  Contrary to common assumptions, a transcritical domain exists during the
early times of liquid hydrocarbon fuel injection at supercritical pressure. A
sharp two-phase interface is sustained before substantial heating of the
liquid. Thus, two-phase dynamics has been shown to drive the early
three-dimensional deformation and atomisation. A recent study of a
transcritical liquid jet shows distinct deformation features caused by
interface thermodynamics, low surface tension, and intraphase diffusive mixing.
In the present work, the vortex identification method ${\lambda}_{\rho}$, which
considers the fluid compressibility, is used to study the vortex dynamics in a
cool liquid n-decane transcritical jet surrounded by a hotter oxygen gaseous
stream at supercritical pressures. The relationship between vortical structures
and the liquid surface evolution is detailed, along with the vorticity
generation mechanisms, including variable-density effects. The roles of hairpin
and roller vortices in the early deformation of lobes, the layering and tearing
of liquid sheets, and the formation of fuel-rich gaseous blobs are analysed. At
these high pressures, enhanced intraphase mixing and ambient gas dissolution
affect the local liquid structures (i.e., lobes). Thus, liquid breakup differs
from classical sub-critical atomisation. Near the interface, liquid density and
viscosity drop by up to 10% and 70%, respectively, and the liquid is more
easily affected by the vortical motion (e.g., liquid sheets wrap around
vortices). Despite the variable density, compressible vorticity generation
terms are smaller than the vortex stretching and tilting. Layering traps and
aligns the vortices along the streamwise direction while mitigating the
generation of new rollers.
