Inertial ranges for turbulent solutions of complex Ginzburg-Landau equations |
| |
| Affiliation: | 1. Shaanxi Engineering Research Center of Controllable Neutron Source, School of Science, Xijing University, Xi’an 710123, PR China;2. Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran;3. Department of information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah, Saudi Arabia;4. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia;5. Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia |
| |
| Abstract: | We consider the spatially periodic, complex Ginzburg-Landau (CGL) equation in regimes close to that of a critical or supercritical focusing non-linear Schrödinger (NLS) equation, which is known to have solutions that exhibit self-similar blow-up. We use the NLS blow-up solutions as a template to develop a theory of how nearly self-similar intermittent burst events can create a power-law inertial range in the time-averaged wave-number spectrum of CGL solutions. Numerical experiments in one dimension with a quintic (critical) and septant (supercritical) non-linearity show a that power-law inertial range emerges which differs from that predicted by the theory. However, as one approaches the NLS limit in the supercritical case, a second power-law inertial range is seen to emerge that agrees with the theory. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
