A new approach to obtain the closure formulas for the von Kármán–Howarth and Corrsin equations is presented, which is based on the Lagrangian representation of the fluid motion, and on the Liouville theorem associated to the kinematics of a pair of fluid particles. This kinematics is characterized by the finite scale separation vector which is assumed to be statistically independent from the velocity field. Such assumption is justified by the hypothesis of fully developed turbulence and by the property that this vector varies much more rapidly than the velocity field. This formulation leads to the closure formulas of von Kármán–Howarth and Corrsin equations in terms of longitudinal velocity and temperature correlations following a demonstration completely different with respect to the previous works. Some of the properties and the limitations of the closed equations are discussed. In particular, we show that the times of evolution of the developed kinetic energy and temperature spectra are finite quantities which depend on the initial conditions.

Von Kármán--Howarth and corrsin equations closure based on Lagrangian description of the fluid motion / DE DIVITIIS, Nicola. - In: ANNALS OF PHYSICS. - ISSN 0003-4916. - ELETTRONICO. - 368:(2016), pp. 296-309. [10.1016/j.aop.2016.02.010]

Von Kármán--Howarth and corrsin equations closure based on Lagrangian description of the fluid motion

DE DIVITIIS, Nicola
2016

Abstract

A new approach to obtain the closure formulas for the von Kármán–Howarth and Corrsin equations is presented, which is based on the Lagrangian representation of the fluid motion, and on the Liouville theorem associated to the kinematics of a pair of fluid particles. This kinematics is characterized by the finite scale separation vector which is assumed to be statistically independent from the velocity field. Such assumption is justified by the hypothesis of fully developed turbulence and by the property that this vector varies much more rapidly than the velocity field. This formulation leads to the closure formulas of von Kármán–Howarth and Corrsin equations in terms of longitudinal velocity and temperature correlations following a demonstration completely different with respect to the previous works. Some of the properties and the limitations of the closed equations are discussed. In particular, we show that the times of evolution of the developed kinetic energy and temperature spectra are finite quantities which depend on the initial conditions.
2016
corrosion equation; fully developed chaos; liouville theorem; lyapunov exponent; Von Kármán-Howarth equation;physics and astronomy (all)
01 Pubblicazione su rivista::01a Articolo in rivista
Von Kármán--Howarth and corrsin equations closure based on Lagrangian description of the fluid motion / DE DIVITIIS, Nicola. - In: ANNALS OF PHYSICS. - ISSN 0003-4916. - ELETTRONICO. - 368:(2016), pp. 296-309. [10.1016/j.aop.2016.02.010]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/928301
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