Dependency of optimal jet control position on Reynolds-number in cylinder flow via resolvent analysis

Flow around a circular cylinder is a typical unstable separated flow, and its unsteady loads control has been a key research focus in fluid mechanics. This paper proposes a feature-driven flow control position design methodology based on resolvent analysis effective gain, and studies the Reynolds number dependence of the optimal control position. Resolvent analysis is first conducted on the time-averaged flow, with the effective gain quantitatively characterizing the sensitivity to tangential jet excitation on the cylinder surface. By applying steady jet control at the position corresponding to peak effective gain, complete suppression of unsteady vortex shedding is achieved. Subsequently, a relationship between the optimal control position and Reynolds number is proposed: θ opt = − 154.26 R e − 0.5 + 87.59 ( 47 ≤ R e ≤ 200 ) . The R e − 0.5 power-law dependency fundamentally originates from viscosity-dominated boundary layer dynamics. This relationship reveals a critical physical law: the optimal tangential jet position consistently resides at Δ θ = 9.1 ° upstream of the flow separation position. Finally, we propose a variable of the effective range of the Coanda effect, explaining the viscous wall-attachment physics mechanism that maintains this fixed upstream offset. Flow field analysis further demonstrates that the optimal control position invariably coincides with 12.4% of the maximum surface vorticity in the uncontrolled case. This study indicates that the separation position of cylinder flow is a key feature, providing important guidance for the design of control positions.