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A KARHUNEN–LOÉVE ANALYSIS OF TURBULENT THERMAL CONVECTION
Author(s) -
TARMAN I. HAKAN
Publication year - 1996
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19960115)22:1<67::aid-fld332>3.0.co;2-c
Subject(s) - mathematics , turbulence , karhunen–loève theorem , orthogonal functions , projection (relational algebra) , mathematical analysis , flow (mathematics) , closure problem , truncation (statistics) , geometry , physics , mechanics , algorithm , statistics
The Karhunen–Loéve (K–L) procedure is applied to a turbulent thermal convection database which is generated numerically through integration of the Boussinesq equation in a periodic box with stress‐free boundary conditions using a Fourier collocation spectral method. This procedure generates a complete set of mutually orthogonal functions in terms of which the turbulent flow fluctuation field is represented optimally in the mean square sense. A study is performed ranging from the direct projection of the database onto the set, resulting in a considerable data compression, to developing a system of dynamical equations employing the set as a basis for approximating the Boussinesq equation. In the latter a new strategy is proposed and tested for the treatment of the mean component of the turbulent flow. Finally, the direct projection and the dynamical equations are used to study the effects of truncation on the representation of the turbulent flow.