Influence of depth-ratio on turbulence transition in the wake of wall-mounted prisms

This paper presents a numerical investigation of the turbulence transition phenomenon in the wake of wall-mounted prisms. Large-eddy simulations are performed at $Re = 1\times 10^3 {-}5\times 10^3$ for prisms with a range of aspect ratio (height to width) from $0.25$ to $1.5$ , and depth ratios (length to width) between $1$ and $4$ . The results show that the wake irregularity is enhanced with increasing depth ratio, evidenced by higher turbulent kinetic energy ( ${\approx}90\,\%$ ) near the leading edge, and the onset of irregular, unsteady vortex shedding. This is attributed to interactions between Kelvin–Helmholtz instability (KHI) of the shear layer and large-scale vortex shedding, and it is induced by an unsteady shear layer, resembling flapping-like motion. These interactions elevate the flow momentum due to increased turbulence intensity and mixing, contributing to the wake transition phenomenon. To this end, this study defines the role of depth ratio in the transition phenomenon by showing that increasing depth ratio (e.g. from $1$ to $4$ ) leads to earlier onset of KHIs in the shear layer. These instabilities intensify with depth ratio, resulting in stronger interactions between shear layer and large-scale vortex shedding. Specifically, KHI-induced vortices interact more frequently with large-scale wake structures for higher depth ratio prisms, exciting larger flow fluctuations and irregular wake patterns. This interaction alters the frequency and coherence of vortex shedding, revealing a complex coupling mechanism that drives the transition to turbulence.