A pair of oblate bubbles rising in line: a linear stability analysis

The stability of two bubbles rising initially in line through a viscous liquid is revisited using a global linear stability analysis formulated within an arbitrary Lagrangian–Eulerian framework, complemented by fully resolved embedded boundary method simulations. Whereas previous studies attributed the promoted in-line stability of oblate bubbles to a deformation-enhanced wake entrainment, the present analysis demonstrates that the dominant stabilizing mechanism arises instead from an inclination-induced rotational feedback generated as the trailing bubble (TB) experiences the asymmetric shear of the leading bubble’s wake. This inclination–shear coupling, rather than deformation itself, governs the recovery of stability with increasing aspect ratio. Furthermore, the results reveal that the unstable drafting–kissing–tumbling mode originates from short-range, two-way coupling between the bubbles, whereas the asymmetric side-escape mode corresponds to a long-range, one-way interaction dominated by the TB response. In addition, a previously unreported oscillatory global mode emerges from the unsteady recirculation linking the two bubbles, acting as a hydrodynamic spring whose effective stiffness and damping govern the oscillation frequency and growth rate. Together, these findings identify inclination-induced lift as the primary mechanism controlling the stability of rising bubble pairs and provide a unified framework for interpreting their stationary and oscillatory transitions across a broad range of inertial and deformable regimes.