On a domain enclosed by no-slip boundaries, two-dimensional, geostrophic flows have been studied by numerical simulations of the Navier-Stokes equation with the β-plane approximation at intermediate Reynolds numbers and a range of values for β. The β effect causes a refinement of the flow structures, and the presence of basin modes has been revealed by means of frequency spectra. The presence and apparent stability of basin modes on a domain enclosed by no-slip boundaries is a rather surprising observation, because these modes are solutions of the inviscid flow equations on a bounded domain (with free-slip boundaries). To understand the persistence of these basin modes, the viscous boundary layers near the no-slip walls have been investigated. The mean flow in forced simulations shows a zonal band structure, much unlike the regular Fofonoff-like solution observed when free-slip boundary conditions are used.