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Stability and dynamics of the laminar flow past rectangular prisms

Published online by Cambridge University Press:  03 April 2025

Alessandro Chiarini Open the ORCID record for Alessandro Chiarini [Opens in a new window]  and
Edouard Boujo Open the ORCID record for Edouard Boujo [Opens in a new window]
Alessandro Chiarini*
Affiliation:
Complex Fluids and Flows Unit, Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna-son, Okinawa 904-0495, Japan Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, Milano 20156, Italy
Edouard Boujo*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland
*
Corresponding authors: Alessandro Chiarini, [email protected]; Edouard Boujo, [email protected]
Corresponding authors: Alessandro Chiarini, [email protected]; Edouard Boujo, [email protected]
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Abstract

The laminar flow past rectangular prisms is studied in the space of length-to-height ratio ($1 \leqslant L/H \leqslant 5$), width-to-height ratio ($1.2 \leqslant W/H \leqslant 5$) and Reynolds number ($Re \lessapprox 700$); $L$ and $W$ are the streamwise and cross-flow dimensions of the prisms. The primary bifurcation is investigated with linear stability analysis. For large $W/L$, an oscillating mode breaks the top/bottom planar symmetry. For smaller $W/L$, the flow becomes unstable to stationary perturbations and the wake experiences a static deflection, vertical for intermediate $W/L$ and horizontal for small $W/L$. Weakly nonlinear analysis and nonlinear direct numerical simulations are used for $L/H = 5$ and larger $Re$. For $W/H = 1.2$ and 2.25, the flow recovers the top/bottom planar symmetry but loses the left/right one, via supercritical and subcritical pitchfork bifurcations, respectively. For even larger $Re$, the flow becomes unsteady and oscillates around either the deflected (small $W/H$) or the non-deflected (intermediate $W/H$) wake. For intermediate $W/H$ and $Re$, a fully symmetric periodic regime is detected, with hairpin vortices shed from the top and bottom leading-edge (LE) shear layers; its triggering mechanism is discussed. At large $Re$ and for all $W/H$, the flow approaches a chaotic state characterised by the superposition of different modes: shedding of hairpin vortices from the LE shear layers, and wake oscillations in the horizontal and vertical directions. In some portions of the parameter space the different modes synchronise, giving rise to periodic regimes also at relatively large $Re$.

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1008 , 10 April 2025 , A33
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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