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Infrared Reynolds number dependency of the two-dimensional inverse energy cascade
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 667, 463-473 p.Article in journal (Refereed) Published
##### Abstract [en]

High resolution simulations of forced two-dimensional turbulence reveal that the inverse cascade range is sensitive to an infrared Reynolds number $Re_{\alpha}=k_f/k_{\alpha}$, where $k_f$ is the forcing wave number and $k_{\alpha}$ is a frictional wave number based on linear friction. In the limit of high $Re_{\alpha}$, the classic $k^{-5/3}$-scaling is lost and we obtain steeper energy spectra. The sensitivity is traced to the formation of vortices in the inverse energy cascade range. Thus, it is hypothesized that the dual limit $Re_{\alpha} \rightarrow \infty$ and $Re_{\nu}=k_d/k_f \rightarrow \infty$, where $k_d$ is the small-scale dissipation wave number, will lead to a steeper energy spectrum than $k^{-5/3}$ in the inverse energy cascade range. It is also found that the inverse energy cascade is maintained by nonlocal triad interactions.

##### Place, publisher, year, edition, pages
2011. Vol. 667, 463-473 p.
##### Keyword [en]
Two-dimensional turbulence, inverse energy cascade, coherent vortices, non-locality
##### National Category
Other Physics Topics
##### Identifiers
ISI: 000287052900018ScopusID: 2-s2.0-79951619915OAI: oai:DiVA.org:kth-25709DiVA: diva2:359540
##### Funder
Knut and Alice Wallenberg Foundation
##### Note
QC 20101029Available from: 2010-10-28 Created: 2010-10-28 Last updated: 2011-03-24Bibliographically 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)
##### Note
QC 20101029Available from: 2010-10-29 Created: 2010-10-28 Last updated: 2011-03-24Bibliographically approved

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Vallgren, Andreas
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