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Third-Order Stokes Wave Solutions of the Free Surface capillary- gravity Wave and the Interfacial Internal Wave

China Ocean Engineering 2017年第6期31卷 781-787页

作者： MENG Rui-jun CUI Ji-feng CHEN Xiao-gang ZHANG Bao-le ZHANG Hong-bo College of Science Inner Mongolia University of Technology Hohhot 010051 China

Based on the Stokes wave theory, the capillary-gravity wave and the interfacial internal wave in two-layer constant depth＇s fluid system are investigated. The fluids are assumed to be incompressible, inviscid and irrotational. The third-order Stokes wave solutions are given by using a perturbation method. The results indicate that the third-order solutions depend on the surface tension, the density and the depth of each layer. As expected, the first-order solutions are the linear theoretical results （the small amplitude wave theoretical results）. The second-order and the third-order solutions describe the nonlinear modification and the nonlinear interactions. The nonlinear impact appears not only in the n （n〉~2） times＇ high frequency components, but also in the low frequency components. It is also noted that the wave velocity depends on the wave number, depth, wave amplitude and surface tension.

关键词： surface tension capillary-gravity waves Stokes wave theory third-order Stokes wave solutions

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Absorbing Boundary Conditions for Simulating Water waves Near Solid Bodies

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Journal of Applied Mathematics and Physics 2024年第10期12卷 3502-3520页

作者： José Marie Orellana Mathematical and Numerical Modelling Laboratory (M2N) National Conservatory of Arts and Crafts Paris France

The objective of this paper is to present a new method for designing absorbing or non-reflective boundary conditions (ABC) or (NRBC), illustrated by the case study of the modelling of a solid body in water, specifically the capillary gravity waves generated by its motion at the surface. The study analyses the flow of an inviscid, barotropic, and compressible fluid around the stationary solid body. The dynamic behaviour of the fluid is analysed using a two-dimensional coupled Neumann-Kelvin model extended with capillarity and inertia terms. For computational purposes, it is necessary to truncate the unbounded spatial domain with artificial boundaries and then introduce appropriate absorbing boundary conditions. The propagation of short wavelength waves in a convective fluid medium with significant differences in properties between the interior and the surface of the fluid presents a number of difficulties in the design of these conditions. The results are illustrated numerically and commented upon.

关键词： Absorbing Boundary Condition Fluid-Structure Interaction capillary-gravity waves Numerical Simulations

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On Two Types of Stability of Solutions to a Pair of Damped Coupled Nonlinear Evolution Equations

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Advances in Pure Mathematics 2024年第5期14卷 354-366页

作者： Mark Jones School of Computer Science and Mathematics Kingston University London UK

The stability of a set of spatially constant plane wave solutions to a pair of damped coupled nonlinear Schrödinger evolution equations is considered. The equations could model physical phenomena arising in fluid dynamics, fibre optics or electron plasmas. The main result is that any small perturbation to the solution remains small for all time. Here small is interpreted as being both in the supremum sense and the square integrable sense.

关键词： Nonlinear Schrödinger Equation Stability capillary-gravity waves

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