NAVIER-STOKES EQUATIONS ON THE β-PLANE

We show that, given a sufficiently regular forcing, the solution of the two-dimensional Navier-Stokes equations on the periodic beta-plane (i.e. with the Coriolis force varying as f(0) + beta(y)) will become nearly zonal: with the vorticity omega(x, y, t) = (omega) over bar (y, t) + (omega) over tilde (x, y, t), one has vertical bar(omega) over tilde vertical bar(2)(Hs) <= beta(-1) M-s(...) as t -> infinity. We use this show that, for sufficiently large beta, the global attractor of this system reduces to a point.