Dimensional characterizations for homogeneous and isotropic turbulence Original Research Article

We consider a homogeneous turbulent flow placed in the Kolmogorovʹs range. We study the relations between the order of magnitude of the viscosity and the order of the main physical sizes – the characteristic velocity and length – for the turbulent perturbation, by using the Method of Multiple Scales. These relations are obtained in the frame of the Kolmogorovʹs fundamental theory and his hypotheses of similarity. First, we obtain the lower and upper limits for the exponent of the order of magnitude of the viscosity in the case of a homogeneous turbulence placed in the inertial subrange. Furthermore, we also determine the range of the exponent of the order of magnitude of the characteristic turbulent velocity, in terms of the exponent of the order of magnitude of the viscosity, for small characteristic turbulent length. The above formulas are useful for the general study of a homogeneous turbulent flow by using the homogenization of the microstructure.