUNCTIONS , STABILITY , ATTACK , EIGENVECTORS , ISOLATION , EIGENVALUES , VORTICES , CYLINDRICAL BODIES , CONFIGURATIONS , WALLS , PERTURBATIONS , FLUIDS , FLOW , PARALLEL ORIENTATION , EQUATIONS , GRAVITY WAVES , ELLIPSES , ORIFICES


Subject Categories : Theoretical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE