Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?
Abstract
We study turbulence in the one-dimensional Burgers equation with a white-in-time, Gaussian random force that has a Fourier-space spectrum ∼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.
- Publication:
-
Physical Review Letters
- Pub Date:
- May 2005
- DOI:
- 10.1103/PhysRevLett.94.194501
- arXiv:
- arXiv:nlin/0406049
- Bibcode:
- 2005PhRvL..94s4501M
- Keywords:
-
- 47.27.Gs;
- 05.45.-a;
- Isotropic turbulence;
- homogeneous turbulence;
- Nonlinear dynamics and chaos;
- Nonlinear Sciences - Chaotic Dynamics;
- Condensed Matter - Statistical Mechanics;
- Mathematics - Analysis of PDEs
- E-Print:
- previous version replaced, with major changes