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Testing Batchelor's similarity hypotheses for decaying two-dimensional turbulence
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2010 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 22, no 9, 091704- p.Article in journal (Refereed) Published
Abstract [en]

We carry out three high resolution direct numerical simulations of the two-dimensional Navier-Stokes equation to test Batchelor's similarity hypotheses of an equilibrium spectral range and an inertial subrange where the enstrophy wave number spectrum has the form Phi(k)=C chi(2/3)k(-1), where chi is the mean enstrophy dissipation rate and C is a constant. We use very different initial conditions in the three simulations and find that Batchelor's hypotheses are well satisfied in each simulation. However, there is a small but significant difference between the equilibrium range spectrum of one of the simulations as compared to the spectra of the other two. We suggest that the difference is linked to the stronger degree of large scale variation of the enstrophy dissipation which is observed in this simulation as compared to the other two.

Place, publisher, year, edition, pages
2010. Vol. 22, no 9, 091704- p.
Keyword [en]
flow simulation, Navier-Stokes equations, turbulence
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-25760DOI: 10.1063/1.3488997ISI: 000282437100017Scopus ID: 2-s2.0-79251574687OAI: oai:DiVA.org:kth-25760DiVA: diva2:359719
Note
QC 20101029Available from: 2010-10-29 Created: 2010-10-29 Last updated: 2017-12-12Bibliographically 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.
Series
Trita-MEK, ISSN 0348-467X ; 2010:06
Keyword
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
Identifiers
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)
Opponent
Supervisors
Note
QC 20101029Available from: 2010-10-29 Created: 2010-10-28 Last updated: 2011-03-24Bibliographically approved

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