Klöwer, Milan (2017) Energy-budget based backscatter in a non-linear shallow water model driven by double gyre wind forcing. (Master thesis), Christian-Albrechts-Universität Kiel, Kiel, Germany, 92 pp.

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Abstract

The parametrization of sub-grid scale processes is one of the key challenges towards improved numerical simulations of atmospheric and oceanic circulation. Numerical weather prediction models as well as climate models would benefit from more sophisticated turbulence closures that allow for less spurious dissipation at the grid-scale and consequently higher and more realistic levels of eddy kinetic energy (EKE). Recent studies [Jansen & Held, 2014; Jansen et al., 2015] propose to use a hyperviscous closure in combination with an additional deterministic forcing term as a negative viscosity to represent backscatter of energy from unresolved scales. The sub-grid EKE is introduced as an additional prognostic variable [Eden & Greatbatch, 2008] that is fed by dissipation at the grid scale, and enables recycling of EKE via the backscatter term at larger scales. This parametrization was shown to work well in a primitive equation model in channel configuration. Here, we apply the parametrization to a shallow water model driven by double gyre wind forcing with no-slip boundary conditions and provide evidence for its general application. Introducing a Rossby number-based scaling for the strength of the backscatter, which is physically based on upscale (downscale) cascades of balanced (unbalanced) flow, we overcome essentially the numerical instabilities at the boundary that otherwise limit the practicability of the backscatter parametrization. In terms of mean state and variability, a coarse resolution model is largely improved towards a high resolution truth at low additional computational cost.

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