Paramaterization of submesoscale eddies in the ocean surface boundary layer
How can we best represent the effects of unresolved submesoscale eddies in the surface boundary layer in ocean circulation models?
Aims of the Project
To model and diagnose the dynamical processes in submesoscale instabilities and eddies in an idealised nuemrical model of the ocean surface boundary layer.
2. To implement a new parameterisation of unresolved submesoscale eddies (“GEOMETRIC”) and test the extent to which it is able to reproduce the missing physics.
3. To refine the application of GEOMETRIC to the submesoscale using the results of the numerical calculations.
The ocean is populated by a vigorous mesoscale eddy field on scales of 10-100 km which is partially resolved by state-of-the-art ocean climate models. However, these mesoscale eddies are themselves unstable in the surface boundary layer of the ocean, leading to a second, recently discovered, class of “submesoscale eddies” with scales of around 1-5km. These submesoscale eddies are not resolved by any state-of-the-art climate ocean models, yet are believed to be of crucial importance for the transfer of heat, carbon and other trace substances between the atmosphere and ocean interior, and for ocean biogeochemistry.
Recently, we have developed a new parameterisation of mesoscale eddies – “GEOMETRIC” – based on the fundamental conservation laws of momentum and energy. We have shown that GEOMETRIC leads to many enhancements in our ability to parameterise the physics of unresolved mesoscale eddies in coarse-resolution ocean climate models.
The goal of this collaborative project is to explore the extent to which GEOMETRIC can parameterise the physics of unresolved submesoscale eddies in mesoscale eddy-permitting ocean climate models. The project draws on the combined expertise of the Oxford and National Oceanography Centre supervisors in the fluid dynamics of eddy-mean flow interaction and in state-of-the-art, eddyresolving numerical ocean modelling.
The student will start by setting up and diagnosing the submesoscale instabilities in an idealised numerical model at sufficiently high spatial resolution to resolve the submesoscale eddies (e.g., 0.5-1 km lateral grid spacing, similar to that used in Brannigan et al., 2017). They will then implement GEOMETRIC in this model at coarser resolutions and test the extent to which it is able to reproduce the missing physics. The results will also be compared with the exisiting state-of-the-art submesoscale eddy pararameterisation, due to Fox Kemper et al. (2008), which performs substantially less well in the mesoscale eddy test in Fig. 1 (Bachman et al., 2017). As the project evolves, we expect to refine the application of GEOMETRIC to the submesoscale using the results of the numerical calculations, in an iterative manner.
Fig. 1: Demonstration of GEOMETRIC in a model of mesoscale turbulent eddies in an idealised ocean jet. (a) Snapshot of the buoyancy field. (b) Comparision of mesoscale eddy diffusivities diagnosed from a numerical model (x axis) and those predicted by GEOMETRIC (y axis). See Bachman et al. (2017) for further details.
Fig 2. Illustration of the relative vorticity field (red positive, blue negative) in a submesoscaleresolving model (Brannigan et al., 2017). The subemescale eddies are superimposed on the two larger mesoscale eddies.
Specialised skills required
The student will need strong mathematical/physical science skills, and an interest in/aptitude for computational work. Prior knowledge of ocean physics and fluid dynamics is not essential, but would be advantageous.
Bachman, S. D., D. P. Marshall, J. R. Maddison, and J. Mak, 2017: Evaluation of a scalar eddy transport coefficient based on geometric constraints. Ocean Modell., 109, 44–54.
Brannigan, L., D. P. Marshall, A. Naveira Garabato, A. J. G. Nurser, and J. Kaiser, 2017: Submesoscale instabilities in mesoscale eddies. J. Phys. Oceanogr., 47, 3061-3085.
Fox-Kemper, B., Ferrari, R., Hallberg, R., 2008: Parameterization of mixed layer eddies. Part I: Theory and diagnosis. J. Phys. Oceanogr., 38, 1145-1165 Mak, J., J. R. Maddison, D. P. Marshall, and D. R. Munday, 2018: Implementation of a geometrically and energetically constrained mesoscale eddy parameterization in an ocean circulation model. J. Phys. Oceanogr., 48, 2363-2382.
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