Dynamics of near-shore vortices
2000
This work addresses two problems: 1) the dispersion induced by a cloud
of vortices near a straight coast-line when the bottom is flat and the coastal
boundary is a vertical plane or when the bottom is a planar slope; 2) the
dynamics of vortices moving over a planar sloping bottom.
Vortices near a vertical boundary are studied by the well-known method of
images. For a plane sloping bottom we describe and develop a model,
first introduced by Peregrine (1996) that uses a sector of a vortex ring to
model a vortex in a wedge of fluid, where the wedge is formed by the water
surface and by the planar sloping bottom. Numerical simulations using
these free-slip analytical models are used to investigate the dispersion of
vorticity and of a passive tracer induced by clouds of vortices. The results of
the two models are compared. The dispersion of vortices and particles is
mainly affected by the formation of vortex dipoles. The shoreline sets a
preferential direction for the dispersion process and the dispersion normal
to the shoreline is generally smaller, or bounded when the vortices forming
the dipole have different absolute circulation. The dispersion of particles is
generally smaller than the dispersion of vortices.
In the second part of this work the analytical model of Peregrine (1996) for
vortices moving over a planar slope at an angle a with the horizontal is
tested against a set of laboratory experiments. Experiments were made by
studying the dynamics of a vortex dipole moving towards a planar sloping
beach. We measured the minimum distance from the shoreline reached
by the vortices and their along-shore speed. The parameter ranges
examined were 3vortices). We find a good agreement between the
predictions and the observations when Re >~ 1500.
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