Numerical Studies of Steady Flow in a Two-Dimensional Square Cavity at High Reynolds Numbers

1975 ◽  
Vol 38 (3) ◽  
pp. 889-895 ◽  
Author(s):  
Satoru Ozawa
Keyword(s):  
Steady Flow ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Square Cavity ◽  
Numerical Studies ◽  
High Reynolds Numbers ◽  
High Reynolds

Experiments on laminar film flow along a periodic wall

2002 ◽  
Vol 457 ◽  
pp. 133-156 ◽  
Author(s):  
M. VLACHOGIANNIS ◽  
V. BONTOZOGLOU
Keyword(s):  
Film Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Imaging Method ◽  
Three Dimensional Flow ◽  
Numerical Studies ◽  
High Reynolds Numbers ◽  
Gravity Driven ◽  
Temporary Decrease ◽  
High Reynolds

Experimental results are reported on the structure of gravity-driven film flow along an inclined periodic wall with rectangular corrugations. A fluorescence imaging method is used to capture the evolution of film height in space and time with accuracy of a few microns. The steady flow is found to exhibit a statically deformed free surface, as predicted by previous asymptotic and numerical studies. Though usually unstable, its characteristics determine much of the subsequent non-stationary dynamics. Travelling disturbances are observed to evolve into solitary multi-peaked humps, and pronounced differences from the respective phenomena along a flat wall are noted. Finally, a remarkable stabilization of the flow at high Reynolds numbers is documented, which proceeds through the development of a three-dimensional flow structure and leads to a temporary decrease in film thickness and recession of solitary waves.

scholarly journals Revisiting Batchelor's theory of two-dimensional turbulence

2007 ◽  
Vol 591 ◽  
pp. 379-391 ◽  
Author(s):  
DAVID G. DRITSCHEL ◽  
CHUONG V. TRAN ◽  
RICHARD K. SCOTT
Keyword(s):  
Reynolds Number ◽  
Mathematical Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Two Dimensional ◽  
Simple Modification ◽  
High Reynolds Numbers ◽  
Decaying Turbulence ◽  
High Reynolds

Recent mathematical results have shown that a central assumption in the theory of two-dimensional turbulence proposed by Batchelor (Phys. Fluids, vol. 12, 1969, p. 233) is false. That theory, which predicts a χ2/3k−1 enstrophy spectrum in the inertial range of freely-decaying turbulence, and which has evidently been successful in describing certain aspects of numerical simulations at high Reynolds numbers Re, assumes that there is a finite, non-zero enstrophy dissipation χ in the limit of infinite Re. This, however, is not true for flows having finite vorticity. The enstrophy dissipation in fact vanishes.We revisit Batchelor's theory and propose a simple modification of it to ensure vanishing χ in the limit Re → ∞. Our proposal is supported by high Reynolds number simulations which confirm that χ decays like 1/ln Re, and which, following the time of peak enstrophy dissipation, exhibit enstrophy spectra containing an increasing proportion of the total enstrophy 〈ω2〉/2 in the inertial range as Re increases. Together with the mathematical analysis of vanishing χ, these observations motivate a straightforward and, indeed, alarmingly simple modification of Batchelor's theory: just replace Batchelor's enstrophy spectrum χ2/3k−1 with 〈ω2〉 k−1 (ln Re)−1).

Steady flow with separation past a thin airfoil at high Reynolds numbers

1994 ◽  
Vol 29 (2) ◽  
pp. 277-281 ◽  
Author(s):  
O. L. Zaitsev ◽  
V. V. Sychev
Keyword(s):  
Steady Flow ◽  
Reynolds Numbers ◽  
High Reynolds Numbers ◽  
Thin Airfoil ◽  
High Reynolds
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