Energy Spectrum of Turbulent Velocity Pulsations at Arbitrary Values of Fluid Viscosity

• 作者: Edward V. Teodorovich
• 来源期刊: 现代物理(英文)
• 学科: 物理学
• 关键词: Spectral Flux Spectral Energy Density Local and Nonlocal Interactions Inertial Term Renormalization-Group Invariance Epsilon-Expansion Procedure
• 年，卷（期）: 2020,（10）
• 页码范围: 1502-1513
• 页数: 12页
• 分类号: O35

摘要

The problem of calculating the energy spectrum of turbulent velocity pulsations in the case of homogeneous isotropic and stationary turbulence is considered. The domain of turbulent energy production is treated as “a black box” on which boundary the spectral energy flux is given. It is assumed that the spectrum is formatted due to intermodal interactions being local in the wave-number space that leads to a cascade mechanism of energy transfer along the wave-number spectrum and the possibility of using the renormalization-group method related to the Markovian features of the process under consideration. The obtained formula for energy spectrum is valid in a wide wave-number range and at arbitrary values of fluid viscosity. It is shown that in functional formulation of the statistical theory of turbulence, the procedure of separating local intermodal interactions, which govern energy transfer (straining effect), and filtering out nonlocal interactions, which have no influence on energy transfer (sweeping effect), is directly described without providing additional arguments or conjectures commonly used in the renormalization-group analysis of turbulent spectra.