A Constitutive Equation of Turbulence

Even though applications of direct numerical simulations are on the rise, today the most usual method to solve turbulence problems is still to apply a closure scheme of a defined order. It is not the case that a rising order of a turbulence model is always related to a quality improvement. Even more...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Peter W. Egolf, Kolumban Hutter
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Newton’s law of viscosity Reynolds shear stress Kraichnan’s direct interaction approximation Boussinesq’s closure approximation Prandtl’s mixing-length model difference-quotient turbulence model Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
Acceso en línea:	https://doaj.org/article/ef956db5e9eb4c1688701c78864ad797
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:ef956db5e9eb4c1688701c78864ad797
record_format	dspace
spelling	oai:doaj.org-article:ef956db5e9eb4c1688701c78864ad7972021-11-25T17:31:49ZA Constitutive Equation of Turbulence10.3390/fluids61104142311-5521https://doaj.org/article/ef956db5e9eb4c1688701c78864ad7972021-11-01T00:00:00Zhttps://www.mdpi.com/2311-5521/6/11/414https://doaj.org/toc/2311-5521Even though applications of direct numerical simulations are on the rise, today the most usual method to solve turbulence problems is still to apply a closure scheme of a defined order. It is not the case that a rising order of a turbulence model is always related to a quality improvement. Even more, a conceptual advantage of applying a lowest order turbulence model is that it represents the analogous method to the procedure of introducing a <i>constitutive equation</i> which has brought success to many other areas of physics. First order turbulence models were developed in the 1920s and today seem to be outdated by newer and more sophisticated mathematical-physical closure schemes. However, with the new knowledge of fractal geometry and fractional dynamics, it is worthwhile to step back and reinvestigate these lowest order models. As a result of this and simultaneously introducing generalizations by multiscale analysis, the first order, nonlinear, nonlocal, and fractional Difference-Quotient Turbulence Model (DQTM) was developed. In this partial review article of work performed by the authors, by theoretical considerations and its applications to turbulent flow problems, evidence is given that the DQTM is the missing (apparent) constitutive equation of turbulent shear flows.Peter W. EgolfKolumban HutterMDPI AGarticleNewton’s law of viscosityReynolds shear stressKraichnan’s direct interaction approximationBoussinesq’s closure approximationPrandtl’s mixing-length modeldifference-quotient turbulence modelThermodynamicsQC310.15-319Descriptive and experimental mechanicsQC120-168.85ENFluids, Vol 6, Iss 414, p 414 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Newton’s law of viscosity Reynolds shear stress Kraichnan’s direct interaction approximation Boussinesq’s closure approximation Prandtl’s mixing-length model difference-quotient turbulence model Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
spellingShingle	Newton’s law of viscosity Reynolds shear stress Kraichnan’s direct interaction approximation Boussinesq’s closure approximation Prandtl’s mixing-length model difference-quotient turbulence model Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85 Peter W. Egolf Kolumban Hutter A Constitutive Equation of Turbulence
description	Even though applications of direct numerical simulations are on the rise, today the most usual method to solve turbulence problems is still to apply a closure scheme of a defined order. It is not the case that a rising order of a turbulence model is always related to a quality improvement. Even more, a conceptual advantage of applying a lowest order turbulence model is that it represents the analogous method to the procedure of introducing a <i>constitutive equation</i> which has brought success to many other areas of physics. First order turbulence models were developed in the 1920s and today seem to be outdated by newer and more sophisticated mathematical-physical closure schemes. However, with the new knowledge of fractal geometry and fractional dynamics, it is worthwhile to step back and reinvestigate these lowest order models. As a result of this and simultaneously introducing generalizations by multiscale analysis, the first order, nonlinear, nonlocal, and fractional Difference-Quotient Turbulence Model (DQTM) was developed. In this partial review article of work performed by the authors, by theoretical considerations and its applications to turbulent flow problems, evidence is given that the DQTM is the missing (apparent) constitutive equation of turbulent shear flows.
format	article
author	Peter W. Egolf Kolumban Hutter
author_facet	Peter W. Egolf Kolumban Hutter
author_sort	Peter W. Egolf
title	A Constitutive Equation of Turbulence
title_short	A Constitutive Equation of Turbulence
title_full	A Constitutive Equation of Turbulence
title_fullStr	A Constitutive Equation of Turbulence
title_full_unstemmed	A Constitutive Equation of Turbulence
title_sort	constitutive equation of turbulence
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ef956db5e9eb4c1688701c78864ad797
work_keys_str_mv	AT peterwegolf aconstitutiveequationofturbulence AT kolumbanhutter aconstitutiveequationofturbulence AT peterwegolf constitutiveequationofturbulence AT kolumbanhutter constitutiveequationofturbulence
_version_	1718412261045829632

A Constitutive Equation of Turbulence

Ejemplares similares