Finitedimensional approximation of the motions of incompressible fluids within an ellipsoid
Abstract
The motion of an inviscid incompressible liquid in an ellipsoid is studied. The accuracy of a description of such motion is primarily determined by how well the active modes have been taken into account by the model. A system of ordinary differential equations is used to formulate an approximation of hydrodynamics. This approximation reduces the problem to the choice of a system of reference fields along which the expansion is constructed. Field velocity is determined by a polynomial representation of coordinates. The rotational stability of a liquid around one of the major axes of an ellipsoid is studied using the system of equations which has been developed. It is shown that in the first approximation the development of instability may be described within the framework of a three or fivemode model dependent on ellipsoidal parameters.
 Publication:

Akademiia Nauk SSSR Fizika Atmosfery i Okeana
 Pub Date:
 August 1977
 Bibcode:
 1977FizAO..13..820G
 Keywords:

 Approximation;
 Ellipsoids;
 Galerkin Method;
 Incompressible Fluids;
 Inviscid Flow;
 Rotating Liquids;
 Differential Equations;
 Flow Stability;
 Flow Velocity;
 Hydrodynamic Equations;
 Fluid Mechanics and Heat Transfer