The QDIA and regularized QDIA closures for inhomogeneous turbulence over topography

Terence J. O'Kane, Jorgen S. Frederiksen

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42 Citations (Scopus)


The dynamics and spectra of the quasi-diagonal direct interaction approximation (QDIA) closure for inhomogeneous two-dimensional turbulence over mean (single realization) topography are compared with results from direct numerical simulations (DNS). A more efficient version of the closure, termed the cumulant update QDIA (CUQDIA), has also been formulated and tested. Studies are performed for a range of resolutions, for large scale Reynolds numbers between very low (RL < 1) and moderate (RL ≊ 300) and for wide ranges of topographic spectra and initial mean field and transient spectra. The QDIA-type closures are shown to be computationally tractable for general inhomogeneous flows, particularly in cumulant update form, and to perform extremely well when the turbulence is weak. At low (RL ≊ 60) to moderate (RL ≊ 300) Reynolds numbers the presence of significant amplitude small-scale mean fields and topography reduces the under-estimation of small-scale transient kinetic energy that is characteristic of the Eulerian direct interaction approximation (DIA). A regularized version of the CUQDIA closure (RCUQDIA) in which interactions are localized in wavenumber space, depending on specified cut-off ratios, has also been tested at moderate Reynolds number for cases when the small-scale mean fields and topography are weak. Excellent agreement has been found between the RCUQDIA closure and DNS results for turbulent flows with properties broadly similar to atmospheric spectra.

Original languageEnglish
Pages (from-to)133-165
Number of pages33
JournalJournal of Fluid Mechanics
Issue number504
Publication statusPublished - 10 Apr 2004
Externally publishedYes

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