The stability of the Arctic Ocean boundary current
The warm Atlantic Water (AW) flows through the Arctic Ocean in a narrow boundary current locked to the continenal slope underneath. The steep topography forms a 'potential vorticity barrier' that makes it hard for the AW to spread into the deep basins---where it has the potential to melt lots of sea ice. But the boundary current itself can be hydrodynamically unstable, giving rise to a 'macro-turbulent' eddy field which stirs things up and spreads AW into the basins.
The instability mechanisms and the resulting eddy field mostly need to be parametrized in ocean climate models since the eddy scales are smaller than the typical model grid size. The problem is that current parametrizations used in climate models are poorly fit for the job, essentially for two reasons:
- they neglect the influence of bottom topography entirely and
- they are based on 2-layer models of the ocean whereas the Arctic Ocean is characterized by three density layers (light fresh water on the surface, medium-density AW in the middle and dense cold water on the bottom).
As a consequence (other factors play a role as well) ocean climate models do poorly in representing conditions in the Arctic Ocean.
The objective is to study (baroclinic and barotropic) instability in an idealized 3-layer flow along a topographic slope, mimickinig conditions in the Arctic. We will use either the quasi-geostrophic (QG) or the shallow-water (SW) equations, both linearlized around the background large-scale flow, and we will study normal mode solutions that say someting about the nature of small waves that can grow, drawing energy from the large-scale flow.
For the mathematically inclined the 3-layer QG equations can be studied analytically. To obtain results from the SW equations (better suited for steep bottom slopes) we will need to rely on numerical methods to solve the eigenvalue problems.
The ultimate aim in both cases is to find out how the bottom topography influences the growth rates and scales of the waves that can grow at the expense of the energy of the mean current. These two quantities, the growth rate and the scale, will give hints on how eddy stirring is to be parametrized in the climate models.