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Simulations of two-dimensional and quasi-geostrophic turbulence: Internal Report
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2010 (English)Report (Other academic)
Abstract [en]

This report is devoted to the details of the two codes that have been developed aimed at studies of large-scale turbulent flows. For this purpose, a first approach has been to derive and implement a code (PNSE2D) that simulates two-dimensional turbulence by numerically solving the two-dimensional incompressible Navier-Stokes equation in a doubly periodic square domain. The second code (QGE3D) adds complexity by taking into account background rotation and a stable stratification. This latter code solves the QG equation for the potential vorticity derived by Charney (1971), and can be considered an extension from PNSE2D into three dimensions. The motivation for developing new codes instead of using existing codes is that it gives us full control of the codes while they solve the equations in a very simple geometry (periodic boundary conditions). Furthermore, the codes are portable and have been developed to give a high degree of flexibility. The two codes have in common, among other things, the need for high resolution, which required the codes to be parallelized for utilization on parallel machines. Experiments have shown that good speed-up is obtained when increasing the number of processes (essentially increasing the number of cpu:s). The codes rely on a message passing interface (MPI) and a fast FFT-library, FFTW. The codes have been validated by the conservation of the inviscid invariants, i.e. energy and enstrophy in two-dimensional turbulent flows, and energy and potential enstrophy in QG turbulence.

Place, publisher, year, edition, pages
Stockholm: KTH , 2010. , 35 p.
Keyword [en]
Parallelisation, performance, MPI, Runge-Kutta, quasi-geostrophic, two-dimensional, turbulence
National Category
Computer Science
URN: urn:nbn:se:kth:diva-25711OAI: diva2:359543
QC 20101029Available from: 2010-11-01 Created: 2010-10-28 Last updated: 2010-11-01Bibliographically approved
In thesis
1. Dynamic properties of two-dimensional and quasi-geostrophic turbulence
Open this publication in new window or tab >>Dynamic properties of two-dimensional and quasi-geostrophic turbulence
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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 twodimensionaland quasi-geostrophic turbulence so far reported in the literature.The direct numerical simulations have focused on the statistical characteristicsof turbulent cascades of energy and enstrophy, the role of coherent vorticesand departures from universal scaling laws, theoretized more than 40 yearsago. In particular, the investigations have concerned the enstrophy and energycascades in forced and decaying two-dimensional turbulence. Furthermore, theapplicability of Charney’s hypotheses on quasi-geostrophic turbulence has beentested. The results have shed light on the flow evolution at very large Reynoldsnumbers. The most important results are the robustness of the enstrophycascade in forced and decaying two-dimensional turbulence, the sensitivity toan infrared Reynolds number in the spectral scaling of the energy spectrumin the inverse energy cascade range, and the validation of Charney’s predictionson the dynamics of quasi-geostrophic turbulence. It has also been shownthat the scaling of the energy spectrum in the enstrophy cascade is insensitiveto intermittency in higher order statistics, but that corrections apply to the”universal” Batchelor-Kraichnan constant, as a consequence of large-scale dissipationanomalies following a classical remark by Landau (Landau & Lifshitz1987). Another finding is that the inverse energy cascade is maintained bynonlocal triad interactions, which is in contradiction with the classical localityassumption.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. ix, 54 p.
Trita-MEK, ISSN 0348-467X ; 2010:06
two-dimensional turbulence, decaying turbulence, quasi-geostrophic turbulence, direct numerical simulation (DNS), coherent vortices, energy cascade, enstrophy cascade, intermittency, massively parallel simulations, locality iii
National Category
Other Physics Topics
urn:nbn:se:kth:diva-25712 (URN)978-91-7415-763-5 (ISBN)
Public defence
2010-11-19, D1, Lindstedtsvägen 17, Stockholm, 10:15 (English)
QC 20101029Available from: 2010-10-29 Created: 2010-10-28 Last updated: 2011-03-24Bibliographically approved

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