Spectral Characteristics of Turbulent Velocity Fluctuations at Different Reynolds Numbers

Abstract

Different approaches to the theoretical description of the energy characteristics of turbulence are considered on a wide wavenumber range including both the inertial and the dissipation intervals. The description is based on the hypothesis on the locality of intermodal interactions and the cascade mechanism of energy transfer over the wavenumber spectrum. The concept of the Markovian nature of the transfer makes it possible to use the methods of renormalization group and to derive a renorm group equation supplementing the conventionally used dimensional considerations and the energy balance equation. Within the framework of a model that does not contain unphysical singularities of the type of the inverse spectral flux formulas for the spectral characteristics are obtained beyond the turbulence generation region at different Reynolds numbers determined by the turbulent energy pumping parameters on the small wavenumber range modeled by an external random force.