E​RCOFTAC PC Italy

Reynolds-Number Effects on Shear-Layer Separation and Reattachment

Roberto Corsini, Andrea Cimarelli, Enrico Stalio
(Dipartimento di Ingegneria “Enzo Ferrari”, Universita Degli Studi di Modena e Reggio Emilia, Modena, IT)

Video : Direct numerical simulation of the leading-edge separated shear layer over a 5:1 rectangular cylinder for Reynolds numbers 3000 ≤ Re ≤ 14 000. Isocontours of spanwise vorticity (black −ωz, white +ωz) show instability onset, transition to turbulence, shearlayer breakdown, and reattachment along the side surface. The mean reattachment length results from a balance between shear-layer entrainment and wake pressure recovery. At low Re, engulfment by large-scale coherent vortices enhances entrainment and advances reattachment; increasing Re accelerates transition but fragments turbulence into finer structures, reducing net entrainment and shifting reattachment downstream.

Recent publications

1. R. Corsini, A. Cimarelli, E. Stalio. Turbulent transport of momentum and passive scalar around a rectangular cylinder. J. Fluid Mech., 1019:A33, 2025. doi: 10.1017/jfm.2025.10619.
2. A. Cimarelli, R. Corsini, E. Stalio. Reynolds number effects in separating and reattaching flows with passive scalar transport. J. Fluid Mech., 984:A20, 2024. doi: 10.1017/jfm.2024.215.
3. R. Corsini, A. Cimarelli, E. Stalio. DNS of the Flow About a 5:1 Rectangular Body with Sharp Corners. In Direct and Large Eddy Simulation XIII (ed. C. Marchioli, M. V. Salvetti, P. Garcia-Villalba M. & P. Schlatter, pp. 9–16, 2024. doi: 10.1007/978-3-031-47028-8 2.

Scientific abstract

Scientific abstract Flow separation and reattachment govern momentum and scalar transport in a wide range of bluff-body configurations, with significant implications for drag, wake development, and heat/mass transfer. A dominant mechanism in these flows is turbulent entrainment across the separated shear layer, which affects its growth, the tendency to reattach, and wake pressure recovery. However, the Reynolds-number scaling of entrainment in sharp-edged flows and its coupling to separation-bubble dynamics remain only partially understood.

This contribution is based on a direct numerical simulation (DNS) campaign of the turbulent flow around a 5:1 rectangular cylinder at Reynolds numbers Re = 3000, 8000, and 14 000 (based on freestream velocity and body thickness), including passivescalar transport at a fixed Schmidt number Sc = 0.71. The configuration is part of the BARC benchmark initiative (https://www.aniv-iawe.org/barc/) and provides a canonical setting to study laminar separation at sharp leading edges, shear-layer instability and transition, reattachment along the side surface, and subsequent wake development. These simulations complement higher-Re experiments and bridge the gap with lower-Re DNS, providing support for the observation that several integral quantities exhibit only weak Reynolds-number dependence beyond Re ≳ 104, consistent with the emergence of an incipient asymptotic high-Re regime (Cimarelli et al., J. Fluid Mech., 2024).

The video visualization, obtained from the DNS database, synthesizes the leadingedge shear layer evolution through instantaneous isocontours of spanwise vorticity and highlights the onset of shear-layer instability, breakdown to turbulence, and mean reattachment. Beyond its aesthetic value, the visualization supports a quantitative entrainment analysis based on Taylor’s hypothesis, whereby the mean inflow across a turbulent interface scales with a characteristic velocity difference. Evaluated between transition and reattachment locations, the entrainment parameter is found to be β ≈ 0.16 at Re = 3000, decreasing to β ≈ 0.12 at Re = 8000 and 14 000. Although increasing Re advances transition, the shear-layer turbulence progressively fragments into finer-scale structures and experiences wall-induced confinement near reattachment, weakening net entrainment and shear-layer growth. As a result, the mean reattachment location shifts downstream. At the lowest Reynolds number, in contrast, large-scale coherent vortices promote engulfment away from the wall, enhance entrainment, and shorten the reattachment length.

These results demonstrate that, over the Re range examined, reattachment is not a monotonic consequence of earlier transition, but rather the outcome of a balance between shear-layer entrainment, wake pressure recovery, and reverse-boundary-layer dynamics. The same physical mechanism rationalizes observed trends in base pressure and scalar transport and provides a high-fidelity reference dataset for turbulence-model development and entrainment-based flow-control strategies (e.g., interface manipulation, wall-normal momentum transfer, or edge treatments).