Optimal interface distortion of a round liquid jet

A thorough understanding of the mechanisms driving the atomization process of liquid jets is of fundamental interest in applications ranging from medicinal spray generation to fuel injection. Atomization often begins with the deformation and distortion of the fluid interface by initially linear growth mechanisms. Depending on the parameters, the inflectional profile of a liquid jet injected into a stationary gas environment can support the growth of primary exponential instabilities of Kelvin-Helmholtz type. However, even when the eigenvalue spectrum reveals the flow as exponentially stable, interface perturbations may amplify through non-modal or algebraic mechanisms. The present work generalizes the analysis of primary distortions of the jet interface by casting it as an optimization problem for the surface-tension energy. The base flow of the linear analysis is computed in two-fluid simulations using a volume-of-fluid approach. Consideration of the budget of the perturbation kinetic energy provides insight into the principal physical mechanisms in various settings.