  We develop a new nonlinear stability method, the Energy-Enstrophy (EZ)
method, that is specialized to two-dimensional hydrodynamics; the method is
applied to a beta-plane flow driven by a sinusoidal body force, and retarded by
drag with damping time-scale mu^{-1}. The standard energy method (Fukuta and
Murakami, J. Phys. Soc. Japan, 64, 1995, pp 3725) shows that the laminar
solution is monotonically and globally stable in a certain portion of the
(mu,beta)-parameter space. The EZ method proves nonlinear stability in a larger
portion of the (mu,beta)-parameter space. And by penalizing high wavenumbers,
the EZ method identifies a most strongly amplifying disturbance that is more
physically realistic than that delivered by the energy method. Linear
instability calculations are used to determine the region of the
(mu,beta)-parameter space where the flow is unstable to infinitesimal
perturbations. There is only a small gap between the linearly unstable region
and the nonlinearly stable region, and full numerical solutions show only small
transient amplification in that gap.

Fluid Dynamics;Chaotic Dynamics;Atmospheric and Oceanic Physics;Geophysics