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Doktorsdisputation

Dynamic properties of two-dimensional and quasi-geostrophic turbulence


Respondent	Huvudhandledare	Bihandledare	Datum
Andreas Vallgren	Erik Lindborg	Geert Brethouwer	2010-11-19

Opponent
Guido Boffetta, University of Turin

Betygsnämd
Peter Ditlevsen, Nils Bohr Institute, Copenhagen Jonas Nycander, MISU Anna-Karin Tornberg, Kungliga Tekniska Högskolan

Abstract

Two codes have been developed and implemented for use on massively parallelsuper computers to simulate two-dimensional and quasi-geostrophic turbulence. The codes have been found to scale well with increasing resolution and width ofthe simulations. This has allowed for the highest resolution simulations of two-dimensional and quasi-geostrophic turbulence so far reported in the literature. The direct numerical simulations have focused on the statistical characteristics of turbulent cascades of energy and enstrophy, the role of coherent vortices and departures from universal scaling laws, theoretized more than 40 years ago. In particular, the investigations have concerned the enstrophy and energy cascades in forced and decaying two-dimensional turbulence. Furthermore, the applicability of Charney’s hypotheses on quasi-geostrophic turbulence has been tested. The results have shed light on the flow evolution at very large Reynolds numbers. The most important results are the robustness of the enstrophy cascade in forced and decaying two-dimensional turbulence, the sensitivity to an infrared Reynolds number in the spectral scaling of the energy spectrum in the inverse energy cascade range, and the validation of Charney’s predictions on the dynamics of quasi-geostrophic turbulence. It has also been shown that the scaling of the energy spectrum in the enstrophy cascade is insensitive to intermittency in higher order statistics, but that corrections apply to the ”universal” Batchelor-Kraichnan constant, as a consequence of large-scale dissipation anomalies following a classical remark by Landau (Landau & Lifshitz 1987). Another finding is that the inverse energy cascade is maintained bynonlocal triad interactions, which is in contradiction with the classical locality assumption.
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