Approximate inertial manifolds for the 2d model of atmosphere

In order to understand the mechanism of long term weather prediction and climate, we construct explicitly in this paper an infinite number of approximate inertial manifolds M _j,m for the 2D model of large scale atmosphere to approximate the global attractor of the model. Associated with each manifold, there exists a thin neighborhood of it, into which the orbits of the model enter with a finite time. These neighborhoods contain and localize the global attractor. The thickness of these neighborhoods decreases with increasing m for a fixed j. Moreover we also obtain the time analyticity of the solutions of the model and the behavior of the small structures.