  The two-layer quasigeostrophic flow model is an intermidiate system between
the single-layer 2D barotropic flow model and the continuously stratified, 3D
baroclinic flow model. This model is widely used to investigate basic
mechanisms in geophysical flows, such as baroclinic effects, the Gulf Stream
and subtropical gyres. The wind forcing acts only on the top layer. We consider
the two-layer quasigeostrophic model under stochastic wind forcing. We first
transformed this system into a coupled system of random partial differential
equations and then show that the asymptotic probabilistic dynamics of this
system depends only on the top fluid layer. Namely, in the probability sense
and asymptotically, the dynamics of the two-layer quasigeostrophic fluid system
is determinied by the top fluid layer, or, the bottom fluid layer is slaved by
the top fluid layer.
  This conclusion is true provided that the Wiener process and the fluid
parameters satisfy a certain condition. In particular, this latter condition is
satisfied when the trace of the covariance operator of the Wiener process is
controled by a certain upper bound, and the Ekman constant $r$ is sufficiently
large. Note that the generalized time derivative of the Wiener process models
the fluctuating part of the wind stress forcing on the top fluid layer, and the
Ekman constant $r$ measures the rate for vorticity decay due to the friction in
the bottom Ekman layer.
