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Dissipation and enstrophy statistics in turbulence: are the simulations and mathematics converging?

Presented by: 
RM Kerr University of Warwick
Tuesday 24th July 2012 - 14:45 to 15:05
INI Seminar Room 1
Session Chair: 
Eckart Meiburg
This presentation will be based upon the Focus on Fluids article with this title to appear in JFM 700 (2012). The Focus will be on: Yeung, Donzis, & Sreenivasan, 2012 Dissipation, enstrophy and pressure statistics in turbulence simulations at high Reynolds numbers. J. Fluid Mech. 700 and the two themes of the FoF are that Yeung et al resolves a remaining question about the convergence of higher-order statistics and that this result is related to new mathematics on temporal intermittency in turbulence in Gibbon, J.D. 2009 Estimating intermittency in three- dimensional Navier-Stokes turbulence. J. Fluid Mech. 625. What Yeung et al. finds is that even if the fluctuations of the higher-order vorticity and strain statistics are so large that they do not converge individually, their ratios do converge. Gibbon (2009) shows that this type of behaviour is expected and Gibbon (TODW01) will present specific predictions for the ordering of these statistics at any given time and the t ype of maximum growth during the most intermittent periods. However, Yeung et al does not give time variations, so a direct comparison is not possible. My new results are from simulations of the reconnection of anti-parallel vortex tubes, an example of the events assumed by Gibbon (2009), where this time-dependent analysis has been done. This simulation develops, after just two reconnection steps, most of the properties associated with fully-developed turbulence, including a -5/3 spectrum with the proper coefficient and the expected enstrophy production skewness, and the intermittency ratios are consistent with Yeung et al. Turbulence develops after reconnections by: Forming orthogonal vortices, which wrap up as in the Lundgren spiral vortex model. The temporal ordering and growth of the higher-order vorticity statistics obey the bounds of the new mathematical predictions exactly. Thus the connection between the latest high Reynolds number calculations and the latest mathematics is demonstrated.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons