Eddy-induced transport in the Southern Ocean

Ocean eddies are turbulent departures from the mean flow [13] and have significant impact on the ocean climate [7]. Properties of mesoscale eddies influence stratification in the Southern Ocean and can have drastic impacts on the strength of global circulations over long timescales [8]. However, it can be expensive to fully resolve eddies in a long-time scale climate model with current computational capabilities [7]. Thus, it is commonplace to simplify an ocean system via parameterisations. There are different parameterisations based on different methods [8]. The current standard is the Gent and McWilliams parameterisation (GM) [4] which uses down-gradient Fickian diffusion of isopycnal layer height (surfaces of constant density) to parametrise the eddytransport [2]. This parameterisation acts as a sink of global potential energy by flattening isopycnals via eddy-induced advection [3]. However, there are several problems including eddy Reynolds stresses being neglected [9].

In 1999, Marshall et al. demonstrated in numerical experiments that in a zonally periodic channel, relatively small changes in the potential vorticity (PV) gradient on an interior isopycnal surface cause significant changes to the strength of eddy-induced circulation [10] as seen in Figure 1. This sensitivity to PV gradients is not captured in any ocean model using GM, suggesting that a PV parameterisation would be more appropriate. In physical terms, changes in PV gradients due to surface warming can lead to unexpectedly large changes in global circulation [8]. Thus, a PV parametrisation can improve current ocean models to reflect this PV gradient sensitivity. There are still unresolved problems with a PV parameterisation. In GM, local fluid incompressibility (given by the sum of the eddy thickness fluxes equating to zero) is automatically achieved by using a boundary vanishing diffusivity [9]. However, this is not satisfied in a down-gradient PV closure without imposing an additional constraint [5]. It might be possible to rescale positive and negative PV fluxes to satisfy incompressibility. This project aims to
construct a PV parameterisation satisfying the integral constraint.

The main objectives are,
1. Systematically diagnose variations in eddy-induced overturning with PV gradients.
2. Investigate the discrepancies of the potential vorticity closure in [10].
3. Develop a new PV parameterisation to satisfy the integral constraint.
4. Test this parameterisation in simple and complex models.