中文摘要：

建立水下湍流多层相位屏的理论和模型是开展水下湍流研究的主要问题。考虑水下湍流的统计特性，通过三维协方差矩阵预测的方法进行了水下湍流的统计特性和连续性的模拟。提出重叠分配矩阵的方法，优化多层相位屏的模拟，分析了计算效率和湍流统计特性表征之间的关系。结果表明：重叠分配矩阵方法能有效提高单层相位屏的生成效率。三维协方差矩阵预测方法可以使相位屏具有层间相关性，其在单层相位屏内的统计特性也与理论符合较好，但是在小尺度和大尺度下与理论值有一定偏差。该研究将传统的独立多层二维相位屏拓展到了空间相关的多层相位屏，使得利用多层相位屏描述水下湍流更加符合物理实际。

英文摘要：

Constructing the theory and simulation for multilayer phase screen of underwater turbulence were the main problems of the research for underwater turbulence. Considering the statistical property of underwater turbulence, here 3D covariance matrix was used to model the statistical property and continuity of underwater turbulence. Here overlapping allocation matrix was put forward and the simulation of multilayer phase screen was optimized. Furthermore, the relation between computational efficiency and the characterization of statistical property of underwater turbulence was analyzed. The results show that overlapping allocation matrix can improve the computational efficiency for a layer of phase screen. Also utilizing 3D covariance matrix could obtain the correlation of phase screens, which is in conformity with theory for statistical property in a layer. However, utilizing 3D covariance matrix led to deviation in small scale and large scale. This research expends original independent 2D phase screen into the multilayer phase screen which has spatial correlation. And that is why this model is morecorrespond to the reality of underwater turbulence.