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2021 | OriginalPaper | Chapter

4. Overview of Closure Methods for the Closure Problem of Turbulence

Author : Jan Friedrich

Published in: Non-perturbative Methods in Statistical Descriptions of Turbulence

Publisher: Springer International Publishing

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Abstract

In the preceding chapter, we introduced a statistical formulation of hydrodynamic turbulence. An inherent difficulty in both the moment formulation in Sect. 3.​3 and the formulation via kinetic equations in Sect. 3.​4 is the hierarchical character of the corresponding system of equations. The latter can be considered as a signature of the spatio-temporal complexity that is inherent in turbulent systems. Despite the fact that moment and kinetic approach differ in the way the hierarchy of equations arises, they share the property that equations of statistical quantities of order n involve unclosed terms of order \(n+1\). Hence, in both approaches, we are faced with the amply defined closure problem of turbulence.

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previous chapter Statistical Formulation of the Problem of Turbulence
next chapter Non-Perturbative Methods
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Metadata
Title
Overview of Closure Methods for the Closure Problem of Turbulence
Author
Jan Friedrich
Copyright Year
2021
Book
Non-perturbative Methods in Statistical Descriptions of Turbulence

Print ISBN: 978-3-030-51976-6

Electronic ISBN: 978-3-030-51977-3

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-51977-3_4

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