Navier-Stokes equations on the β-plane

الأصل · EN

We show that, given a sufficiently regular forcing, the solution of the two-dimensional Navier--Stokes equations on the periodic β-plane (i.e.with the Coriolis force varying as f₀+βy) will become nearly zonal: with the vorticity ω(x,y,t)=(y,t)+(x,y,t), one has ||ₕₛ²≤β⁻¹ Mₛ(..) as t→∞. We use this show that, for sufficiently large β, the global attractor of this system reduces to a point.