This thesis presents a numerical exploration of the dynamics governing
rotating flow driven by a surface stress in the " sliced cylinder " model
of Pedlosky & Greenspan (1967) and Beardsley (1969), and its close
relative, the " sliced cone " model introduced by Griffiths & Veronis
(1997). The sliced cylinder model simulates the barotropic wind-driven
circulation in a circular basin with vertical sidewalls, using a depth
gradient to mimic the effects of a gradient in Coriolis parameter. In the
sliced cone the vertical sidewalls are replaced by an azimuthally uniform
slope around the perimeter of the basin to simulate a continental slope.
Since these models can be implemented in the laboratory, their dynamics
can be explored by a complementary interplay of analysis and numerical
and laboratory experiments. ¶
In this thesis a derivation is presented of a generalised
quasigeostrophic formulation which is valid for linear and moderately
nonlinear barotropic flows over large-amplitude topography on an f-plane,
yet retains the simplicity and conservation properties of the standard
quasigeostrophic vorticity equation (which is valid only for small depth
variations). This formulation is implemented in a numerical model based
on a code developed by Page (1982) and Becker & Page (1990). ¶
The accuracy of the formulation and its implementation are confirmed by
detailed comparisons with the laboratory sliced cylinder and sliced cone
results of Griffiths (Griffiths & Kiss, 1999) and Griffiths & Veronis
(1997), respectively. The numerical model is then used to provide insight
into the dynamics responsible for the observed laboratory flows. In the
linear limit the numerical model reveals shortcomings in the sliced cone
analysis by Griffiths & Veronis (1998) in the region where the slope and
interior join, and shows that the potential vorticity is dissipated in an
extended region at the bottom of the slope rather than a localised region
at the east as suggested by Griffiths & Veronis (1997, 1998). Welander's
thermal analogy (Welander, 1968) is used to explain the linear
circulation pattern, and demonstrates that the broadly distributed
potential vorticity dissipation is due to the closure of geostrophic
contours in this geometry. ¶
The numerical results also provide insight into features of the flow at
finite Rossby number. It is demonstrated that separation of the western
boundary current in the sliced cylinder is closely associated with a
" crisis " due to excessive potential vorticity dissipation in the viscous
sublayer, rather than insufficient dissipation in the outer western
boundary current as suggested by Holland & Lin (1975) and Pedlosky
(1987). The stability boundaries in both models are refined using the
numerical results, clarifying in particular the way in which the western
boundary current instability in the sliced cone disappears at large
Rossby and/or Ekman number. A flow regime is also revealed in the sliced
cylinder in which the boundary current separates without reversed flow,
consistent with the potential vorticity " crisis " mechanism. In addition
the location of the stability boundary is determined as a function of the
aspect ratio of the sliced cylinder, which demonstrates that the flow is
stabilised in narrow basins such as those used by Beardsley (1969, 1972,
1973) and Becker & Page (1990) relative to the much wider basin used by
Griffiths & Kiss (1999). ¶
Laboratory studies of the sliced cone by Griffiths & Veronis (1997)
showed that the flow became unstable only under anticyclonic forcing. It
is shown in this thesis that the contrast between flow under cyclonic and
anticyclonic forcing is due to the combined effects of the relative
vorticity and topography in determining the shape of the potential
vorticity contours. The vorticity at the bottom of the sidewall smooths
out the potential vorticity contours under cyclonic forcing, but distorts
them into highly contorted shapes under anticyclonic forcing. In
addition, the flow is dominated by inertial boundary layers under
cyclonic forcing and by standing Rossby waves under anticyclonic forcing
due to the differing flow direction relative to the direction of Rossby
wave phase propagation. The changes to the potential vorticity structure
under strong cyclonic forcing reduce the potential vorticity changes
experienced by fluid columns, and the flow approaches a steady free
inertial circulation. In contrast, the complexity of the flow structure
under anticyclonic forcing results in strong potential vorticity changes
and also leads to barotropic instability under strong forcing. ¶
The numerical results indicate that the instabilities in both models
arise through supercritical Hopf bifurcations. The two types of
instability observed by Griffiths & Veronis (1997) in the sliced cone are
shown to be related to the western boundary current instability and
" interior instability " identified by Meacham & Berloff (1997). The
western boundary current instability is trapped at the western side of
the interior because its northward phase speed exceeds that of the
fastest interior Rossby wave with the same meridional wavenumber, as
discussed by Ierley & Young (1991). ¶
Numerical experiments with different lateral boundary conditions are also
undertaken. These show that the flow in the sliced cylinder is
dramatically altered when the free-slip boundary condition is used
instead of the no-slip condition, as expected from the work of Blandford
(1971). There is no separated jet, because the flow cannot experience a
potential vorticity " crisis " with this boundary condition, so the western
boundary current overshoots and enters the interior from the east. In
contrast, the flow in the sliced cone is identical whether no-slip,
free-slip or super-slip boundary conditions are applied to the horizontal
flow at the top of the sloping sidewall, except in the immediate vicinity
of this region. This insensitivity results from the extremely strong
topographic steering near the edge of the basin due to the vanishing
depth, which demands a balance between wind forcing and Ekman pumping on
the upper slope, regardless of the lateral boundary condition. The
sensitivity to the lateral boundary condition is related to the
importance of lateral friction in the global vorticity balance. The
integrated vorticity must vanish under the no-slip condition, so in the
sliced cylinder the overall vorticity budget is dominated by lateral
viscosity and Ekman friction is negligible. Under the free-slip condition
the Ekman friction assumes a dominant role in the dissipation, leading to
a dramatic change in the flow structure. In contrast, the much larger
depth variation in the sliced cone leads to a global vorticity balance in
which Ekman friction is always dominant, regardless of the boundary
condition.
| Identifer | oai:union.ndltd.org:ADTP/216700 |
| Date | January 2001 |
| Creators | Kiss, Andrew Elek, Andrew.Kiss@anu.edu.au |
| Publisher | The Australian National University. Research School of Earth Sciences |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | http://www.anu.edu.au/legal/copyright/copyrit.html), Copyright Andrew Elek Kiss |
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