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

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

2011-11-13

arxiv.org/abs/1111.2999v2

Physical Review E (Rapid Communications), 85, 015301(R) (2012)

Nonlinear Sciences

Chaotic Dynamics

5 pages, 2 figures, Published in Phys. Rev E (Rapid Communications)

Scientific paper

10.1103/PhysRevE.85.015301

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.

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