I have conducted my Master's thesis as a member of TeamOcean at Niels Bohr Institute, Copenhagen under the supervision of Kurt Roth (IUP Heidelberg) and Markus Jochum (NBI Copenhagen).

During my project, I examined the dependence of cross-equatorial flow in low-resolution ocean models on lateral diffusivity ("viscosity"). To this end, I ran state-of-the-art ocean simulations using CESM on the AEGIR Cluster, and evaluated my findings with a self-developed shallow-water model and plain old theory.

Why is this important?

The strength of cross-equatorial flow has huge implications on the world climate. It effectively couples both the northern and southern hemisphere in latitude, but also the Atlantic, Pacific and Indian Oceans in longitude, exchanging heat and matter between regions that lie thousands of kilometers apart. Equatorial processes like the El Niño–Southern Oscillation (ENSO) influence countless human lives, e. g. through the extreme weather events observed during El Niño. Another example is the Atlantic Meridional Overturning Circulation (AMOC) and the resulting Gulf Stream, which is the reason for the mild European climate compared to that of e. g. the east coast of North America.

 

The following figure shows the two branches of the AMOC, connecting far north, far south, and everything in-between.

  • Flow in the Atlantic along two isopycnals. Data from CESM model output. Shading indicates meridional velocity.

Because climate simulations are one of the most powerful tools to both understand the current state of nature and to predict its future state, it is very important that cross-equatorial flow in the ocean is modeled accurately. Since the value of ocean viscosity is not derived from first principles but rather chosen in a heuristical manner (see e.g. Jochum et al., 2008), it would be unfortunate if the chosen viscosity had a large impact on cross-equatorial flow and thus the results of the simulation.

How are viscosity and flow across the equator connected?

Frictional effects in the ocean are in fact critical to transform potential vorticity, which is conserved in the absence of friction to a large degree of accuracy. A simple expression for the evolution of potential vorticity along streamlines in a homogeneous ocean reads:

 

 

with relative vorticity ζ, planetary vorticity f, layer height h, viscosity A, and material derivative D/dt.

Since f is much larger than ζ, and because f changes its sign across the equator, flow crossing from one hemisphere far into the other has to undergo a change of sign of its potential vorticity (see e.g. Killworth, 1991). This implies that, in the absence of friction (A=0), cross-equatorial flow is indeed impossible.

Results

Surprisingly, I have found that even viscosity changes by several orders of magnitude only lead to a 10% change of the overturning strength. The picture that the chosen viscosity must have a big influence on the global overturning in a model does thus not hold up. In fact, it can be shown that the meridional transport in a western boundary layer (Munk layer) is independent of viscosity to a leading order - the layer will simply adjust its width to compensate for a changed viscosity.

 

However, the chosen viscosity does have a critical local influence on the equatorial regions. One example is the region of the Indonesian Throughflow. In this region, a reduced viscosity prevents a large fraction of the flow from the southern hemisphere (approaching the equator in the New Guinea Current) to cross into the northern hemisphere - instead, it curves back into the southern hemisphere. As a result, the Indonesian Throughflow becomes considerably saltier:

Along with these experimental results, I have conducted a theoretical study, trying to reproduce the behavior I have observed in CESM. In order to study the dominant processes that are responsible for the observed response of cross-equatorial flow on viscosity, I have developed and implemented a highly idealized shallow-water model that is forced by a mass imbalance in the north and reaches around the equator. The results from this model agree with theory: The overturning is independent from viscosity in this model, as shown in this animation of the layer height in the model (note the varying width of the western boundary layer to accommodate for a changed viscosity).

Even though the width of the boundary layer changes by a lot, and even though nonlinearities (eddies) are created in low-viscosity simulations, the resulting steady-state looks very similar. This model has in fact not been able to model the observed 10% change of the overturning under viscosity changes, which shows that, in CESM, higher-order processes must be at work that I have not included into my model.

A PDF version of my thesis can be found on GitHub, along with its LaTeX source files.