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We obtain a logarithmically sharp estimate for the space-analyticity radius of the solutions of the damped-driven 2D Navier-Stokes equations with periodic boundary conditions and relate this to the small scales in this system. This system is inspired by the Stommel-Charney barotropic ocean circulation model.

On the domain of analyticity and small scales for the solutions of the damped-driven 2d Navier–Stokes equations