We examined the effect of hydrogen (H2) enrichment on methane (CH4) in a canonical non-premixed bluff-body stabilized burner operating under typical central jet-dominated flame mode. In the chosen mode of operation, globally, the flow field and flame feature three important successive spatial regions: the recirculation zone, neck zone and jet-like flame zone. In such configuration, the flame is exposed to a higher stretch rate in the neck zone and eventually undergoes local extinction. Such local extinction and subsequent re-ignition of broken flame branches have strong implications over the hydrodynamic instability of the coaxial annular air shear layer. It is well known that H2 addition increases the flame extinction strain rate and thus alters the local extinction phenomenon. To understand this phenomenon, we performed experiments at 10%, 20 %, 30%, and 50 % hydrogen proportion in the H2-CH4 blend. High repetition rate (5 KHz) PIV and OH PLIF measurements are performed simultaneously to perceive the quantitative insights. The results obtained from POD and 1D wavelet transform indicated the suppression of vortex shedding at the annular air shear layer for H2 addition greater than 20 %, and thus quantified the beneficial effect of H2 addition in turbulent flame stabilization.