Based on the developed trans/supercritical spray model,the Large eddy simulation of trans-/supercritical cryogenic liquid nitrogen jet was carried out in present work.The effects of dif-ferent sub-grid models on the trans-/supercritical jet is first discussed.Then,the interaction between jet dynamics and thermodynamics under different conditions is analyzed.The results show that the effects of different sub-grid models on the jet dynamic is mainly reflected in the downstream region of jet,which is different from the difference in jet thermodynamics.There are two important charac-teristics of trans-/supercritical jets:On the one hand,the inherent high density gradient will hinder the radial fluctuation of jet and delay the jet breakup;On the other hand,the unique pseudo-boiling phenomenon in the transcritical jet will lead to isothermal expansion of jet and inhibit the mixing of jet with the ambient fluid.The thermal-shield layer of transcritical jets will hinder the effective heat exchange between the jet and ambient fluid.However,the local turbulence-thermodynamic interactions can lead to distortion and weakening of the thermal-shield layer,which in turn pro-motes hydrodynamic instability and accelerates the stretching and dissolution of the finger-like structure.