Based on the Navier-Stokes （N-S） equations for viscous, incompressible fluid and the VOF method, 2-D and 3-D Numerical Wave Tanks （NWT） for nonlinear shallow water waves are built. The dynamic mesh technique is ap...Based on the Navier-Stokes （N-S） equations for viscous, incompressible fluid and the VOF method, 2-D and 3-D Numerical Wave Tanks （NWT） for nonlinear shallow water waves are built. The dynamic mesh technique is applied, which can save computational resources dramatically for the simulation of solitary wave propagating at a constant depth. Higher order approximation for cnoidal wave is employed to generate high quality waves. Shoaling and breaking of solitary waves over different slopes are simulated and analyzed systematically. Wave runup on structures is also investigated. The results agree very well with experimental data or analytical solutions.展开更多
The conventional Boussinesq model is extended to the third order in dispersion and nonlinearity. The new equations are shown to possess better linear dispersion characteristics. For the evolution of periodic waves ove...The conventional Boussinesq model is extended to the third order in dispersion and nonlinearity. The new equations are shown to possess better linear dispersion characteristics. For the evolution of periodic waves over a constant depth, the computed wave envelops are spatially aperiodic and skew. The model is then applied to the study of wave focusing by a topographical lens and the results are compared with Whalin′s (1971) experimental data as well as some previous results from the conventional Boussinesq model. Encouragingly, improved agreement with Whalin′s experimental data is found. [WT5”HZ]展开更多
One of</span><span style="color:red;"> </span><span style="font-family:Verdana;">Newton’s mathematical solutions to a hypothetical orbital problem, recently verified by an ...One of</span><span style="color:red;"> </span><span style="font-family:Verdana;">Newton’s mathematical solutions to a hypothetical orbital problem, recently verified by an independent physics model, is applied to the fluid particle motion in shallow water surface gravity waves. What is the functional form of the central force, with origin at the ellipse’s center, which will keep a body in the orbit? Newton found out it is the spring force, which is linear. All fluid particles in shallow water waves move in ellipses. By a superposition of solutions in a linear problem, the application of Newton’s result to shallow water waves is combined with a feature not noticed by Newton: the orbital period is independent of the semi-major and semi-minor axes. Two conclusions reached are that the wave period of shoaling waves should be constant and that there is no friction in these waves.展开更多
Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only ...Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only in the alongshore direction and the beach slope is assumed to be a constant in the on-offshore direction. By solving the linear shallow water equations we obtain numerical solutions for a wide range of physical parameters, including storm size （2a）, storm speed （U）, and beach slope （a）. Based on the numerical results, it is determined that edge wave packets are generated if the storm speed is equal to or greater than the critical velocity, Ucr, which is defined as the phase speed of the fundamental edge wave mode whose wavelength is scaled by the width of the storm size. The length and the location of the positively moving edge wave packet is roughly Ut/2 〈 y 〈 Ut, where y is in the alongshore direction and t is the time. Once the edge wave packet is generated, the wavelength is the same as that of the fundamental edge wave mode corresponding to the storm speed and is independent of the storm size, which can, however, affect the wave amplitude. When the storm speed is less than the critical velocity, the primary surface signature is a depression directly correlated to the atmospheric pressure distribution.展开更多
In this paper, three types of nonlinear evolution equations such as (2n + 1)th order KdV equation, etc, are studied. And their solitary wave solutions of rational form obtained are available and possess the simplest f...In this paper, three types of nonlinear evolution equations such as (2n + 1)th order KdV equation, etc, are studied. And their solitary wave solutions of rational form obtained are available and possess the simplest form so far. At last, the Hamiltonian form of (2n + 1)th order general KdV equation is generalized.展开更多
文摘Based on the Navier-Stokes （N-S） equations for viscous, incompressible fluid and the VOF method, 2-D and 3-D Numerical Wave Tanks （NWT） for nonlinear shallow water waves are built. The dynamic mesh technique is applied, which can save computational resources dramatically for the simulation of solitary wave propagating at a constant depth. Higher order approximation for cnoidal wave is employed to generate high quality waves. Shoaling and breaking of solitary waves over different slopes are simulated and analyzed systematically. Wave runup on structures is also investigated. The results agree very well with experimental data or analytical solutions.
文摘The conventional Boussinesq model is extended to the third order in dispersion and nonlinearity. The new equations are shown to possess better linear dispersion characteristics. For the evolution of periodic waves over a constant depth, the computed wave envelops are spatially aperiodic and skew. The model is then applied to the study of wave focusing by a topographical lens and the results are compared with Whalin′s (1971) experimental data as well as some previous results from the conventional Boussinesq model. Encouragingly, improved agreement with Whalin′s experimental data is found. [WT5”HZ]
文摘One of</span><span style="color:red;"> </span><span style="font-family:Verdana;">Newton’s mathematical solutions to a hypothetical orbital problem, recently verified by an independent physics model, is applied to the fluid particle motion in shallow water surface gravity waves. What is the functional form of the central force, with origin at the ellipse’s center, which will keep a body in the orbit? Newton found out it is the spring force, which is linear. All fluid particles in shallow water waves move in ellipses. By a superposition of solutions in a linear problem, the application of Newton’s result to shallow water waves is combined with a feature not noticed by Newton: the orbital period is independent of the semi-major and semi-minor axes. Two conclusions reached are that the wave period of shoaling waves should be constant and that there is no friction in these waves.
基金supported by an NSF grant to Cornell University,the China Scholarship Council and a Korean government MLTMA grant Development of Korea Operational Oceanographic System (KOOS) to KORDI
文摘Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only in the alongshore direction and the beach slope is assumed to be a constant in the on-offshore direction. By solving the linear shallow water equations we obtain numerical solutions for a wide range of physical parameters, including storm size （2a）, storm speed （U）, and beach slope （a）. Based on the numerical results, it is determined that edge wave packets are generated if the storm speed is equal to or greater than the critical velocity, Ucr, which is defined as the phase speed of the fundamental edge wave mode whose wavelength is scaled by the width of the storm size. The length and the location of the positively moving edge wave packet is roughly Ut/2 〈 y 〈 Ut, where y is in the alongshore direction and t is the time. Once the edge wave packet is generated, the wavelength is the same as that of the fundamental edge wave mode corresponding to the storm speed and is independent of the storm size, which can, however, affect the wave amplitude. When the storm speed is less than the critical velocity, the primary surface signature is a depression directly correlated to the atmospheric pressure distribution.
文摘In this paper, three types of nonlinear evolution equations such as (2n + 1)th order KdV equation, etc, are studied. And their solitary wave solutions of rational form obtained are available and possess the simplest form so far. At last, the Hamiltonian form of (2n + 1)th order general KdV equation is generalized.
