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Analysis of the Two-Point Velocity Correlations in Turbulent Boundary Layer Flows

Oberlack, Martin (1995):
Analysis of the Two-Point Velocity Correlations in Turbulent Boundary Layer Flows.
In: Center for Turbulence Research. Annual research briefs 1995, Stanford University/NASA Ames, pp. 209-220, [Book Section]

Abstract

The general objective of the present work is to explore the use of Rapid Distortion Theory (RDT) in analysis of the two-point statistics of the log- layer. RDT is applicable only to unsteady flows where the non-linear turbulence-turbulence interaction can be neglected in comparison to linear turbulence-mean interactions. Here we propose to use RDT to examine the structure of the large energy-containing scales and their interaction with the mean flow in the log-region. The contents of the work are twofold: First, two-point analysis methods will be used to derive the law-of-the- wall for the special case of zero mean pressure gradient. The basic assumptions needed are one-dimensionality in the mean flow and homogeneity of the fluctuations. It will be shown that a formal solution of the two- point correlation equation can be obtained as a power series in the von Karman constant, known to be on the order of 0.4. In the second part, a detailed analysis of the two-point correlation function in the log-layer will be given. The fundamental set of equations and a functional relation for the two-point correlation function will be derived. An asymptotic expansion procedure will be used in the log-layer to match Kolmogorov's universal range and the one-point correlations to the inviscid outer region valid for large correlation distances.

Item Type: Book Section
Erschienen: 1995
Creators: Oberlack, Martin
Title: Analysis of the Two-Point Velocity Correlations in Turbulent Boundary Layer Flows
Language: English
Abstract:

The general objective of the present work is to explore the use of Rapid Distortion Theory (RDT) in analysis of the two-point statistics of the log- layer. RDT is applicable only to unsteady flows where the non-linear turbulence-turbulence interaction can be neglected in comparison to linear turbulence-mean interactions. Here we propose to use RDT to examine the structure of the large energy-containing scales and their interaction with the mean flow in the log-region. The contents of the work are twofold: First, two-point analysis methods will be used to derive the law-of-the- wall for the special case of zero mean pressure gradient. The basic assumptions needed are one-dimensionality in the mean flow and homogeneity of the fluctuations. It will be shown that a formal solution of the two- point correlation equation can be obtained as a power series in the von Karman constant, known to be on the order of 0.4. In the second part, a detailed analysis of the two-point correlation function in the log-layer will be given. The fundamental set of equations and a functional relation for the two-point correlation function will be derived. An asymptotic expansion procedure will be used in the log-layer to match Kolmogorov's universal range and the one-point correlations to the inviscid outer region valid for large correlation distances.

Title of Book: Center for Turbulence Research. Annual research briefs 1995
Publisher: Stanford University/NASA Ames
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
16 Department of Mechanical Engineering
Date Deposited: 30 Aug 2011 14:27
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