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Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?

Dhrubaditya Mitra·Jeremie Bec·Rahul Pandit·Uriel Frisch
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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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Dhrubaditya Mitra, Jeremie Bec, Rahul Pandit, Uriel Frisch. 2005-02-18. Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?. https://doi.org/10.1103/physrevlett.94.194501

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