We study the dependence of the flame sheet response of an open V-flame when subjected to simultaneous but independently controlled – (1) narrowband, coherent disturbances, (2) mean flow velocity, and (3) turbulent broadband disturbances. We re-examine the data presented in Humphrey et al. (2018). Flame edge and flow field were obtained from Mie scattering images and PIV vector fields, respectively. We determine the flame sheet response, which allows us to understand the effects of kinematic restoration on the local and global flame dynamics. We find some highly nonlinear behaviors in the flame sheet response, which have not been reported previously. In particular, we observe (1) oscillations in the rise and peak region of the flame response, and (2) early onset of the nonlinear coupling between narrowband and broadband disturbances, resulting in oscillatory decay immediately downstream of the flame holder region. The spatial oscillations seen in the flame response arise only when unalike disturbances such as vortical and flame wrinkle disturbances have a comparable wavelength and, thus, interfere. We then find that higher nominal velocity and turbulent intensities increase asymmetry in the flame response, and subsequently affect the local and global heat release response (HRR). We analytically calculate HRR from flame sheet response. We find that there is a monotonic increase in the response with increasing flame length for lower nominal velocities, possibly due to higher flame symmetry. Moreover, the HRR calculated from flame sheet response captures the effect of kinematic restoration very well. Notably, there is a decrease in HRR with increasing turbulence intensity due to enhanced smoothing from kinematic restoration at higher turbulence levels. We further find that the flame response dependence on harmonic forcing manifest in the low-pass filter characteristics of the global HRR response. © 2019 The Combustion Institute