Abstract

In this paper a method for calculation of the incidence dimension D for the pulsating pressure time series of turbulent flow in the “restructured phase space” is presented as result of theoretical study on the strange attractor. Variation rules of incidence dimension values in accordance with embedded space dimensions are obtained and internal rules existing in the superficially chaotic turbulent system are proven. It is demonstrated that in the pulsating pressure system of the high velocity flow, a stable low dimension strange attractors is existed, whose fractional dimensions are then calculated. The fractional dimension of the attractor is about 7<D<8 for silt-laden water system and is 5<D<6 for the clear water system. The fractional dimension gives out the minimum number of status variables needed for describing the attractor’s structure.

Key words: phase space; attractor; correlation dimension; turbulent flow; pulsation stress