A new turbulence energy cascade pattern and its scaling law

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