A HIGH-ORDER SPECTRAL METHOD FOR THE STUDY OF NONLINEAR GRAVITY-WAVES
A HIGH-ORDER SPECTRAL METHOD FOR THE STUDY OF NONLINEAR GRAVITY-WAVES
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DOI：
10.1017/s002211208700288x
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发表时间：
1987-11-01
影响因子：
3.7
通讯作者：
YUE, DKP
中科院分区：
文献类型：
--
作者：
DOMMERMUTH, DG;YUE, DKP
我们开发了一种鲁棒的数值方法来模拟非线性重力波，该方法基于 Zakharov 方程/模式耦合思想，但被推广到包括波陡度高达任意阶 M 的相互作用。通常使用大量（N = O(1000)）自由波模式，其振幅演化通过非线性自由表面条件的伪谱处理来确定。计算量与 N 和 M 成正比，对于高达斯托克斯极限陡度 (ka ∼ 0.35) 约 80% 的波，N 和 M 的收敛速度呈指数级增长。通过与完全非线性半拉格朗日计算的比较，证明了该方法的效率和准确性（Vinje & Brevig 1981）；使用修正的（四阶）Zakharov 方程计算波列的长期演化（Stiassnie & Shemer 1987）；以及行波包的实验测量（Su 1982）。作为该方法有用性的最后一个例子，我们考虑不同载波频率的两个碰撞波包络之间的非线性相互作用。
We develop a robust numerical method for modelling nonlinear gravity waves which is based on the Zakharov equation/mode-coupling idea but is generalized to include interactions up to an arbitrary order M in wave steepness. A large number (N = O(1000)) of free wave modes are typically used whose amplitude evolutions are determined through a pseudospectral treatment of the nonlinear free-surface conditions. The computational effort is directly proportional to N and M, and the convergence with N and M is exponentially fast for waves up to approximately 80% of Stokes limiting steepness (ka ∼ 0.35). The efficiency and accuracy of the method is demonstrated by comparisons to fully nonlinear semi-Lagrangian computations (Vinje & Brevig 1981); calculations of long-time evolution of wavetrains using the modified (fourth-order) Zakharov equations (Stiassnie & Shemer 1987); and experimental measurements of a travelling wave packet (Su 1982). As a final example of the usefulness of the method, we consider the nonlinear interactions between two colliding wave envelopes of different carrier frequencies.