The so-called "Flow-Blurring" (FB) atomizer is known to induce strong interphase constructive interference in a pre-mixing region upstream of the atomizer orifice, resulting in efficient atomization. Its less energetic counterpart, the "Flow-Focusing" (FF) atomizer, exists with different geometries and/or flow conditions. For a fixed geometry, lower gas flowrates and/or higher biofuel flowrates cause FB to revert to FF. In doing so, the pre-mixing region disappears with a lower nozzle pressure drop, and atomization quality suffers. With the use of a previously validated commercial Volume of Fluid (VOF)-to-Discrete Phase Modeling (DPM) methodology, a new flow regime is discovered which lives between FF and FB. This intermediate "Flow-Undulating-Mixing-Swirling" (FUMS) regime replaces the multiphase pre-mixing region with an oscillating biofuel-gas meniscus driven by concentric waves resulting from instabilities at the gas injection annulus. Bubbles form within this oscillating meniscus and rotate within the biofuel, while others get trapped in the biofuel jet, but there is no orifice exit shattering that is typically associated with FB. Biofuel mixing across the lateral axes and swirling are also exhibited in the biofuel jet. While frequencies in the 300 Hz range characterize the base meniscus wave formation, a wide range of time scales evolve as a function of distance from the bubbling/meandering meniscus source.