Stability of gravity-capillary solitary waves on shallow water based on the fifth-order Kadomtsev-Petviashvili equation

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Longitudinal and transverse instabilities of gravity-capillary solitary waves on shallow water are investigated based on the numerical analysis of the fifth-order Kadomtsev-Petviashvili (KP) equation, which describes the wave phenomena on shallow water where the relevant Bond number is less than and close to 1/3. Two-dimensional (2D) depression gravity-capillary solitary waves are stable to longitudinal perturbations. 2D elevation gravity-capillary solitary waves are unstable to longitudinal perturbations and finally evolve into 2D depression gravity-capillary solitary waves. Three-dimensional (3D) finite-amplitude depression gravity-capillary solitary waves are stable to longitudinal perturbations. 3D finite-amplitude elevation gravity-capillary solitary waves are unstable to longitudinal perturbations and finally evolve into an oscillatory state between two different 3D finite-amplitude depression gravity-capillary solitary waves. 3D small-amplitude depression and elevation gravity-capillary solitary waves are unstable to dilation-type longitudinal perturbations and eventually evolve into an oscillatory state between two different 3D finite-amplitude depression gravity-capillary solitary waves. 3D small-amplitude depression and elevation gravity-capillary solitary waves are unstable to contraction-type longitudinal perturbations and eventually become dispersed out toward still water surface. Finally, 2D depression and elevation gravity-capillary solitary waves are unstable to transverse perturbations and eventually evolve into 3D finite-amplitude depression gravity-capillary solitary waves. Therefore, the only stable gravity-capillary solitary waves on shallow water are 3D finite-amplitude depression gravity-capillary solitary waves. In particular, based on the linear stability analysis, a theoretical proof is presented for the long-wave transverse instability of 2D depression and elevation gravity-capillary solitary waves on shallow water.
Publisher
AMER PHYSICAL SOC
Issue Date
2018-07
Language
English
Article Type
Article
Keywords

APPLIED PRESSURE DISTRIBUTION; STEADILY MOVING LOAD; FREE-SURFACE FLOW; DEEP-WATER; TRANSVERSE INSTABILITY; FLOATING ICE; TENSION; GENERATION; DYNAMICS

Citation

PHYSICAL REVIEW E, v.98, no.1

ISSN
2470-0045
DOI
10.1103/PhysRevE.98.012213
URI
http://hdl.handle.net/10203/244831
Appears in Collection
ME-Journal Papers(저널논문)
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