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 50-120kW 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, St(1)=(f(sw))/U and St(2)=(fL(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, =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 St(1) or St(2), but the best result is obtained from a combination of St(1) and St(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.