Energy spectrum of turbulent velocity pulsations in a wide range of wave numbers (renorm-group approach)

Abstract

Based on the concept of cascade mechanism of energy transfer over the wave-number spectrum and related to the locality property of intermodal interactions forming the energy spectrum, the unified formula for spectral energy density is obtained that is valid in a wide range of wave numbers including both inertial and dissipation ranges. The form of the spectrum is governed by three parameters, namely, a value of wave number chosen as the normalization point assigned to the edge of the domain of the stochasticity emergence due to the development of instability of large-scale flows and the turbulent energy production, the spectral energy flux through the boundary of energy production domain in the wave-number space (the energy pumping rate), and the fluid kinematic viscosity.