Europhys. Lett.
Volume 69, Number 1, January 2005
Page(s) 81 - 87
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 08 December 2004
Europhys. Lett., 69 (1), pp. 81-87 (2005)
DOI: 10.1209/epl/i2004-10300-9

A new turbulence energy cascade pattern and its scaling law

Zhao 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