On the Deformation of a Drop in a Stably Stratified Fluid

We examine the deformation and flow modification induced by a small drop immersed in a stably stratified fluid. The ambient stratification is modelled as linearly increasing with depth. Using a matched asymptotic expansions approach, we investigate the flow field and droplet shape in the limits of zero Reynolds number and small Peclet number. Two cases are considered: (i) a stationary drop with its internal density matched to the ambient fluid at the drop centre, and (ii) a drop translating under gravity. In both scenarios, stratification significantly alters the surrounding flow and leads to a prolate droplet shape, in contrast to the oblate deformation typically observed due to weak inertial effects in a homogeneous fluid. To further elucidate the underlying dynamics, we systematically explore the competition between inertial and stratification effects on droplet deformation, revealing distinctive shape transitions driven by their relative influence. These findings highlight the interplay between stratification and interfacial deformability in low-inertia environments relevant to oceanic microphysics.