Using a barotropic model in spherical geometry, we construct new
solutions for
steadily travelling vortex pairs and study their stability properties.
We consider pairs
composed of both point and finite-area vortices, and we represent the rotating
background
with a set of zonal strips of uniform vorticity. After constructing the
solution
for a single point-vortex pair, we embed it in a rotating background, and
determine
the equilibrium configurations that travel at constant speed without changing
shape.
For equilibrium solutions, we find that the stability depends on the relative
strength
(which may be positive or negative) of the vortex pair to the rotating
background:
eastward-travelling pairs are always stable, while westward-travelling
pairs are unstable
when their speeds approach that of the linear Rossby–Haurwitz waves.
This
finding also applies (with minor differences) to the case when the vortices
are of finite
area; in that case we find that, in addition to the point-vortex-like instabilities,
the
rotating background excites some finite-area instabilities for vortex pairs
that would
otherwise be stable. As for practical applications to blocking events,
for which the
slow westward pairs are relevant, our results indicate that free barotropic
solutions
are highly unstable, and thus suggest that forcing mechanisms must play
an important
role in maintaining atmospheric blocking events.
Entrapping of a vortex pair interacting with a fixed point vortex revisited. I. Point vortices
