Note on the emergence of large scale coherent structure under small scale random bombardments: The discrete case

We continue our study on mathematical justification of the emergence of large scale coherent structure in a two dimensional fluid system under small scale random bombardments. We treat the case of small scale random bombardments at discrete times which is different from our earlier work [Commun. Pure Appl. Math. 59, 467 (2006)], where we approximated the small scale random kicks by a continuous in time random process. In the absence of geophysical effects, the large scale structure emerging out of the small scale random forcing is the same as the case of continuous in time forcing that we studied before.