Attractor Dimensions of Three-Dimensional Navier-Stokes-α Model for Fast Rotating Fluids on Generic-Period Domains: Comparison with Navier-Stokes Equations
Abstract
The three-dimensional Navier-Stokes-α model for fast rotating geophysical fluids is considered. The Navier-Stokes-α model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian averaging and tend to the Navier-Stokes equations as α→ 0+. We estimate upper bounds for the dimensions of global attractors and study the dependence of the dimensions on the parameter α. All the estimates are uniform in α, and our estimate of attractor dimensions remain finite when α→ 0+.
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