Analytic and numerical solutions for the free surface wave induced by an uniform flow over a sloping step

• Main Authors: Zhang, Zhi- Xiang, 張智翔
• Other Authors: Chang, Hsien-Kuo
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/2f5vkc

碩士 === 國立交通大學 === 土木工程系所 === 105 === The problem of a steady and uniform free-surface flow of an ideal fluid propagating over a sloping step on the bottom is investgated in this thesis. Based on the method of King and Bloor (1987) for the case of a vertical step, the generalized Schwarz-Christoffel transformation is used to map the physical plane onto the upper half-plane where the flow field is a sink at the origin. The nonlinear governing equations can be linearized for the case of small step and be solved by the help of Fourier transformation. The linear solution shows that the free-surface and drag force on the step respond to the height of the step and Froude number, but is independent of the slope of the inclined step. A closed form of nonlinear equations is obtained by the finite-difference method discretizing governing equations. The numerical solution with high accuracy are iteratively calculated by the Linear solutions, based upon small step height are solved by Fourier transform. As the step height is increased, solutions to the exact nonlinear equations are obtained by using finite-difference methods and Marquardt- Levenberg algorithm. For a supercritical flow the free-surface rises in the downstream and the drag on the step is in the same direction of the uniform flow. Contrarily, the free-surface falls down in the downstream and the drag on the step is in the opposite direction of the uniform flow for a subcritical flow. The numerical solution of free-surface depends on both the height and slope of the step. However, drag force on the step only depends on the height of the step, but is unconnected from the slope of the step.