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逢 甲 大 學 應 用 數 學 系 專 題 演 講

逢 甲 大 學 應 用 數 學 系 專 題 演 講. 講 者: 陳冠宇教授 ( 中山大學應用海洋物理研究所 ) 題 目: KdV type equations and their applications in internal solitary waves 日 期: 100 年 03 月 23 日(三 ) 下午 3:30-4:30 ( 當日下午3: 00 理學 217 室茶會 ) 地 點:理學 B07 室 ( 歡 迎 參 加 . 敬 請 張 貼 ). 逢 甲 大 學 應 用 數 學 系 專 題 演 講.

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逢 甲 大 學 應 用 數 學 系 專 題 演 講

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  1. 逢 甲 大 學 應 用 數 學 系 專 題 演 講 講 者:陳冠宇教授 (中山大學應用海洋物理研究所) 題 目:KdV type equations and their applications in internal solitary waves 日 期:100年03月23日(三)下午3:30-4:30 (當日下午3:00理學217室茶會) 地 點:理學B07室 (歡 迎 參 加 . 敬 請 張 貼)

  2. 逢 甲 大 學 應 用 數 學 系專 題 演 講 Abstract : • For an equation that includes both nonlinearity and dispersion, it is implicitly assumed that nonlinear and dispersion terms are of the same order of magnitude. Both terms get into the equation separately in an additive manner; hence, dispersion and nonlinearity can be treated separately. For example, Korteweg-de Vries (KdV) is the simplest equation that includes both nonlinearity and dispersion. In this talk, One-Dimensional Advection Equation is first introduced with the lowest order quadratic nonlinearity. On the other hand, the generality of linear KdV equation gives the lowest order quadratic dispersion, which induces spreading due to difference in wavenumber. Adding these two effects together, a KdV equation in shallow water is explicitly derived. The difference between KdV Equation and Boussinesq Equations is explained, and the interaction of two solitons and soliton formation from a smooth initial profile are shown to explain the evolution of KdV equation. • In fluid of two layers, internal solitary waves (ISWs) propagating along the interface is an application of KdV equation. Other KdV type equations, such as modified KdV (MKdV), extended KdV (eKdV), eKdV-Burger and Kadomtsev- Petviashvili (KP) equations are introduced to include shoaling, dissipation, cubic nonlinearity and 2-D effects. • Finally, oblique nonlinear interactions based on the KP equation (also known as the two-dimensional KdV equation) are extended to ISWs to explain why the amplitude does not decrease due to the geometric spreading of the cylindrical wave fronts in the South China Sea. This resonance theory is used to explain a satellite image exhibiting special features and it is proposed that wave arcs of different amplitude resonate, providing a mechanism for reinforcing a wave by boosting the amplitude. It is suggested the amplitude of the ISW that propagates across the SCS basin depends on the interaction of ISWs originating from different sources; hence, studying the generation of an ISW from a single source location cannot predict the ISW correctly.

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