Asymptotic nonlinear wave modeling through the Dirichlet-to-Neumann operator
Asymptotic nonlinear wave modeling through the Dirichlet-to-Neumann operator
复制标题
通过 Dirichlet-to-Neumann 算子进行渐近非线性波建模
DOI：
--
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
A. Nachbin
中科院分区：
文献类型：
--
作者：
W. Artiles;A. Nachbin
推广了Matsuno[16]的系统和Nachbin[23]的地形跟踪Boussinesq系统，得到了新的非线性发展方程。该方法考虑了有限深度、高度可变的二维不可压缩无粘流体上的有限振幅表面重力波。通过对高波纹条上Dirichlet-to-Neumann算子的摄动分析，实现了非线性位势理论方程的渐近简化。这是通过使用曲线坐标系来实现的。不是对速度势进行长波展开，而是在波陡度参数中展开傅立叶类型的运算符。新奇之处在于，地形可以在很大范围内变化。它还可以具有复杂的轮廓，包括多值函数的轮廓。得到的演化方程是变系数Boussinesq型方程。这些方程代表了一个完全色散系统，即原始的(双曲正切)色散关系不被截断。该公式是在周期性扩展的区域上完成的，因此，作为应用，它可以产生高效的傅立叶(FFT)解算器。这项工作的初步交流已经发表在《物理评论快报》上[1]。
New nonlinear evolution equations are derived that generalize the system by Matsuno [16] and a terrain-following Boussinesq system by Nachbin [23]. The regime considers finite-amplitude surface gravity waves on a two-dimensional incompressible and inviscid fluid of, highly variable, finite depth. The asymptotic simplification of the nonlinear potential theory equations is performed through a perturbation anaylsis of the Dirichlet-to-Neumann operator on a highly corrugated strip. This is achieved through the use of a curvilinear coordinate system. Rather than doing a long wave expansion for the velocity potential, a Fourier-type operator is expanded in a wave steepness parameter. The novelty is that the topography can vary on a broad range of scales. It can also have a complex profile including that of a multiply-valued function. The resulting evolution equations are variable coefficient Boussinesq-type equations. These equations represent a fully dispersive system in the sense that the original (hyperbolic tangent) dispersion relation is not truncated. The formulation is done over a periodically extended domain so that, as an application, it produces efficient Fourier (FFT) solvers. A preliminary communication of this work has been published in the Physical Review Letters [1].