Development of an efficient buoyant jet integral model of a bubble plume coupled with a population dynamics model for bubble breakup and coalescence to predict the transmission loss of a bubble curtain

Abstract

The underwater noise radiated during the impact pile-driving of offshore foundations is a major threat to the habitat of several marine creatures. The bubble curtain is a widely used noise mitigation system. A major uncertainty in modeling the acoustic properties of a bubble curtain is the unknown local bubble size distribution. For an accurate estimation, a buoyant jet integral model of a bubble plume is coupled with an existing simplified model of the population dynamics for bubble breakup and coalescence. In this simplified model, the bubble population is divided into two fractions and two one-parameter distribution are used to approximate the overall bubble size distribution. Due to its formulation the resulting bubble formation model is efficient and the calculation time for a typical case is less than five seconds. In comparison to similar approaches, the model incorporates the bubble formation at the nozzle and the high gas fraction in close distance to the nozzle. The approach is validated with three different laboratory bubble size measurements. Subsequently, it is integrated into an existing model of the local acoustic wavenumber of the bubble curtain. The resulting approach is compared with measurements and allows for a prediction of the acoustic properties of a bubble curtain for different nozzle hose configurations, air flow rates and water depth.