| Abstrakt: |
Recent mathematical results have shown that a central assumption in the theory of two-dimensional turbulence proposed by Batchelor (Phys. Fluids, vol. 12, 1969, p. 233) is false. That theory, which predicts a ?2/3k?1enstrophy spectrum in the inertial range of freely-decaying turbulence, and which has evidently been successful in describing certain aspects of numerical simulations at high Reynolds numbers Re, assumes that there is a finite, non-zero enstrophy dissipation ? in the limit of infinite Re. This, however, is not true for flows having finite vorticity. The enstrophy dissipation in fact vanishes.We revisit Batchelor's theory and propose a simple modification of it to ensure vanishing ? in the limit Re? ?. Our proposal is supported by high Reynolds number simulations which confirm that ? decays like 1/ln Re, and which, following the time of peak enstrophy dissipation, exhibit enstrophy spectra containing an increasing proportion of the total enstrophy ?2/2 in the inertial range as Reincreases. Together with the mathematical analysis of vanishing ?, these observations motivate a straightforward and, indeed, alarmingly simple modification of Batchelor's theory: just replace Batchelor's enstrophy spectrum ?2/3k?1with ?2k?1(ln Re)?1). [ABSTRACT FROM AUTHOR] |
