# Effect of Waves on the Behavior of Emergent Buoyantly Rising Submarines Using CFD
## 4 Results and Discussion
### Effect of Oblique Waves  
This subsection details the effect of oblique waves on the behavior of emergent buoyantly rising submarines. As shown in Figure 13a,b, the developing pitching rule of a submarine rising in a bow wave is similar to submarines rising in head waves; and the developing pitching rule of submarines rising in quartering waves is similar to submarines rising in following waves. During the rising procedure underwater, when the water surface above the submarine sail translates to a wave valley from a wave peak, the pitching angle velocity, of the submarine, \(q\), rising in the bow (quartering) wave is larger than that of the submarine rising in static water; otherwise, when the water surface transitions from a wave valley to a wave peak, \(q\) is below the value when the submarine is rising in static water. After 11 s, pitching oscillation occurs when the submarine rises in both the bow wave and quartering wave. The pitch of the submarine rising in 30\({}^{\circ}\) bow wave ranges from \(-1.79^{\circ}\) to \(2.90^{\circ}\), the pitch of the submarine rising in 60\({}^{\circ}\) bow wave ranges from \(-2.57^{\circ}\) to \(2.89^{\circ}\), the pitch of submarine rising in a 30\({}^{\circ}\) quartering wave is always above 5\({}^{\circ}\), and the pitch of submarine rising in 60\({}^{\circ}\) quartering wave ranges from \(0.62^{\circ}\) to \(7.87^{\circ}\). During the oscillating procedure, when the submarine rises in the 30\({}^{\circ}\) bow wave, the deck and half of the sail are under the water surface when the submarine experiences a wave peak; both the deck and sail are above the water surface when the submarine experiences a wave valley, as shown in Figure 14a,b. When the submarine rises in the 60\({}^{\circ}\) bow wave during oscillation, the deck is near the water surface when the submarine experiences a wave peak. Both the deck and sail are above the water surface when the submarine experiences a wave valley, as shown in Figure 14c,d. Figure 12: Effect of head and following waves on transverse motion. When the submarine rises in the 30\({}^{\circ}\) quartering wave during oscillation, the deck and half of the sail are under the water surface when the submarine experiences a wave peak. Both the deck and sail are above the water surface when the submarine experiences a wave valley, as shown in Figure 15a,b. When the submarine rises in the 60\({}^{\circ}\) quartering wave during oscillation, the bottom of the sail is near the water surface when the submarine experiences a wave peak; the sail and part of the deck could be above the water surface when the submarine experiences a wave valley, as shown in Figure 15c,d. Figure 13: Effect of oblique wave behavior of emergent buoyantly rising submarine. As shown in Figure 12(c)-f, the effect of an oblique wave on the transverse motion of the emergent buoyantly rising submarine is different from the effect of beam sea. When the submarine rises in beam sea, it rolls to one side during the rising procedure underwater because the effect of the wave force and the maximum roll angle prior to the submarine emerging through the water surface is only 4.11\({}^{\circ}\). When the submarine rises in the 30\({}^{\circ}\) bow wave, the maximum roll angle prior to the submarine emerging through the water surface is 8.14\({}^{\circ}\). When the submarine rises in the 60\({}^{\circ}\) bow wave, the maximum roll angle prior to the submarine emerging through the water surface is 15.89\({}^{\circ}\). When the submarine rises in the 30\({}^{\circ}\) and 60\({}^{\circ}\) bow waves, the pitch angle is larger than that when the submarine rises in static water prior to 4.54 s; however, the pitch angle when the submarine rises in the beam sea is approximately the same as that when the submarine rises in static water. Therefore, the vertical position of the sail when the submarine rises in 30\({}^{\circ}\) and 60\({}^{\circ}\) bow waves is higher than that when the submarine rises in the beam sea.