| dc.description.abstract | Understanding ocean circulation and its driving variables is essential for comprehending the Earth’s
climate system. A low-order model with a reduced parameters set was developed by Maas (1994;2004),
using the first moments of the buoyancy and Navier-Stokes equations. As a result, the centre of
mass and the basin averaged angular momentum are used as the key diagnostics. In this research,
different possibilities of this model under meridional differential forcing are explored: a finite Prandtl
number, the full Coriolis force and internal waves. For a finite Prandtl number, a linear stability
analysis was performed and bifurcations were searched using the continuation program MatCont.
For Prandtl is one, the system always evolved towards a steady fixed point. For larger finite Prandtl
numbers, a Hopf bifurcation was found. If the rescaled Rayleigh number and Coriolis parameter pass
a critical value, the system evolves towards a limit cycle. For infinite Prandtl numbers, the effect
of implementing the full Coriolis force was investigated. This means that the reciprocal Coriolis
parameter ˜ f was not neglected. This changed the system as no longer a Hopf bifurcation was found.
The system always evolves towards a fixed point. Lastly, the first steps in implementing internal
waves into the low-order model were made using a conceptual model. In a two dimensional (y, z)
plane and under the assumptions of a static density field with slanted isopycnals internal waves can
developed and cause mixing of the density field. Depending on the angle of the internal waves with
the isopycnals, this changed the centre of mass. Future research should be on the comparison of
the low-order model to numerical models, concerning the finite Prandtl number and the full Coriolis
force. Regarding internal waves, future research should be on the expansion to shear flow, the
implications of a three dimensional scenario and more detailed mixing processes. | |
