Nelkin scaling for the Burgers equation and the role of high-precision calculations

Abstract

Nelkin scaling, the scaling of moments of velocity gradients in terms of the Reynolds number, is an alternative way of obtaining inertial-range information. It is shown numerically and theoretically for the Burgers equation that this procedure works already for Reynolds numbers of the order of 100 (or even lower when combined with a suitable extended self-similarity technique). At moderate Reynolds numbers, for the accurate determination of scaling exponents, it is crucial to use higher than double precision. Similar issues are likely to arise for three-dimensional Navier--Stokes simulations.Comment: 5 pages, 2 figures, Published in Phys. Rev E (Rapid Communications