A high-order spectral method for the study of nonlinear gravity waves

Author:

Dommermuth Douglas G.,Yue Dick K. P.

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference28 articles.

1. Su, M. Y. 1982 Evolution of groups of gravity waves with moderate to high steepness.Phys. Fluids 25,2167–2174.

2. Oikawa, M. & Yajima, N. 1974 A perturbation approach to nonlinear systems. II. Interaction of nonlinear modulated waves.J. Phys. Soc. Japan 37,486–496.

3. Stiassnie, M. & Shemer, L. 1987 Energy computations for evolution of class I and class II instabilities of Stokes waves.J. Fluid Mech. 174,299–312.

4. Orszag, S. A. 1971 Numerical simulation of incompressible flows within simple boundaries: accuracy.J. Fluid Mech. 49,75–112.

5. Fornberg, B. & Whitham, G. B. 1978 A numerical and theoretical study of certain nonlinear wave phenomena.Phil. Trans. R. Soc. Lond. A289,373–404.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3