Experimental investigations of the forced response of swirl-stabilized turbulent flames to upstream flow disturbances were performed in an industrial scale gas turbine combustor operating with natural gas fuel and CO₂/air. We measured flame transfer functions (FTFs) for a wide range of forcing frequency over a broad range of operating conditions with 50–120 kW thermal power. A sensitivity analysis was then performed in order to identify the key dimensionless parameters controlling the forced swirl flame dynamics. Two different dimensionless parameters, S t ₁ = (fδ _sw )/U and S t ₂ = (f L _f )/U, are used as dimensionless frequencies, while the dependence of the FTF gain on the turbulent flame speed is taken into account using a dimensionless flame length, ξ = L _f /D _c . The implementation of the nondimensionalization strategy using several time and length scales reveals that all FTFs are well characterized by either S t ₁ or S t ₂, but the best result is obtained from a combination of S t ₁ and S t ₂, which accounts for the interference mechanisms of vortical and acoustic disturbances in the system. As a consequence, the occurrence of local minima and local maxima, a clear manifestation of destructive and constructive interferences of acoustically forced swirl-stabilized flames, is well captured by the dimensionless numbers. This methodology is then applied to extensive FTF data measured from a different gas turbine combustor. A comparison of the FTFs for the two different gas turbine combustion systems provides insight into generalized transfer function behaviors in the dimensionless domain. This study focuses on velocity-coupled combustion instability, and these generalizations may not extend to situations where other coupling mechanisms dominate.