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.File | Dimensione | Formato | |
---|---|---|---|
De Divitiis_preprint_vonkármán–howarth_2016.pdf
accesso aperto
Tipologia:
Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
263.58 kB
Formato
Adobe PDF
|
263.58 kB | Adobe PDF | |
De Divitiis_von-kármán–howarth_2016.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
567.76 kB
Formato
Adobe PDF
|
567.76 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.