Vorticity statistics of bounded two-dimensional turbulence

H.J.H. Clercx, D. Molenaar, G.J.F. Heijst, van

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Vorticity statistics play an important role in the determination of small-scale dynamics in forced two-dimensional turbulence. On the basis of the Hölder-continuity of the vorticity field ømega(t,\bfx), the scaling behavior of vorticity structure functions S_p(ømega(\ell)), of order p, provides clues on small-scale intermittency. Confirming earlier ideas of Sulem and Frisch (JFM 72, 1975), Eyink (Phys. D 91, 1996) proved the following scaling of the second-order structure function S_2(ømega(\ell))\equiv\langle|ømega(t,\bfx+\bfr)-ømega(t,\bfx)|^2\rangle\sim\ell^\zeta_2, with \quad\zeta_2\leq 2/3 and \quad\ell\leq\ell_f. Here, \ell=|\bfr|, \ell_f is the typical energy-injection scale, associated to an external forcing and the brackets \langle\cdot\rangle denote combined space- and time-averaging. The only assumption used to derive this scaling was a constant enstrophy flux to small scales, in the so-called enstrophy cascade range. On the contrary, using the classical Batchelor argument for the advection of a passive scalar, Falkovich and Lebedev (PRE 50, 1994) argued that one must have \zeta_p=0 for all p. With new direct numerical simulations we address these issues for a bounded square domain, using the no-slip boundary condition for the velocity. Our results are compared with the earlier experimental results of Paret and Tabeling (PRL 83, 1999).
Original languageEnglish
Title of host publication57th Annual Meeting of the Division of Fluid Dynamics, Seattle (USA), 21-23 November 2004
Publication statusPublished - 2004


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