The patterns of surface capillary-gravity short-crested waves with uniform current fields in coastal waters

A fully three-dimensional surface gravitycapillary short-crested wave system is studied as two progressive wave-trains of equal amplitude and frequency, which are collinear with uniform currents and doubly-periodic in the horizontal plane, are propagating at an angle to each other. The first- and second-order asymptotic analytical solutions of the short-crested wave system are obtained via a perturbation expansion in a small parameter associated with the wave steepness, therefore depicting a series of typical three-dimensional wave patterns involving currents, shallow and deep water, and surface capillary waves, and comparing them with each other.

Nonlinear Capillary-Gravity Waves Produced by a Vertically Oscillating Plate

The nonlinear capillary-gravity wave produced by a vertically oscillating plate, in which the contact-angle model is considered, is studied by use of the Boundary Integral Equation Method (BIEM). The present numerical experiment shows that the code is robust and efficient for modeling the generation and propagation of capillary-gravity waves. It is found that the wave heights of stationary periodic nonlinear waves radiated away from the plate are dependent on the parameters involved in the contact-angle model. The effect of the contact-angle hysteresis and the nonlinearity of capillary-gravity waves on the wave profile is discussed in the paper.

Slope wavenumber spectrum models of capillary and capillary-gravity waves

Capillary and capillary-gravity waves possess a random character, and the slope wavenumber spectra of them can be used to represent mean distributions of wave energy with respect to spatial scale of variability. But simple and practical models of the slope wavenumber spectra have not been put forward so far. In this article, we address the accurate definition of the slope wavenumber spectra of water surface capillary and capillary-gravity waves. By combining the existing slope wavenumber models and using the dispersion relation of water surface waves, we derive the slope wavenumber spectrum models of capillary and capillary-gravity waves. Simultaneously, by using the slope wavenumber models, the dependence of the slope wavenumber spectrum on wind speed is analyzed using data obtained in an experiment which was performed in a laboratory wind wave tank. Generally speaking, the slope wavenumber spectra are influenced profoundly by the wind speed above water surface. The slope wavenumber spectrum increases with wind speed obviously and do not cross each other for different wind speeds. But, for the same wind speed, the slope wavenumber spectra are essentially identical, even though the capillary and capillary-gravity waves are excited at different times and locations. Furthermore, the slope wavenumber spectra obtained from the models agree quite well with experimental results as regards both the values and the shape of the curve.

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

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.

Absorbing Boundary Conditions for Simulating Water Waves Near Solid Bodies

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.

Third-Order Stokes Wave Solutions of the Free Surface Capillary- Gravity Wave and the Interfacial Internal Wave

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.

NON-PROPAGATING SOLITARY WAVES WITH THE CONSIDERATION OF SURFACE TENSION

In this paper,the governing equation for the non-propagating solitary waves,similar to the cubicSchr(?)dinger equation,is derived by the multiple scales with the consideration of surface tension.The non-propagatingsolitary wave solution is given.It is explained by the capillary-gravity wave theory that the crests are sharpened and thetroughs are flattened in the transversal harmonic of the non-propagating solitary waves.On σ～kh plane,twoparameter regions are obtained in which the non-propagating solitary wave can occur,but all existing experimentalparameters are in region 1(Fig.1).