BEHAVIOR OF N-MODE TRUNCATED NAVIER-STOKES EQUATIONS WITH EXTERNAL FORCE ACTING ON VARIOUS MODES

The fixed points of N-mode truncated Navier-Stokes equations on a two- dimensional torus with force acting on various modes are investigated. Their behavior is rather different. If the absolute value of the wave vector for the excited mode (Absolute value of k) is small, behavior of the fixed point P0 (to be defined in the text) approaches a limit w ithout involving many modes. If Absolute value of k is large enough, i n order to get a stabilized behavior, a great number of modes must be considered. Furthermore, when two or more modes are present in the ext ernal force, the behaviour of the truncated equations is rather differ ent from that of the truncated system with one mode excited directly o nly. In many models there is no fixed point P0 at all.