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Stability and dynamics of two-dimensional fully nonlinear gravity-capillary solitary waves in deep water
Wang Z(王展); Wang, Z (reprint author), Chinese Acad Sci, Inst Mech, Key Lab Mech Fluid Solid Coupling Syst, Beijing 100190, Peoples R China.
Source PublicationJOURNAL OF FLUID MECHANICS
2016
Volume809Pages:530-552
ISSN0022-1120
Abstract

The stability and dynamics of two-dimensional gravity capillary solitary waves in deep water within the fully nonlinear water-wave equations arc numerically studied. It is well known that there are two families of symmetric gravity capillary solitary waves depression waves and elevation waves bifurcating from infinitesimal periodic waves at the minimum of the phase speed. The stability of both branches was previously examined by Calvo & Akylas (J. Fluid Mech., vol. 452, 2002, pp. 123-143) by means of a numerical spectral analysis. Their results show that the depression solitary waves with single-valued profiles are stable, while the elevation branch experiences a stability exchange at a turning point on the speed amplitude curve. In the present paper, we provide numerical evidence that the depression solitary waves with an overhanging structure arc also stable. On the other hand, Dias et of. (Eur. j. Mech. B, vol. 15, 1996, pp. 17-36) numerically traced the elevation branch and discovered that its speed amplitude bifurcation curve features a 'snake-like' behaviour with many turning points, whereas Calvo & Akylas (J. Fluid Mech., vol. 452, 2002, pp. 123-143) only considered the stability exchange near the first turning point. Our results reveal that the stability exchange occurs again near the second turning point. A branch of asymmetric solitary waves is also considered and found to be unstable, even when the wave profile consists of a depression wave and a stable elevation one. The excitation of stable gravity capillary solitary waves is carried out via direct numerical simulations. In particular, the stable elevation waves, which feature two troughs connected by a small dimple, can he excited by moving two fully localised, well-separated pressures on the free surface with the speed slightly below the phase speed minimum and removing the pressures simultaneously after a period of time.

KeywordCapillary Waves Solitary Waves Surface Gravity Waves
DOI10.1017/jfm.2016.685
URL查看原文
Indexed BySCI ; EI
Language英语
WOS IDWOS:000388867800021
WOS Keywordcapillary waves ; solitary waves ; surface gravity waves
WOS Research AreaMechanics ; Physics
WOS SubjectMechanics ; Physics, Fluids & Plasmas
Funding OrganizationNational Natural Science Foundation of China [11232012] ; Key Research Program of Frontier Sciences, CAS [QYZDB-SSW-SYS015]
DepartmentLMFS水环境流体力学(LEM)
Classification一类
RankingTrue
Citation statistics
Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/59940
Collection流固耦合系统力学重点实验室
Corresponding AuthorWang, Z (reprint author), Chinese Acad Sci, Inst Mech, Key Lab Mech Fluid Solid Coupling Syst, Beijing 100190, Peoples R China.
Recommended Citation
GB/T 7714
Wang Z,Wang, Z . Stability and dynamics of two-dimensional fully nonlinear gravity-capillary solitary waves in deep water[J]. JOURNAL OF FLUID MECHANICS,2016,809:530-552.
APA Wang Z,&Wang, Z .(2016).Stability and dynamics of two-dimensional fully nonlinear gravity-capillary solitary waves in deep water.JOURNAL OF FLUID MECHANICS,809,530-552.
MLA Wang Z,et al."Stability and dynamics of two-dimensional fully nonlinear gravity-capillary solitary waves in deep water".JOURNAL OF FLUID MECHANICS 809(2016):530-552.
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