Non-uniqueness of the eddy diffusivity and its impact on eddy parameterisation
File(s)
Author(s)
Sun, Luolin
Type
Thesis
Abstract
Oceanic mesoscale eddies have significant influence on oceanic circulations, but cannot be fully resolved in non-eddy-resolving models, which necessitates eddy parametrisations. A conventional approach is to use the mesoscale eddy diffusivity to parametrise the effects of the eddy-induced transport. Such a diffusive parametrisation often uses an isotropic eddy diffusivity that is a constant in space and time, but in reality, the eddy-induced transport is inhomogeneous and anisotropic. Motivated by the lack of full representation, this thesis parametrises the eddy-induced transport by introducing an anisotropic transport tensor. We obtain the high-resolution tracer solution and velocity flow by simulating passive tracers in a three-layer double-gyre quasigeostrophic ocean model. We apply a scale-aware spatial decomposition to decompose the velocity flow and the tracer field so that spatio-temporal dependencies are introduced to their large-scale components and small-scale eddies. An eddy forcing is then derived to quantify the eddy transport, and is reformulated into the divergence of an eddy tracer flux. Then, we derive an isopycnal transport tensor that is assumed to relate the tracer flux to the large-scale tracer gradient, and compute it for a tracer pair by using the inversion method. This tensor is reduced to be only associated with the divergent tracer flux, so the symmetric and asymmetric components of the reduced tensor quantify the diffusive and advective eddy transport, respectively. Finally, we use this reduced tensor to parametrise the eddy effects by reproducing the eddy forcing with the reference tracer field in the non-eddy-resolving model. We demonstrated the tracer-dependence of the transport tensor by comparing tensors computed for different tracers. We also found that this non-uniqueness can be amplified by the dominant rotational component of the tracer flux. The non-uniqueness of the transport tensor disrupted parametrisations but this disruption was reduced by the ensemble-averaging. The eddy-induced transport was shown to have significant impact on the large-scale tracer advection, such as the reduced advection along the eastward jet by the anisotropic mixing and the augmented meridional transport by the eddy advection. Parametrising these effects by a transport tensor, that was uniquely obtained for linearly initialised tracers, notably improved the non-eddy-resolving solution.
Version
Open Access
Date Issued
2021-09
Date Awarded
2022-04
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Berloff, Pavel
Shevchenko, Igor
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)