The length of the supersonic jet ejected from the military aircraft must be reduced in order to decrease its heat signature and aeroacoustic noise and thereby to enhance its stealth capability. The reduction or manipulation of the supersonic core can be achieved through various passive control techniques. Considering this, the present study explores the mixing characteristics of supersonic jets with and without passive controls. Passive controls in the form of grooves configured at the exit of a Mach 1.73 convergent-divergent nozzle are investigated computationally. Particularly, the supersonic jet decay characteristics and flow development for a plain nozzle and a nozzle with semi-circular, square, and triangular grooves are presented. Besides, the study explores different turbulence models namely, Spalart-Allmaras, realisable k-ε, std k-ω, Shear Stress Transport (SST) k-ω and SST Transition. The realisable k-ε turbulence model is found to be the most effective one in capturing the supersonic jet structure. It is observed that the grooves produce large distortions in the jet structure, accompanied by significant mass entrainment and lateral spread. Interestingly, semi-circular grooves are proven to be most effective in all cases of expansion level than square and triangular grooves. For the semi-circular grooves, a maximum of 48.5% reduction in supersonic core length of the correctly expanded jet at Nozzle Pressure Ratio (NPR) of 5 is achieved. The reduction in supersonic core length for semi-circular grooves is 31% for the overexpanded jet at NPR 4 and 29% for the underexpanded jet at NPR7.