Abstract:
The interaction between two co-rotating vortices, embedded in a steady
external strain field, is studied in a coupled Quasi-Geostrophic – Surface
Quasi-Geostrophic (hereafter referred to as QG-SQG) model. One vortex
is an anomaly of surface density, and the other is an anomaly of internal
potential vorticity. The equilibria of singular point vortices and their
stability are presented first. The number and form of the equilibria are
determined as a function of two parameters: the external strain rate
and the vertical separation between the vortices.
A curve is determined analytically which
separates the domain of existence of one saddle-point, and that of one
neutral point and two saddle-points. Then, a Contour-Advective Semi-Lagrangian
(hereafter referred to as CASL) numerical model of the coupled QG-SQG equations is used to
simulate the time-evolution of a sphere of uniform potential vorticity,
with radius $R$ at depth $-2H$ interacting with a disk of uniform density
anomaly, with radius $R$, at the surface. In the absence of external strain,
distant vortices co-rotate, while closer vortices align vertically, either
completely or partially (depending on their initial distance). With strain,
a fourth regime appears in which vortices are strongly elongated and drift
away from their common center, irreversibly. An analysis of the vertical
tilt and of the horizontal deformation of the internal vortex
in the regimes of partial or complete alignment is used to quantify the
three-dimensional deformation of the internal vortex in time.
A similar analysis is performed to understand the
deformation of the surface vortex.
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