Algebraization of 2-D Ideal Fluid Hydrodynamical Systems and Their Finite-Mode Approximations

Abstract

Starting from the description of ideal 2-D hydrodynamics in the framework of the Lie algebra of area-preserving diffeomorphisms sdiff two observations are made: 1st — this construction may be generalized by means of the central extension of the latter algebra, giving equations equivalent to variants of the vorticity equation on the β-plane; 2nd — a regular way to obtain finite-mode analogs of 2-D hydrodynamical equations preserving the essential algebraic features of these latter exists due to the relation between sdiff and su(N), N— ≻ ∞, algebras recently pointed out in literature.