International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 6, Pages 313-320

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

Copyright © 2001 Jinqiao Duan and Beniamin Goldys. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.