  We investigate generalized Navier-Stokes (GNS) equations that couple
nonlinear advection with a generic linear instability. This analytically
tractable minimal model for fluid flows driven by internal active stresses has
recently been shown to permit exact solutions on a stationary two-dimensional
sphere. Here, we extend the analysis to linearly driven flows on rotating
spheres. We derive exact solutions of the GNS equations corresponding to
time-independent zonal jets and superposed westward-propagating Rossby waves,
qualitatively similar to those seen in planetary atmospheres. Direct numerical
simulations with large rotation rates obtain statistically stationary states
close to these exact solutions. The measured phase speeds of waves in the GNS
simulations agree with analytical predictions for Rossby waves.
