Thermoacoustic instabilities under lean operation in gas turbine burners hinder the development of lean premixed combustion mode of operation, thus limiting the potential to decrease NOx emissions. A method to improve stability of lean combustion while maintaining low thermal NOx formation is to add hydrogen in typical gas turbine fuels such as natural gas. The present work examines the thermoacoustic dynamic characteristics of hydrogen-enriched methane blends in a swirl stabilized model gas turbine combustor. We blend CH4 with increasing H2 molar content (from 0% to 40%) at a global equivalence ratio of ϕ=0.55 on a constant Reynolds number Re = 19000. The reference case of pure methane is susceptible to blow off at the same equivalence ratio. On increasing the hydrogen content at 10% H2, the flammability limits are extended. However, further increase of the H2 content leads to manifestation of random short bursts of dynamic pressure and heat release. Thermoacoustic dynamics are intermittently injected between a quiescent state and a regime of high amplitude oscillations. On further increasing H2 content, the dynamics are attracted towards a limit cycle; a fully established high amplitude regime, where no requiescence is observed. In this regime, heat release rate and dynamic pressure oscillate in phase and at the same frequency. Based on the observed dynamics, we seek a mixture property to characterize the dynamic state, the combustor operates in. We show that the extinction strain rate associated with each mixture can collapse the dynamic transitions from quiescent to intermittent instabilities and finally to fully established thermoacoustic oscillations. In each dynamic state, we examine the mechanism that affiliates coherent structures of the underlying thermodynamic flow field with the flame through the relation of the spatial distribution of the flow imposed strain rate over the extinction strain rate of each mixture. It is shown that the flame anchoring locations for a given mixture are dictated by the flow imposed strain rate and then that increased extinction resistance couples the flame with naturally excited to swirling flows helical instabilities, that may instigate mechanisms responsible for intermittent heat release rate bursts. Finally, the combustor demonstrates a limit cycle behaviour where the flow-imposed strain rate oscillates about the extinction strain rate along the inner shear layers causing local extinction of the flame at the root close to the centerbody.