The study and understanding of transcritical and supercritical jet flow are critical in liquid rockets, gas turbines, and diesel engines, as high-pressure atmospheres in these devices’ mixing chambers drastically modify the morphology of their jets. In the transcritical jet, new elongated entities called finger-like structures appear and characterize the fluid flow phenomenon. This study examines these entities by simulating two classical cases based on Mayer’s experiments. The turbulence is described by the Large-eddy simulation technique with a sub-grid scale model known as the selective structures-function model. Real-gas behavior is evaluated by the Soave-Redlich-Kwong equation, and the transport properties are estimated by Chung’s methods. From the results, a longitudinal modulation which triggers an azimuthal modulation is observed. Then, bulges are formed on the jet surface. Cross-sectional views reveal pairs of streamwise vortices with inverted rotational directions, which are located on either side of the bulges (on the outer edge of the dense core). These transversal, turbulent movements seem to be engaged with the elongation of the bulges and the subsequent formation of finger-like structures. The existence of the counter-rotating vortices is related with the baroclinic vorticity. Then, since one may refer to the Rayleigh-Taylor instability when it is baroclinically generated, this instability could give an explanation of the origin of the finger-like structures. Transcritical parcels emitted at the end of the dense core are bounded by a thermal-shield. Finger-like structures are not observed in the supercritical case. The thermal-shield is absent from the supercritical parcels.