This work presents new results describing the action of an acoustic transverse standing wave on a methane-air premixed V-flame located at a pressure antinode. Investigations of the jet highlight a mode conversion from a transverse cavity mode to a longitudinal mode, involving a "plugging" flow-rate modulation. This essential mechanism generates vortical structures convected toward the flame stabilized on a vertical rod introduced inside the burner and aligned with its axis. Depending on acoustic conditions, they develop through one of the following patterns: a pairing process, a multiple-vortex interaction in the jet outer layer, or a helical mode in the inner layer behind the rod. The flame responses are arranged in the physical space defined by the acoustic pressure amplitude ((P) over tilde (ref)) and the Strouhal numbers, St characteristic of the dominant (outer or inner) shear-layer. A harmonic flame response at the forcing frequency, f(0), is not the only possible behavior. The other behaviors observed are an asymmetrical "elongated wrinkled flame" due to the helical mode; an "aperiodic fluctuating flame"; and a "sub-harmonic rolled-up flame" due to the pairing process, which induces strong CH* emission fluctuations at f(0)/2. Several flame dynamics evolutions are noted when (P) over tilde (ref) increases. The heat release rate (h.r.r.) always begins to fluctuate at f(0). Then, depending on St, it can undergo the nonlinear frequency bifurcation; and next, it may fluctuate at f(0) again in addition to f(0)/2. Another scenario shows the h.r.r. losing any kind of ordered modulation before it eventually fluctuates at f(0). The flame stabilization is described at blowout via the leading edge behavior. Foot-displacement amplitude, and foot-width thinning and straightening are complementary dynamics and morphology features that characterize flame destabilization. The different patterns, observed as (P) over tilde (ref) increases, of successive ordered flame responses, sometimes alternating with aperiodic responses, appear as the main elements in understanding the processes involved in thermoacoustic instabilities. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.