THE 3D QUASIGEOSTROPHIC FLUID DYNAMICS UNDER RANDOM FORCING ON BOUNDARY

Abstract

The three-dimensional baroclinic quasigeostrophic flow model has been widely used to study basic mechanisms in oceanic flows and climate dynamics. In this paper, we consider this flow model under random wind forcing and time-periodic fluctuations on fluid boundary (the airsea interface). The time-periodic fluctuations are due to periodic rotation of the earth and thus periodic exposure of the earth to the solar radiation. After overcoming the difficulty due to the low regularity of an associated Ornstein-Uhlenbeck process, we establish the well-posedness of the baroclinic quasigeostrophic flow model in the state space. Then we demonstrate the existence of the random attractors, again in the state space. We also discuss the relevance of our result to climate modeling