Linear Stability Analysis of Two-Dimensional Mixed Convective Flow Past a Square Cylinder

Linear stability analysis of two-dimensional mixed convective flow past a heated square section cylinder is performed, to determine the flow stability for given flow parameters, and to study the onset of vortex shedding suppression as the Richardson number (Ri) increases. All analyses are performed in the assisted buoyancy regime \(({\text{Ri}} > 0)\) . The results from the linear stability analysis are also validated against the results from Direct Numerical Simulation (DNS). The Reynolds number (Re) and the Prandtl number (Pr) are fixed at 100 and \(0.7\) , respectively, and the effect of Richardson number on the suppression of vortex shedding phenomena is studied, by varying \({\text{Ri}}\) in the range \(\left[ {0.13,0.17} \right]\) . A critical Richardson number of \(0.16\) corresponding to the onset of suppression of vortex shedding was found through DNS. Through the linear stability analysis, this transition from unsteady to steady flow field was found to occur via a Hopf bifurcation. The behavior of the eigenmodes of the most unstable perturbations was studied. Lastly, a discussion has been made regarding the possible mechanisms that cause the transition in flow stability.