International Journal of Mathematics and Mathematical Sciences 
Volume 28 (2001), Issue 6, Pages 313-320
doi:10.1155/S0161171201012443

Ergodicity of stochastically forced large scale geophysical flows

Jinqiao Duan1 and Beniamin Goldys2

 1Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616, IL, USA
2School of Mathematics, The University of New South Wales, Sydney 2052, Australia
Received 30 March 2001

Abstract

We investigate the ergodicity of 2D large scale quasigeostrophic flows under random wind forcing. We show that the quasigeostrophic flows are ergodic under suitable conditions on the random forcing and on the fluid domain, and under no restrictions on viscosity, Ekman constant or Coriolis parameter. When these conditions are satisfied, then for any observable of the quasigeostrophic flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long.