Energy Spectrum of Turbulence Flow

Abstract

This paper presents the structure of the motion of fluid particles in three cases of turbulent flow using the energy spectrum analysis. Firstly, three-dimensional turbulent flow is studied. The energy spectrum obeys the kolmogorov -5/3 law. Energy fed into the turbulence goes primarily into the larger eddies. The transfer of energy from large scales to small scales occurs. From these, smaller eddies are generated, and then still smaller ones. The process continues until the length scale is small enough for viscous action to be important and dissipation to occur. This sequence is called the energy cascade. Secondly, two-dimensional turbulent flow is investigated. The energy spectrum obeys a power law E(k) oc {3. This turbulent motion has the ordinary energy cascade from larger eddies to
the smaller ones, and simultaneously there is the reverse cascade in which the energy turns back to the larger eddies. It means that two smaller eddies are combined to a larger one. Finally, the turbulence structure of transition in pipe flow, which has slope of energy spectrum of -3.3, is investigated. The energy spectrum of the turbulent pipe flow has the slope about -3.3 which is quite close to that of the minus third power law of two-dimensional turbulent flow. It is expected that the turbulent motion of transition in pipe flow is probably related to that of the minus third power law. However, the detailed
physical meaning for the slope -3.3 is not clear yet