Masters Thesis Defence by Bjarke Tobias Olsen – Niels Bohr Institutet - Københavns Universitet

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Masters Thesis Defence by Bjarke Tobias Olsen

Two-dimensional Shallow Water (SW) models with cartesian geometry are evaluated for different numerical methods for solving the prognostic equations. These methods include the newly developed Hybrid Eulerian-Lagrangian (HEL) method, e.g Kaas et al. 2013, the Locally Mass-Conserving Semi-Lagrangian (LMCSL) method and the Spectral Transform Method (STM). The methods are evaluated, using total wavenumber spectra of kinetic energy and passive tracer variance, and the emphasis of the evaluation is on the distribution and nonlinear transfer of energy and tracer variance between scales. The theory of two-dimensional turbulent and incompressible fluids are used as a guideline in the evaluation.

The kinetic energy spectra show a power-law nature with a scaling much steeper than that of a downscale enstrophy range. This can not be fully explained, but contributing factors are the symmetry and the anisotropy of the flow, as well as numerical damping of the methods.

The variance spectra for the passive tracer show a power-law nature for all three methods, with a scaling near that of a downscale enstrophy range, but it is not in accordance with the steep scaling of the kinetic energy, and may be because the tracer variance is freely decaying.

The evaluation show that the HEL method produce less diffusive solutions, and preserve gradients better than the other two methods, but whether the results are also more "realistic" is not clear.