Presentation title: “Normal modes in 3D shallow-water waveguides: main equations and their analytical solutions”
(The 1st lecture of the series of “Normal modes in 3D shallow-water waveguides: from theory to computational models and applications”)
Presenter: Dr. Pavel S. Petrov
Time: 15:00-16:30, July 3, 2018
Location: Academic lecture hall on the 15th floor of the Underwater Acoustic Engineering Building
Short Bio of the presenter:
Pavel S. Petrov received his Master’s degree in Mathematics from Irkutsk State University, Russia; and his Doctorate degree in Theoretical Physics from Il’ichev Pacific Oceanological Institute, Russia. From 2012, Dr. Pavel S. Petrov is a Researcher in Il’ichev Pacific Oceanological Institute, and also an adjunct Associate Professor in Far Eastern Federal University. He has received the Humboldt Research Fellowships twice, and went to Universities in German as a visiting scholar. He also worked as a short-term post-doctoral researcher in University of Haifa, Israel, collaborating with Professor Boris Katsnelson. Dr. Pavel S. Petrov received the Illychef Prize for Young Scientists in Acoustics and Ocean Research from Il’ichev Pacific Oceanological Institute in 2017, due to the series of high-level papers on 3-dimension sound prorogation models his published.
The research focuses of Dr. Pavel S. Petrov includes acoustic propagation, absorption and scattering, computational ocean acoustics, mathematical modeling of wave processes, asymptotic methods and so on. Dr. Pavel S. Petrov has made significant contributions to the 3- dimensional ocean sound propagation and applications. Several programing codes on 3-dimensional sound field calculation written by him has been uploaded to the famous open-source website on underwater acoustics – Ocean Acoustics Library, which can be downloaded for free.
Abstract of the presentation:
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.
