Geoscience Reference
In-Depth Information
chapter, which describe the evolution of a coastal current
in terms of large-amplitude shelf waves.
radii of the sources and sinks. The jet supported unsta-
ble Rossby waves with azimuthal wave numbers ranging
from 3 to 8.
Pierini et al.
[2002] analyzed Rossby normal modes over
a 2 m wide experimental slope connecting water depths of
30 and 60cm. The slope was confined by walls to a finite
length of 4.3 or 3.3m, and the tank was rotated with peri-
ods ranging from 30 to 50s. A paddle was used to drive
deep fluid gradually and barotropically onto the slope,
where it excited Rossby normal modes between the walls
confining the slope. The phases of these modes agreed well
with numerical solutions of a barotropic shallow-water
model, but their amplitudes exhibited some substantial
discrepancies.
Most recently,
Cohen et al.
[2010] generated topographic
Rossby waves in an experimental slope configuration sim-
ilar to that of
Caldwell et al.
[1972]. They constructed
an annular channel between radii of 1 and 6.5m, with
a fluid whose depth was uniform in the innermost 1.5m
and decreased linearly by 0.4m over the outermost 4m.
Shelf waves were excited by a radially oscillating paddle
of length 2 or 0.4m. The resulting wave velocities were
measured using particle imaging velocimetry. The disper-
sion relation and radial velocity of the experimentally
generated waves was found to agree closely with a the-
ory derived from the linearized barotropic shallow-water
equations.
Cohen et al.
[2012] performed similar experi-
ments in an annular channel between radii of 0.25 and
1m, with linear decrease in the depth from the center to
zero at the outer edge. Topographic waves were gener-
ated via three radially aligned paddles and compared with
linearized shallow-water theory. Approximating the conti-
nental boundary as a vertical wall, rather than a vanishing
ocean depth, was found to distort the frequencies in the
wave dispersion relation, resulting in disagreement with
the experimental results.
12.1.1. Shelf Waves
Ibbetson and Phillips
[1967] performed some of the ear-
liest laboratory experiments relevant to Rossby shelf wave
dynamics. They constructed a rotating annulus between
radii of 72.4 and 102.0 cm, similar to that described in
Section 12.2. A background PV gradient was provided
simply by the curvature of the free surface, required to
balance the centrifugal force. Rossby waves were gener-
ated by the oscillatory rotation of a vertical paddle posi-
tioned across the breadth of the channel, with periods
between 20 and 100 s. In an open annulus the damping
rate of the resulting Rossby waves was found to be of the
same order of magnitude as the theoretical prediction (see
Section 12.3.1). When a 60
◦
arc of the annulus adjacent
to the paddle was enclosed, the waves intensified at the far
boundary, equivalent to western boundary intensification
in the real ocean.
Caldwell et al.
[1972] performed the first experi-
ments that directly represented the continental slope and
deep ocean. They constructed an annular channel in
which the fluid depth increased exponentially with radius
over the inner half of its width and remained constant
over the outer half, following the theoretical approxima-
tion of
Buchwald and Adams
[1968]. Rossby shelf waves
were generated via one or two radially oscillating pad-
dles and visualized via aluminium tracer particles and
streak photography. The measured dispersion relation for
the waves was found to agree closely with the linear the-
ory of
Buchwald and Adams
[1968].
Caldwell and Eide
[1976] used a similar setup to study Rossby waves over
a shelf whose depth increased linearly with radius and
Kelvin waves in a channel of uniform depth. Both were
found to agree well with theoretical predictions once the
assumption of a nondivergent horizontal velocity field
was relaxed [
Buchwald and Melville
, 1977].
Colin de Verdiere
[1979] examined Rossby wave-driven
mean flows in a rotating cylinder of radius 31 cm. The
curvature of the fluid's free surface supplied a background
vorticity gradient, and an array of sources and sinks was
used to excite a traveling wave with azimuthal wave num-
ber 12. The Rossby waves were found to generate a strong
mean flow along planetary vorticity contours, equiva-
lent to isobaths on a continental shelf.
Sommeria et al.
[1991] performed similar experiments in an annular chan-
nel between radii of 21.6 and 86.4 cm, with a depth that
increased linearly with radius. Forcing was again supplied
by an inner ring of sources and an outer ring of sinks,
or vice versa, in the floor of the channel. The resulting
net radial transport drove an azimuthal jet via the Cori-
olis force, whose direction was dictated by the relative
12.1.2. Coastal Currents
Even the simplest representation of a coastal current
flowing along a continental slope requires a more sophis-
ticated treatment in the laboratory than topographic
Rossby waves, and a much smaller body of analytical
theory exists to predict their behavior. As a result, lab-
oratory studies of coastal currents followed two decades
after the first experiments with topographic Rossby waves.
Whitehead and Chapman
[1986] performed the first such
study, generating a coastal current by attaching a rectilin-
ear slope to the outside of a cylindrical tank. A buoyant
gravity current was released at the outer edge of the tank,
then propagated around the edge of the tank and then
along the slope. The gravity current was found to widen
and reduce its speed by a factor of up to 4 upon reaching
the slope. If the current's speed fell below that of the first
