Wave-turbulence interaction in shallow water numerical models: asymptotic limits, and subgrid interactions
Wheadon, Andrew John
Date: 23 February 2018
University of Exeter
PhD in Mathematics
The ability to directly simulate all atmospheric motion is currently well beyond the limits of the computers available to us. As such techniques must be developed that accurately model important processes in an affordable manner. Large-scale balanced motion is well understood, but as affordable resolution increases, models are able ...
The ability to directly simulate all atmospheric motion is currently well beyond the limits of the computers available to us. As such techniques must be developed that accurately model important processes in an affordable manner. Large-scale balanced motion is well understood, but as affordable resolution increases, models are able to resolve scales where large-scale turbulence and small-scale waves are important. This requires a new set of techniques that respect the interactions between these different kinds of motion. In this thesis we look at two ways of assessing the accuracy of models capable of representing the scales at which these interactions occur. The first approach uses asymptotic limit solutions to derive a set of terms whose scale is known. These terms can then be evaluated as the model approaches a relevant asymptotic regime, and a `good' model should reproduce the expected rate of scaling. We apply this method of asymptotic limit solutions to an Eulerian and a Lagrangian shallow water model. The former is based upon ENDGame, the model currently in use at the Met Office, and the latter is based upon a candidate model from GungHo which is seeking a replacement for ENDGame. In addition, the Eulerian model is evaluated with both small and large timesteps and the results confirm the ability of the semi-implicit scheme to retain accuracy at large timesteps. Errors in the higher-order diagnostics used in this section highlight the need to make these analytic diagnostics consistent with the discretisations of the model in question. The second method involves looking at the exchanges of energy in a spectral shallow water model in order to inform the design of subgrid models. By running a high-resolution simulation and truncating the energy at a certain wavenumber, comparing the result to a run without truncation shows the contribution of the scales below the truncation limit. We extend this by separating the total energy into separate components that may be truncated and evaluated individually in order to give a more complete picture of energy exchanges at the subgrid scale.
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