Inverse jet flame (IJF) configuration is a variant of coaxial nonpremixed jet flame which can produce a non-luminous compact blue flame with independent control of air and fuel jet momentum. In the present work, the effect of central air jet velocity on visible topological features such as, visible flame height and base flame height is investigated experimentally. Also the fluid dynamics behind the evolution of base flame in IJF configuration is unraveled in this study. Notably, buoyancy induced oscillations of IJF, which is relatively unexplored in open literature is studied in this work. Moreover, a systematic classification of IJF based on the evolution of its visible flame features with variation in the central air jet and annular fuel jet velocities is reported. In addition, a semi-empirical correlation for visible flame height of IJF with air-fuel momentum ratio is arrived in the present work which can be useful in the design of IJF based burners utilized for impingement heat transfer applications.