Instability of stationary flows with constant vorticity in vessels of elliptical cross section
Abstract
The problem of the stability of stationary flows of an ideal incompressible fluid in vessels of elliptical cross section is analyzed for the case where the main flow velocity field is a linear function of the coordinates and the vorticity is constant. The spectral problem for linear perturbations is solved by the method of successive approximations. The instability of the flows is demonstrated to a first approximation. The particular case of flow in a triaxial ellipsoid is examined in detail. The flow stability problem examined here is relevant to the study of the properties of fluidfilled gyroscopes and of the behavior of the nuclei of stars and planets.
 Publication:

Prikladnaia Matematika i Mekhanika
 Pub Date:
 June 1986
 Bibcode:
 1986PriMM..50..369V
 Keywords:

 Flow Geometry;
 Flow Stability;
 Ideal Fluids;
 Incompressible Flow;
 Steady Flow;
 Gyroscopes;
 Iterative Solution;
 Perturbation Theory;
 Vessels;
 Fluid Mechanics and Heat Transfer