Breakup of a drop in two-dimensional decaying turbulence - A Lagrangian coherent structure perspective

The deformation and breakup of a liquid drop in turbulent flow is governed by its interaction with surrounding flow structures. In this study, these interactions are investigated in decaying two-dimensional turbulence using a Lagrangian coherent structure (LCS) framework, which provides an objective and frame-invariant description of flow organization. A deformable drop is introduced between vortices, and its evolution is analysed using hyperbolic LCS, identified via finite-time Lyapunov exponent (FTLE) fields, and elliptic LCS, characterised using the polar rotation angle (PRA). It is observed that drop deformation is primarily governed by hyperbolic LCS: repelling FTLE ridges induce localized transverse thinning, while attracting FTLE ridges promote longitudinal stretching along the drop’s principal axis, ultimately leading to breakup. In contrast, elliptic LCS delineate the coherent vortices that surround the drop throughout its evolution. Increasing the density ratio alters the spatial distribution of strong FTLE ridges, modifying deformation pathways and delaying breakup. In addition, instantaneous objective Eulerian coherent structures (OECS) capture short-term deformation patterns consistent with finite-time LCS, offering a computationally efficient alternative. These findings highlight the central role of coherent flow structures in drop dynamics and provide a physically grounded framework for improving breakup models in multiphase flows.