A submarine during surfacing as well as in heaving in a surface position in waves may become unstable. This event occurs because water into the permeable section of the submarine outer hull cannot flow out immediately.  The submarine heave oscillations may lead to a roll Mathieu instability. In this way may appear several kinds of the submarine roll Mathieu instability. The one kind that bit the submarine is the coupling between heave and roll responses. Since the roll restoring moment depends on the actual methacentric height value, the restoring moment changes as the body heaves. This acts like a driving excitation for roll motions. If the natural period of heave motion is close to one-half Another type of heave-roll Mathieu instability occurs when a substantial wave induced heave motion exists in the presence of resonant heave response.  The critical wave period for this is defined in the paper presented. This may be a problem for stability of a surfacing submarine because the heave responses (both due wave and resonant) may be considerable. There is a third type Mathieu instability we might be concerned with, also due heave motion.  This can result in instability if the motion is a fraction or multiple of the heave natural period. This phenomenon can lead to periodic emergence of negative stability of submarine and great rolling amplitudes. The amplitude of the motion can get very high without inputting much energy. Computer time domain simulation is done for the surfacing submarine for examination of the mentioned propositions.

  S.L.Karlinskiy