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A Heuristic Approach to a Non‐Local Theory of Turbulent Channel Flow
Author(s) -
Rüdiger G.
Publication year - 1982
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19820620204
Subject(s) - ansatz , turbulence , formalism (music) , open channel flow , mathematics , flow (mathematics) , cauchy stress tensor , mean flow , statistical physics , heuristic , chézy formula , tensor (intrinsic definition) , classical mechanics , physics , mathematical analysis , mathematical physics , mechanics , mathematical optimization , geometry , art , musical , visual arts
In this paper a non‐local relation is postulated to exist between the one‐point‐correlation tensor and the mean flow rate of strain. Thus the original ansatz of Boussinesq is replaced by an integral relation which naturally includes a wider region of the turbulent medium into the calculation. Using the idealisation of free turbulence we can easily deduce that mean flow profile which has recently been given by Naue et al. and which appears to represent well the channel flow far away the walls. Within our integral formalism this profile proved to be correct for all those even kernels which provide exactly two solutions of a related characteristic equation. Testing some special kernels we find a good representation of the non‐local formalism by a hydrodynamics involving in its stress relation the mean flow derivatives up to the third order.