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|
A new turbulence energy cascade pattern and its scaling law
LAPC, Institute of Atmospheric Physics, Chinese Academy of Sciences Beijing, 100029, PRC
2 National Science Foundation of China - Beijing, 100085, PRC
Corresponding author: email@example.com
Accepted: 26 October 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.
PACS: 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
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