- 01-157 Igor Chueshov, Jinqiao Duan and Bjorn Schmalfuss
- Probabilistic Dynamics of Two-Layer
Apr 25, 01
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Abstract. 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.
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.