Abstract
The stability properties of the two-dimensional flows with the bottom-friction effect are summarized in this review. On the quasi-two-dimensional (Q2D) approximation the dynamics of these flows is described by the 2D Navier-Stokes equation with the linear damping term proportional to the horizontal velocity which originates from the vertical boundary layer on the bottom. Three kinds of stability : the linear stability, the weakly nonlinear stability and the nonlinear stability by the energy method are considered. The linear critical Reynolds number and the wavenumber of the most unstable mode are virtually independent of the form of the velocity profile while the Landau coefficient is sensitive to it. Difference between both linear and nonlinear critical Reynolds numbers is relatively small when the bottom-friction is sufficiently large.
