Using Step Approximation for Simulating Viscous Wave Scattering over Arbitrary Topography

• Main Authors: Yueh-TingLin, 林岳霆
• Other Authors: Tai-Wen Hsu
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/82059656614090168777

博士 === 國立成功大學 === 水利及海洋工程學系碩博士班 === 100 === In this thesis, a viscous plane wave approximation (VPWA) based on integration method with sequent small steps is used to simulate viscous wave propagation over a arbitrary topography. The effect of bottom sliding coefficient and molecular viscosity on wave reflection and reflection coefficient was studied. Chen’s(1996) analytical solution is implemented in the present model to account for air pressure, shear stress, and surface tension of the dynamic free surface boundary conditions for solving the Navier-Stokes equation. Different types of step method, such as IEMM(indirect eigenfunction matching method), TMM(transfer-matrix method) and DEMM(direct eigenfunction matching method) were used to describe viscous plane wave transformation. The numerical results were compared and discussed. Although the inclusion of evanescent modes in DEMM may raise the solution more accurate for wave scattering of potential flow, all evanescent modes are negligible in the theoretical formulation for simplicity. The present theory describes the entire velocity profile from bottom to free surface for wave propagation over an arbitrary bottom for the real fluid. The formulation of the VPWA can be analytically reduced to the traditional formulation by Lamb when the bottom sliding coefficient and molecular are neglected. Similarly, the dispersion relation is simplified to that obtained from linear wave theory(LWT). Typical examples of waves of an ideal fluid, pure water, SAE-30 oil, and glycerin propagating over an uneven bottom were demonstrated by VPWA. The theory was validated by previous analytical solutions of Longuet-Higgins(1958) and Phillips(1977) for velocity profiles inside the boundary layer. Numerical results of velocity profiles with overshoot are in good agreement with laboratory measurements(Lin et al., 1989, 1995). Based on the calculated velocity profile gradient, the wave friction factor was obtained by VPWA as a function of Reynolds number which follows experimental data and empirical formula. The effect of molecular viscosity on wave scattering over trench of different shapes was investigated. Numerical results were compared fairly well with Bender and Dean (2003) and Jung et al. (2008). Wave energy loss becomes larger when the molecular effect increases. Bragg scattering of waves travelling over sinusoidal undulation was also studied using VPWA. Interesting results were found and compared with experimental data.