论文标题
准周期性旅行重力毛细管波
Quasi-periodic traveling gravity-capillary waves
论文作者
论文摘要
我们介绍了一项在理想无限深度的理想流体表面上的空间周期性流动波的数值研究。这是对经典的威尔顿涟漪问题的概括，因为满足分散关系的波数比率是不合理的。我们提出了水波方程的共形映射公式，该公式采用了希尔伯特变换的准周期变体，以从自由表面上的速度潜力来计算流体的正常速度。我们开发了流动水波方程的傅立叶伪 - 光谱离散化，其中一维准周期函数由圆环上的二维周期函数表示。这导致了我们使用Levenberg-Marquardt方法的变体解决的过度确定的非线性最小二乘问题。我们研究了准周期性行进波的各种特性，包括傅立叶共振，圆环的整形空间中的时间演变，不对称的波峰，毛细管波模式从一个重力波槽变为下一次重复的重复，以及在振幅范围内的依赖性，描述了两种偏见的波浪家族。
We present a numerical study of spatially quasi-periodic traveling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wave numbers satisfying the dispersion relation is irrational. We propose a conformal mapping formulation of the water wave equations that employs a quasi-periodic variant of the Hilbert transform to compute the normal velocity of the fluid from its velocity potential on the free surface. We develop a Fourier pseudo-spectral discretization of the traveling water wave equations in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on the torus. This leads to an overdetermined nonlinear least squares problem that we solve using a variant of the Levenberg-Marquardt method. We investigate various properties of quasi-periodic traveling waves, including Fourier resonances, time evolution in conformal space on the torus, asymmetric wave crests, capillary wave patterns that change from one gravity wave trough to the next without repeating, and the dependence of wave speed and surface tension on the amplitude parameters that describe a two-parameter family of waves.
