京都大学 / 新制・課程博士 / 博士(理学) / 甲第22973号 / 理博第4650号 / 新制||理||1668(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 日野 正訓, 教授 泉 正己, 准教授 矢野 孝次 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The research area of current PhD thesis is the analysis of time periodic Navier-Stokes equations in domains with cylindrical outlets to infinity. The objects of investigation is so called non-statonary Poiseuille solution in the straight cylinder and Navier-Stokes equations in system of cylinders. / Disertacijoje nagrinėjami Navjė-Stokso lygčių periodiniai laiko atžvilgiu uždaviniai srityse su cilindriniais išėjimais į begalybę. Pagrindiniai tyrimo objektai yra taip vadinami Puazelio sprendiniai tiesiame cilindre ir Stokso, bei Navjė-Stokso lygčių sistemos cilindrų sistemoje.

Electromagnetic wave propagation over random sea surfaces is a classical problem of interest for the Navy, and significant research has been done over the years. Here we make use of numerical and analytical methods to predict the propagation of microwaves over random rough surface. The numerical approach involves utilization of the direct solution (using Volterra integral equation of the second kind) to currents induced on a rough surface due to forward propagating waves to compute the scattered field. The mean scattered field is computed using the Monte-Carlo method. Since the exact solution (consisting of an infinite series) to induced current density is computationally intensive, there exists a need to predict the propagation using the closely accurate zeroth order induced current (first term of the series) for time-varying multiple realizations of a random rough surface in a computationally efficient manner. The wind-speed dependent, fully-developed, Piersen-Moskowitz sea spectrum has been considered in order to model a rough sea surface, although other partially-developed roughness spectra may also be utilized. An analytical solution based on the zeroth order current density obtained by deriving the mean scattered field as a function of the range and vertical height by directly using the Parabolic Equation (PE) approximation method and the resulting Green's function has been utilized for a comparative study. The analytical solution takes into account the diffused component of the scattered field.