The evolution of the centre of mass and the basin-averaged angular momentum for finite Prandtl number, full Coriolis forcing and internal waves

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.