2018年海洋信息论坛第19期
报告题目：Normal modes in 3D shallow-water waveguides: main equations and their analytical solutions
报告人：Dr. Pavel S. Petrov
时间：
地点：水声楼15楼学术报告厅
报告人简介：
Pavel S. Petrov于2009年获得伊尔库茨克州立大学(Irkutsk State University)数学专业的硕士学位，于2012年获得太平洋研究所(Il’ichev Pacific Oceanological Institute)理论物理专业的正博士学位。自2012年至今，Pavel S. Petrov博士在太平洋研究所担任研究员职位，同时在远东联邦大学(Far Eastern Federal University)兼任副教授职位。期间他两次以洪堡学者奖学金获得者的身份前往德国高校进行访问和进修，并在以色列海法大学Boris Katsnelson教授处做过短期博后。由于在三维声传播模型方面发表了一系列高质量文章，太平洋研究所于2017年授予Pavel S. Petrov博士以“声学与海洋研究领域年轻科学家伊利切夫奖”。
Pavel S. Petrov博士的研究专长包括声传播、吸收与散射、计算海洋声学、波动过程数学建模、渐进方法等。Pavel S. Petrov博士尤其在三维海洋声传播及其应用方面颇有造诣，他编写的多项三维声场计算代码已上传至水声领域著名开源网站Ocean Acoustics Library，可供免费使用。
报告简介：
A normal mode representation of acoustical field in a 3D shallow-water waveguide with inhomogeneous bottom is introduced. The horizontal refraction equations are derived in two different ways. The mode parabolic equation is proposed as an efficient tool for simulating horizontal refraction effects. The computational domain truncation issue is discussed in the context of mode parabolic equations. A Cauchy problem for the mode parabolic equation is considered, and initial conditions (Cauchy data) are proposed. An analytical solution of the horizontal refraction equation is considered in the case of underwater canyon of a specific shape. A family of analytical solutions of mode parabolic equation are derived using the group-theoretical technique based on the Campbell-Hausdorff formula (related ideas and results from the Lie group theory, including Wei-Norman theorem, are quickly introduced in the course of the lecture). Some examples and comparisons of numerical and analytical solutions are considered.