Stability criteria for quasigeostrophic forced zonal flows; I. Asymptotically vanishing linear perturbation energy

This paper opens a series of studies regarding stability criteria for quasi- geostrophic forced zonal flows in the presence of lateral diffusion and bottom dissipation of the vertical vorticity. The criteria, implying the asymptotic vanishing of the perturbation kinetic energy, are expressed in terms of the maximum shear of the basic flow and/or its meridional derivative and they are independent on the perturbation wavenumber. Some stability regions are enlarged with respect to some linear asymptotic stability criteria found in the literature. A comparison with the inviscid case is made.