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Numerical Simulation of a Spanwise
Vortex in a Periodic Forced Flow
E.J. López-Sánchez and G. Ruíz Chavarría
Abstract
In geophysical flows, vortices are present at very different scales. Examples
of them are the meddies, formed at the outlet of the Mediterranean Sea or the vor-
ticity dipoles, occurring when water flushes from a channel into the open sea. In
this paper we investigate the formation and the evolution of a spanwise vortex in
the latter system, when a periodic forcing is imposed. To this end the Navier-Stokes
and continuity equations are solved with a finite volume code (OpenFOAM 2008).
The numerical solution has been obtained for a Reynolds number
Re
=
,
1
000 and
=
.
a Strouhal number
S
02. For comparison, we carried a simulation in a flow
produced by a single pulse. We have found that the spanwise vortex appears in front
of the dipole. It detaches from the bottom and moves away. When flow is produced
by a pulse, this vortex has a horseshoe shape, while for a periodic forcing flow, the
shape of the spanwise vortex evolves in time.
0
1 Introduction
When a fluid leaves a channel and flushes into an open domain the vorticity produced
into the channel leads to the formation of two counter rotating eddies. This pair of
vortices is a coherent structure, known as dipole, which moves away due to its self
induced velocity. The properties of the dipole depend on parameters as the Reynolds
number, the aspect ratio (the quotient of fluid layer depth to the dipole size) and
the Strouhal number. This kind of structures has been the aim of previous works.
For instance, Chaplygin (
2007
) has modeled a 2D dipole in a different way than
considering just two point vortices. The velocity field of the Lamb-Chaplygin dipole
is such that vorticity is different from zero only inside a circle of radius
R
. Earlier on,
Wells and Heijst (
2003
) modeled in two dimension the evolution of a dipole under
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