Stabilization mechanisms and mode-selection dynamics of finite-amplitude capillary waves

Establish the mechanisms that stabilize finite-amplitude capillary waves in the conserved active emulsion model (Eqs. (8a–b)) and characterize the dynamics underlying the secondary instability and the associated selection of dominant modes, ideally via a weakly nonlinear theory.

Background

Near the onset of the oscillatory instability, simulations show finite-amplitude capillary waves that can be long-lived, but eventually a secondary instability introduces additional modes; the authors hypothesize a competition between surface tension and memory-driven destabilization, yet a definitive mechanism is not established.

They suggest that a quantitative resolution will require incorporating nonlinear effects, for instance through weakly nonlinear analysis, to connect stabilization, secondary instability, and mode selection.