Critical ``dimension'' in shell model turbulence
Abstract
We investigate the Gledzer-Ohkitani-Yamada (GOY) shell model within the scenario of a critical dimension in fully developed turbulence. By changing the conserved quantities, one can continuously vary an ``effective dimension'' between d=2 and d=3. We identify a critical point between these two situations where the flux of energy changes sign and the helicity flux diverges. Close to the critical point the energy spectrum exhibits a turbulent scaling regime followed by a plateau of thermal equilibrium. The corrections due to intermittency persist close to the critical point. We identify scaling laws and perform a rescaling argument to derive a relation between the critical exponents. We further discuss the distribution function of the energy flux.
- Publication:
-
Physical Review E
- Pub Date:
- March 2002
- DOI:
- 10.1103/PhysRevE.65.036305
- arXiv:
- arXiv:nlin/0102009
- Bibcode:
- 2002PhRvE..65c6305G
- Keywords:
-
- 47.27.Eq;
- 47.27.Jv;
- 05.70.Jk;
- High-Reynolds-number turbulence;
- Critical point phenomena;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 4 pages, REVTex, 5 figures