Perferred Equilibrium Solutions of the Barotropic Vorticity Equation

The long term behavior of the barotropic vorticity equation (BVE), which benefits to understand the long term climate variations, has been investigated by applying an explicit quadratic conserved finite difference integration scheme. Results suggest an initial pattern predominated at the beginning time evolves to an equilibrium states after a long transition period in which the conserved prerequisites such as the integral kinetic energy, square vorticity and vorticity are broken by accumulated errors. This could lead the BVE indeterministic. Similar phenomena could reappear in integration cases starting at same initial pattern with different small perturbations, different initial patterns, time and grid intervals, and difference schemes. The eventual equilibrium states for the above cases are different from each other but spatially similar. They all possess a single wave structure in the horizontal plane but with random phases. The results further imply that despite indeterministic due to nonlinearity the long term behavior of the BVE is deterministic in spatial structure, shedding light on the long term climate change studies.