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Wedi, Nils Peter (2005): Time-dependent boundaries in numerical models. Dissertation, LMU München: Faculty of Physics
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Abstract

This dissertation describes the development of a new numerical framework enabling the study of principal atmospheric mechanisms as well as aspects of numerical realisability that are neither easily deduced from highly optimised operational numerical weather prediction models nor idealised laboratory studies. The theoretical development and efficient numerical implementation of a generalised time-dependent coordinate transformation is demonstrated, creating a unified numerical framework for investigating the influence of upper and lower boundary conditions on atmospheric and oceanic flows. In technical terms, the dissertation also enhances the adaptivity of numerical models to boundary forcings determined by data. The theoretical development is illustrated with numerical simulations of idealised flows. An example of a practical application is given which incorporates a long-wave-approximation for a finite-amplitude free-surface upper boundary, directly relevant to ocean models. Finally, the utility of the generalised vertical coordinate in simulating stratified flows with intricate geometric, time-dependent boundary forcings is demonstrated in the direct numerical simulation of the laboratory analogue of the quasi-biennial oscillation (QBO), the dominant variability in the equatorial stratosphere. While the laboratory experiment exhibits the principal mechanism of the QBO, and despite numerous studies of the stratospheric phenomenon, a complete understanding of the QBO eludes the efforts. On the basis of the numerical results presented in this thesis, the original explanation of the laboratory experiment is revised. The findings stress the utility of this numerical framework and further elevate the importance of the laboratory setup for its fundamental similarity to the atmosphere. A detailed study of parametric and numerical sensitivities of the oscillation is presented and implications on the successful simulation and on the existing theory of equatorial oscillations are discussed.