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The enstrophy cascade in forced 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.
2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 671, 168-183 p.Article in journal (Refereed) Published
##### Abstract [en]

We carry out direct numerical simulations of two-dimensional turbulence with forcing at different wave numbers and resolutions up to 32768^2 gridpoints. In the absence of large scale drag, a state is reached where enstrophy is quasistationary while energy is growing. In the enstrophy cascade range the energy spectrum has the form $E(k) = K \epsilon_{\omega} ^{2/3} k^{-3}$, without any logarithmic correction, where$\epsilon_{\omega}$ is the enstrophy dissipation and K is of the order of unity. However, K is varying between different simulations and is thus not a perfect constant. This variation can be understood as a consequence of large-scale dissipation intermittency, following the argument by Landau (Landau \& Lifshitz 1959).  In the presence of a large scale drag, we obtain a slightly steeper spectrum. When forcing is applied at a scale which is somewhat smaller than the computational domain no vortices are formed and the statistics remain close to Gaussian in the enstrophy cascade range. When forcing is applied at a smaller scale, long lived coherent vortices form at larger scales  than the forcing scale and intermittency measures become very large at all scales, including the scales of the enstrophy cascade. We conclude that the enstrophy cascade with a $k^{-3}$-spectrum, is a robust feature of the two-dimensional Navier-Stokes equations. However, there is a complete lack of universality of higher order statistics of vorticity increments in the enstrophy cascade range.

##### Place, publisher, year, edition, pages
2011. Vol. 671, 168-183 p.
##### Keyword [en]
Two-dimensional turbulence, enstrophy cascade, intermittency, dissipation, coherent vortices
##### National Category
Other Physics Topics
##### Identifiers
ISI: 000288100100007ScopusID: 2-s2.0-79952816018OAI: oai:DiVA.org:kth-25707DiVA: diva2:359537
##### Note
QC 20101029. Uppdaterat från submitted till published 20110404Available from: 2010-10-28 Created: 2010-10-28 Last updated: 2011-04-04Bibliographically 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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