This paper investigates beam evolution and beam sizes variation of hyperbolic sinusoidal Gaussian (HSG) beam propagating in jet engine exhaust-induced turbulence. We find the received field by solving Huygens-Fresnel integral with a relevant power spectrum. Our results reveal that HSG loses its initial profile until 100 m. Besides, beam with low displacement parameter value is more resistive against turbulence. In terms of beam size, beams with low Gaussian source size expand less as compared to the beams with larger Gaussian source size. In the light of our findings, optical systems in aircrafts like directed infrared counter measure (DIRCM) and laser designators can be developed.