Reliable communication between aerial and undersea vehicles is a challenging issue because radio frequency signals are attenuated drastically in sea water while acoustic waves are not preferable in terrestrial links. Located in the transmittance windows of both sea water and the atmosphere, blue-green laser based free-space optical communication systems are capable of providing high speed, low latency data links for this very scenario. Apart from the absorbing and scattering attenuations in the air-water channel, another limiting factor impacting efficient laser beam propagation is the turbulence induced intensity fluctuations. Pure attenuation in sea water restricts the laser communication distance to ∼100 meters, which will further reduce to ∼10 meters in the presence of oceanic turbulence. Meanwhile, atmospheric turbulence can also substantially degrade the beam quality if the aerial vehicle is at high altitude. In this study, we focus our effort on the turbulence effects on beam propagation in the air-water two-stage links, not taking into account media attenuation or water surface distortions. Considering the complexity of the depth dependence of salinity and temperature in sea water and the altitude dependence of air refractive-index structure constant, we use numerical methods to simulate the beam propagation through the two-stage turbulence channel, which is modeled by discrete phase screens generated with parameterized atmospheric and oceanic turbulence power spectrums. On that basis, beam spread, area scintillation and SNR penalty at the receiver end are analyzed for the uplink as well as the downlink transmission.