We consider stability of a stationary solution of Kolmogorov flow with a bottom friction. Any solution of nonstationary problem which is periodic with respect to $x$, $y$ with periods $2\pi/\alpha$, $2\pi$ is shown to tend to the stationary solution as time tends to infinity when aspect ratio $\alpha$ is equal to or greater than 1.
"Stability of the Basic Solution of Kolmogorov Flow with a Bottom Friction." Tokyo J. Math. 33 (1) 65 - 72, June 2010. https://doi.org/10.3836/tjm/1279719578