 |
| Titel |
Experiments on nonlinear coastal shelf waves in a rotating annulus |
| VerfasserIn |
Andrew Stewart, Paul Dellar, Ted Johnson |
| Konferenz |
EGU General Assembly 2010
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250036961
|
|
|
|
|
|
| Zusammenfassung |
| In many coastal regions, the ocean depth increases very rapidly at a “shelf break” running
approximately parallel to the coastline. A shelf break marks the edge of the continental shelf,
and separates the deep ocean from the relatively shallow near-coastal ocean. Shelf breaks
play an important rôle in steering coastal currents, such as the Aghulas current which flows
southwest along the eastern coast of Africa at speeds of up to 1 ms-1. To investigate the
effect of shelf breaks in stabilising coastal currents, we have carried out laboratory
experiments to generate nonlinear topographic Rossby waves that propagate along a shelf
break in the presence of a mean current.
Our experiments use an annular channel in a rotating cylindrical tank. We model the shelf
break with a tank floor that undergoes a sharp drop at a certain radius Rh. The tank was filled
with homogeneous fluid, and set rotating with constant angular velocity until the fluid inside
rotated as a solid body. We then induced horizontal perturbations to the fluid, which caused
Taylor columns to move inwards and outwards across the shelf. Conservation of potential
vorticity forces these columns to acquire relative vorticity as they cross the shelf, which
allows waves to propagate around the tank. These waves are known as topographic Rossby
shelf waves.
The large-scale flow around shelf breaks has been the subject of a series of theoretical
investigations. These commonly approximate the sharp drop in the depth by a discontinuity,
on the assumption that the horizontal length scale of the flow is much larger than the width of
the shelf break. However, the fluid is still assumed to move in columns, as in shallow water
theory, even as it crosses the shelf. Our present work aims to consolidate a theoretical model
for nonlinear waves propagating along a depth discontinuity in the context of our
laboratory experiments. We assume that rotational effects are dominant, and that fluid
velocities are small compared with the surface gravity wave speed. The system may
thus be described using the shallow water quasigeostrophic equations with a rigid
lid,
Dq-= 0, q = Ï + fh-, Ï = -2 Ï.
Dt H
Here q is the potential vorticity, Ï is the two-dimensional relative vorticity, Ï is the
streamfunction, H is the maximum height of the fluid, f is the Coriolis parameter, h is the
spatially-varying height of the bottom topography, and D-Dt is the advective derivative.
These equations have previously been applied to study topographic Rossby shelf waves in a
straight channel with a discontinuity in the depth part-way across. By looking for solutions
that vary slowly along the channel, a nonlinear wave equation has been derived to describe
the evolution of a potential vorticity front that lies initially along the discontinuity in
depth.
To make predictions about the waves generated in our experiments, we have reformulated
this existing theory for straight channels to describe long nonlinear topographic Rossby shelf
waves in an annular channel. However, we find that the resulting theoretical predictions are
not verified by the experiments, in which short-wave disturbances grow rapidly and
dominate the large-scale flow. Being based on finding solutions that vary slowly
around the channel, the long-wave theory cannot capture the behaviour seen in the
experiments.
Motivated by this discrepancy, we have conducted a numerical study of the
shallow water quasigeostrophic equations given above, without making any further
assumptions about the wavelengths of the disturbances. These calculations suggest that
short-wavelength phenomena with large amplitudes will always appear, even in an initial
flow configuration of very long wavelength, as long as the amplitude of the initial
disturbance is large enough for the waves to be nonlinear. However, the earlier long-wave
theory still gives a qualitatively accurate description of the evolution of very long
waves. |
|
|
|
|
|
|