Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory an...Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.展开更多
This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natura...This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.展开更多
A three-dimensional hydrodynamic model is presented which combines a terrain-following vertical coordinate with a horizontally orthogonal curvilinear coordinate system to fit the complex bottom topography and coastlin...A three-dimensional hydrodynamic model is presented which combines a terrain-following vertical coordinate with a horizontally orthogonal curvilinear coordinate system to fit the complex bottom topography and coastlines near estuaries, continental shelves, and harbors. To solve the governing equations more efficiently, we improve the alternating direction implicit method, which is extensively used in the numerical modeling of horizontal two-dimensional shallow water equations, and extend it to a three-dimensional tidal model with relatively little computational effort. Through several test cases and realistic applications, as presented in the paper, it can be demonstrated that the model is capable of simulating the periodic to-and-fro currents, wind-driven flow, Ekman spirals, and tidal currents in the near-shore region.展开更多
基金This work was financially supported by the Science Foundation of National Education Committee of China
文摘Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.
文摘This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.
基金We appreciate the detailed suggestions and comments provided by the editor and the anonymous reviewers. Several research programs supported the work presented in this article： the National Basic Research Program of China （No. 2015CB954100）, the National Natural Science Foundation of China （Grant No. 41306078）, and the Priority Academic Program Development of Jiangsu Higher Education Institutions （Grant No. 1411109012）.
文摘A three-dimensional hydrodynamic model is presented which combines a terrain-following vertical coordinate with a horizontally orthogonal curvilinear coordinate system to fit the complex bottom topography and coastlines near estuaries, continental shelves, and harbors. To solve the governing equations more efficiently, we improve the alternating direction implicit method, which is extensively used in the numerical modeling of horizontal two-dimensional shallow water equations, and extend it to a three-dimensional tidal model with relatively little computational effort. Through several test cases and realistic applications, as presented in the paper, it can be demonstrated that the model is capable of simulating the periodic to-and-fro currents, wind-driven flow, Ekman spirals, and tidal currents in the near-shore region.
