Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?

Details Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation? Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?

2004-06-22

arxiv.org/abs/nlin/0406049v2

Nonlinear Sciences

Chaotic Dynamics

previous version replaced, with major changes

Scientific paper

10.1103/PhysRevLett.94.194501

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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