This paper explains the basic steps form the classical turbulence mechanics (CTM) to the postclassical turbulence mechanics (PCTM). When the CTM stems from the characterization of the motion states in the infinitesimal surroundings of the flowfield points by the flow velocity at these points then the PCTM complements this characterization by the curvature of the velocity fluctuation streamlines passing these points. The complementation is formalized by the inclusion of the curvature of the velocity fluctuation streamlines to the arguments of the probability distribution of the motion states in the infinitesimal surroundings of the flow field points. The most radical physical outcome of the realized formalism is the characterization of the turbulence viscosity properties by two types of turbulence viscosity against only one shear viscosity within the CTM.
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