Renormalized cumulants and velocity derivative skewness in Kolmogorov turbulence. (24th February 2017)

• Record Type: Journal Article
• Authors: Singha, Tapas; Dutta, Kishore; Nandy, Malay K
• Is Part Of: Journal of physics. Volume 50:Number 12(2017)
• Publication Date: 2017-02-24
• Subjects: Kolmogorov turbulence -- velocity derivative skewness -- renormalized perturbative scheme; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa5d84
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We apply a renormalized perturbative scheme to the Navier–Stokes equation for an incompressible isotropic turbulent velocity field. This allows us to obtain the renormalized expressions for second- and third-order cumulants of the velocity derivative directly from the corresponding Feynman diagrams. The resulting expressions are integrated numerically by excluding and including the dissipation range assuming Kolmogorov and Pao's phenomenological expressions for the energy spectrum. The ensuing values for skewness are found to be S = −0.647 (when the dissipation range is excluded) and S = − 0.682 (when the dissipation is included). These estimated values are compared with various experimental, numerical and theoretical results.