應用平面波近似法模擬黏性波傳遞於幾何地形之研究

Abstract

本文主要是根據Chen（1996）所推導之線性黏性自由液面邊界條件與含有黏性、表面張力之分散關係式，結合底床上黏著度可變動之底床邊界條件，在計算域內以連續微小階梯連結積分方式處理真實水波或是弱黏性波浪與幾何地形交互作用後之情況，進而發展出一套處理真實或是弱黏性流體波動之模式，稱之為黏性平面波近似法（Viscous Plane-Wave Approximation, VPWA）。藉由VPWA可模擬出反射率、透過率與波數之間受表面張力與黏滯阻力聯合作用下的變化。由結果中發現反射率與透過率均會受到流體內部黏性剪力作用而明顯降低，而表面張力則在中、短波長入射時有些微影響。另外，異於一般傳統邊界層內外處理的方式，VPWA可直接連續求得邊界層內外之水平流速，而且與實驗數據比對相吻合。In this paper, a viscous plane-wave approximation (VPWA) is developed to deal with weak viscous wave problems by combining an integration of sequent tiny steps and all boundary conditions. A linear viscous free surface boundary condition derived by Chen (1996) and a sliding bottom boundary condition involved with sliding friction coefficient are considered in VPWA. The reflection and transmission affected by surface tension and viscous drag can be easily calculated by VPWA. Wave number and horizontal velocity profile can be solved as well. In this simulation, reflection and transmission decrease with the increase of viscosity obviously. However, there is a tinny change when surface tension exists. In addition, the whole profile of horizontal velocity inside or outside boundary layer can be directly obtained by VPWA when the bottom is not slipping. Also, the velocity profile of water is identified by experiment data.