A new turbulence energy cascade pattern and its scaling lawZhao Songnian1, Xiong Xiaoyun2, Cai Xiaohong1 and Hu Fei1
1 LAPC, Institute of Atmospheric Physics, Chinese Academy of Sciences Beijing, 100029, PRC
2 National Science Foundation of China - Beijing, 100085, PRC
received 25 August 2004; accepted in final form 26 October 2004
published online 8 December 2004
A new energy cascade principle, synchro-cascade pattern, to better understand the mechanism of turbulence, is presented. Its main features are: self-similarity, intermittency and non-uniformity or non-homogeneity. Using this pattern we analytically illustrate the property of sensitive dependence on the initial state and derive a high-order scaling law for the moment of velocity and energy dissipation in a turbulent flow field. The geometric construction of the energy cascade is characterized using a Cantor complementary set and its related wavelet transform. We provide a new physical interpretation to these scaling laws which predicts that all of the physical space occupied by a fluid will be gradually filled with smaller and smaller eddies, whose scale gradually approaches the dissipative scale of molecular-dynamic viscosity.
47.54.+r - Pattern selection; pattern formation.
02.50.-r - Probability theory, stochastic processes, and statistics.
47.27.-i - Turbulent flows, convection, and heat transfer.
© EDP Sciences 2005