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Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?

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arxiv nlin/0406049 v2 pith:NTWKB6XV submitted 2004-06-22 nlin.CD cond-mat.stat-mechmath.AP

Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?

Dhrubaditya Mitra , Jeremie Bec , Rahul Pandit , Uriel Frisch This is my paper
classification nlin.CD cond-mat.stat-mechmath.AP
keywords artifactburgersequationfindmultiscalingscalinganomalousappear
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abstract

We study turbulence in the one-dimensional Burgers equation with a white-in-time, Gaussian random force that has a Fourier-space spectrum $\sim 1/k$, where $k$ is the wave number. From very-high-resolution numerical simulations, in the limit of vanishing viscosity, we find evidence for multiscaling of velocity structure functions which cannot be falsified by standard tests. We find a new artifact in which logarithmic corrections can appear disguised as anomalous scaling and conclude that bifractal scaling is likely.

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