Stability and instability of generalized Kolmogorov flows on the two-dimensional sphere

Abstract

The Navier--Stokes equations on the two-dimensional rotating sphere with a family of forcing terms, whose stream functions are the Legendre polynomials $P_s$, are considered. The stability and instability properties of the corresponding generalized Kolmogorov flows are studied both analytically and numerically. Logarithmically sharp lower bounds for the dimension of the global attractor are obtained. The effect of rotation on the stability properties of the Kolmogorov flows is discussed.