Application of homogenous scattering theory to an ideally mixed underwater bubble curtain

A bubble curtain is a barrier of rising air bubbles, and it is typically made by driving compressed air through a perforated pipe under water. The bubble curtain can be used as a protective measure to shelter marine life from underwater noise pollution such as controlled underwater explosions, engines, pile driving, and deep-water drilling. In this report we evaluate the protection capabilities of bubble curtains by constructing a simple method to calculate the corresponding sound transmission. Theoretical considerations predict that the speed of sound in a bubble curtain can be smaller than both the speed of sound in air and water because the presence of the bubbles creates a highly compressible mixture. The effect is primarily dependent on the ratio of the total air volume to the overall volume of the mixture. This key parameter is known as the volume fraction of air. Due to the small speeds of sound, there is a significant (acoustic) impedance mismatch between the water and bubble curtain. Impedance is a measure of how much a medium resists the flow of internal sound waves and is defined as the product between density and speed of sound. The result of the large impedance mismatch is that the bubble curtain acts as a high-reflective sound shield, under the right conditions. In short, it does indeed hold high protection capabilities. Our model shows that bubble curtains are most effective in shielding against sound with frequencies up to 100 kHz, although the exact performance varies with certain parameters such as hydrostatic pressure, the size of the bubbles, and the angle of the sound waves relative to the curtain. Our model shows significantly poorer performance of the bubble curtains at frequencies higher than 1 MHz, but the model does not account for disordered localization phenomena in these ranges. An improved future model may shed more light on performance against such frequencies.