Role of baroclinic vorticity production on three-dimensional wake transition of a heated cylinder using a non-Boussinesq model

This study examines the role of buoyancy-induced baroclinic vorticity production in the three-dimensional (3-D) wake transition behind an infinitely long heated square cylinder subjected to aiding and cross-flow buoyancy, using direct numerical simulation (DNS). A non-Oberbeck–Boussinesq (NOB) model is employed, requiring the solution of the full compressible Navier–Stokes equations to capture baroclinic effects under large-scale heating regimes. Simulations are carried out at a Reynolds number of italic Re equals 300 Re = 300 $\textit{Re} = 300$ and a low Mach number ( upper M equals 0.1 M = 0.1 $M = 0.1$ ) to minimise compressibility effects, with air (Prandtl number italic probability equals 0.71 Pr = 0.71 $\textit{Pr} = 0.71$ ) as the working fluid. Previous studies have demonstrated that baroclinic torque significantly enhances the strength of 3-D wake structures, thereby promoting an earlier onset of three-dimensionality compared with the unheated case. However, these effects have been predominantly investigated in cross-buoyancy configurations, and the underlying mechanisms remain insufficiently understood. In the present study, the contributions of streamwise and spanwise baroclinic torque are systematically analysed to elucidate the mechanisms governing flow instability and organisation in thermally influenced wakes. The findings reveal a complex interplay between baroclinic torque and buoyancy, indicating that increasing heating levels weaken the 3-D wake under aiding-buoyancy conditions while strengthening it in cross-buoyancy configurations. Furthermore, the production of spanwise baroclinic torque, whether aligned with or opposed to local vortices, increases flow complexity and influences vortex shedding intensity and vortex dislocations. It also governs the contrasting wake behaviour, resulting in a symmetric wake under aiding buoyancy and an asymmetric wake under cross-buoyancy.