To study the effect of flow disturbances on the supercavitating mechanism and the projectile's stability, several numerical studies are carried out on the flow characteristics of supercavity under various sinusoidal waveform functions. Particular attention is given to the effect of wave height, wavelength, and initial velocity on the cavity profile, and projectile resistance. The results indicate that under the effect of periodic height-increasing waves, the wave height and initial velocity are the key factors affecting the resistance. The peak resistance coefficient increases with the increase of wave height and decreases with the rise of initial velocity. Under the effect of periodic height-decreasing waves, the resistance undergoes ‘Fluctuation’ - ‘Stabilization’ - ‘re-Fluctuation’ - ‘re-Stabilization’ stages, and the dimensionless value ‘f = |(v-vf)|/(vf·t)’ of each stage shows sinusoidal fluctuations. When the minimum value of f approaches 0.0375, the cavity and resistance are relatively stable. While f in (0.0125, 0.025) range, it enters into ‘re-Fluctuation’ stage. When f < 0.0125, it keeps ‘re-Stabilization’ stage. The resistance reaches the ‘Stabilization’ stage earlier with the maximum wave height decreases. As the wavelength decreases, the projectile drag coefficient exhibits opposite characteristics during the ‘Fluctuation’ and ‘re-Fluctuation’ stages.