The influence of compressibility on RT instability of bubble

The study of bubble load is necessary for the design of ships and Marine buildings. However, the bubbles in the fluid are not stable. The Rayleigh-Taylor instability of the bubble will affect the load behavior of the bubble on the surrounding structure. For example, interface Rayleigh-Taylor instability prevents bubble from forming jets with destructive effects. Thus, the instability of the bubble interface affects the damage ability of the underwater warhead. The bubble formed by the detonation products of underwater explosion has high internal pressure and large size. In the underwater explosion, the internal pressure of the bubble can reach tens of thousands of atmospheres. In this case, the compression of the water cannot be ignored. However, in the traditional analytical theory of Rayleigh-Taylor instability for bubble, liquids are assumed to be incompressible. Therefore, an analytical theory of RT instability for bubble containing compressibility is established in this paper. The conclusions of this paper are as follows: For underwater explosion bubble with high internal pressure and large size, compressibility inhibits the interface instability slightly when the bubbles expand. Compressibility promotes interfacial instability when bubble contraction. Moreover, compressibility can bring forward the time when exponential growth of Rayleigh-Taylor instability occurs. In contrast, for low internal pressure bubbles, compressibility simply inhibits Rayleigh-Taylor instability. For micrometer bubble, compressibility reduces the first peak of interfacial disturbance. Similarly, compressibility can bring forward the time when exponential growth of Rayleigh-Taylor instability occurs for micrometer bubble. In addition, the surface tension and viscosity of water can inhibit the interfacial Rayleigh-Taylor instability of micrometer bubble. In contrast, the surface tension and viscosity of water have little effect on the interfacial Rayleigh-Taylor instability of bubble formed by underwater explosions.