Previous theoretical work has shown that, in an unbounded domain,
anticyclones are prohibited from splitting on their own due to
limitations imposed by the conservation of angular momentum. By
explicitly considering the role of angular momentum exchange between
eddies and boundaries (neglected by previous theories), splitting
criteria for an anticyclonic lens colliding with a long and thin
island are established analytically. The inviscid analytical model
consists of an isolated patch of fluid in a reduced gravity
regime. Nonlinear analytical solutions are constructed by connecting
the initial and final states using conserved quantities.
For the conceptual case of a lens pierced by a thin moving wall, the
result is that, in order for a zero potential vorticity lens to split
into two equal offspring, the wall length must be at least 1.19 of the
lens′ radius. Even for infinitesimal splitting, which arises from weak
collisions (where the wall merely ``brushes′′ the lens), the wall must
be the order of the radius. This is because the ``parent′′ lens can
split into two offspring only when the wall allows sufficient
spreading of the lens, which increases its relative angular momentum,
and thereby enables the lens to form two distinct ``offspring.′′
Numerical experiments employing Lagrangian floats reveal that the
splitting is accomplished by a jet that leaks fluid along the wall,
forming a second lens. The fluid initially found along the rim of the
parent lens occupies both the core and the rim of the second lens; the
fluid found at an intermediate radius in the second lens is derived
from fluid situated at an intermediate radius in the parent lens. In
general, a very good agreement between the numerics and the analytical
theory is found. The numerical simulations demonstrate that the
integrated angular momentum is a far stronger constraint than energy
conservation. Using the numerics, we extend the moving wall theory to
the splitting of finite vorticity lenses and lenses on a β-plane. We find
that the basic requirement of mass redistribution by a wall is
relevant in all the regimes that we examined, and, therefore, is
likely to also be relevant to collisions of eddies with actual
islands. This supports our application of the theory to Meddy
splitting by seamounts, where we find that the seamounts can provide
the necessary torque for recently observed Meddy splitting and
destruction.
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