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.

中文翻译：

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开发气泡羽流的有效浮力射流积分模型，结合气泡破裂和聚结的种群动力学模型来预测气泡幕的传输损失

摘要 近海地基冲击打桩过程中辐射的水下噪声对多种海洋生物的栖息地构成了重大威胁。气泡帘是一种广泛使用的降噪系统。气泡幕声学特性建模的一个主要不确定因素是未知的局部气泡尺寸分布。为了准确估计，气泡羽流的浮力射流积分模型与气泡破裂和合并的种群动力学的现有简化模型相结合。在这个简化模型中，气泡群被分为两部分，两个单参数分布用于近似整体气泡大小分布。由于其公式化，生成的气泡形成模型是高效的，典型案例的计算时间不到五秒。与类似方法相比，该模型结合了喷嘴处的气泡形成和靠近喷嘴处的高气体分数。该方法通过三种不同的实验室气泡尺寸测量得到验证。随后，将其集成到气泡幕局部声波数的现有模型中。所得方法与测量结果进行比较，并允许预测不同喷嘴软管配置、空气流速和水深的气泡帘的声学特性。它被集成到气泡幕的局部声波数的现有模型中。所得方法与测量结果进行比较，并允许预测不同喷嘴软管配置、空气流速和水深的气泡帘的声学特性。它被集成到气泡幕的局部声波数的现有模型中。所得方法与测量结果进行比较，并允许预测不同喷嘴软管配置、空气流速和水深的气泡帘的声学特性。