The evolution of an intense barotropic vortex on the beta -plane is analyse
d for the case of finite Rossby deformation radius. The analysis takes into
account conservation of vortex energy and enstrophy, as well as some other
quantities, and therefore makes it possible to gain insight into the vorte
x evolution for longer times than was done in previous studies on this subj
ect. Three characteristic scales play an important role in the evolution: t
he advective time scale T-a (a typical time required for a fluid particle t
o move a distance of the order of the vortex size), the wave time scale T-w
(the typical time it takes for the vortex to move through its own radius),
and the distortion time scale T-d (a typical time required for the change
in relative vorticity of the vortex to become of the order of the relative
vorticity itself). For an intense vortex these scales are well separated, T
-a much less than T-w much less than T-d, and therefore one can consider th
e vortex evolution as consisting of three different stages. The first one,
t less than or equal to T-w, is dominated by the development of a near-fiel
d dipolar circulation (primary beta -gyres) accelerating the vortex. During
the second stage, T-w less than or equal to t less than or equal to T-d, t
he quadrupole and secondary axisymmetric components are intensified; the vo
rtex decelerates. During the last, third, stage the vortex decays and is de
stroyed. Our main attention is focused on exploration of the second stage,
which has been studied much less than the first stage. To describe the seco
nd stage we develop an asymptotic theory for an intense vortex with initial
ly piecewise-constant relative vorticity. The theory allows the calculation
of the quadrupole and axisymmetric corrections, and the correction to the
vortex translation speed. Using the conservation laws we estimate that the
vortex lifetime is directly proportional to the vortex streamfunction ampli
tude and inversely proportional to the squared group velocity of Rossby wav
es. For open-ocean eddies a typical lifetime is about 130 days, and for oce
anic rings up to 650 days. Analysis of the residual produced by the asympto
tic solution explains why this solution is a good approximation for times m
uch longer than the expected formal range of applicability. All our analyti
cal results are in a good qualitative agreement with several numerical expe
riments carried out for various vortices.