Quantic Behavior of Turbulence
C.Çıray, I. Kabakci, E. Bekoğlu, I. Çolak

Abstract
This paper considers a turbulence paradigm which helps to analyze some features of turbulence structure at a physically acceptable level. Highlighted features are dispersion relation, length, and time scales for the whole wave number range of turbulence including one-dimensional energy spectrum. The lowest wave number is restricted only by the dimensions of the domain in which turbulence is active. The highest wave number is limited by measurement capabilities. The physical paradigm conceived for turbulence suggests a combined “particle + dispersive-wave” character of turbulence”, shortly “Quantic Behavior of Turbulence (QBT)”. QBT studies turbulence starting from the molecular activity of fluid particles in a turbulent flow. Coagulations of molecules are demonstrated via numerical simulation of molecular activity for different mean velocities. These groupings of fluid particles can be considered as “infant eddies”. A possible physics for the formation of eddies that characterizes the “discrete nature” of turbulence at low frequencies and associated “dispersive-wave behavior” at high frequencies, is explained. This reasoning leading to define fluctuating velocity as group velocity is discussed.“Calculation of Wave Number” in view of QBT is performed with the help of two equations and an auxiliary relation. The first equation is a physical relation that uses the energy spectrum and the other one is the group-velocity formulation. Related mathematical developments are given in the “Appendix”. Results from different types of flows are illustrated. Salient features of numerical results are exposed. The dispersion relations of different flows are presented. The discrete + wave-like nature of turbulence is highlighted in view of an overall evaluation in “Discussion” at the end of the paper.

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