Second-order random interfacial wave solutions for two-layer fluid with a free surface

1 Introduction Interfacial waves travelling along the interface between two fluids of different densities can be often observed in subsurface layers of the ocean since the upper subsurface layer is warmer over much of the o- cean (Umeyama, 2002). They are…     

The limiting wave height in wind-induced wave trains

The vertical acceleration threshold concept has been applied to evaluate the limiting wave height in the train of wind-induced waves propagated over a horizontal bottom. This concept yields very simple computation of the probability of breaking for stochastic sea in deep and finite water depths. The computations confirmed the available field and laboratory observations that the limiting wave steepness in the deep water is lower than the steepness predicted by Stokes. For shallow water depth, the limiting wave height is smaller than 0.55h. This conclusion is consistent with field as well as wave tank observations.     

四层成层水域内波的研究

运用小振幅波理论研究了四层成层水域的内波运动，给出了四层成层状态下的各界面波波面位移和各层速度势的解析表达式及各层深度平均流速分布和内波波动频散关系，并与三层成层水域内波的解析结果进行了比较。     

Nonlinear wave resistance of a two-dimensional pressure patch moving on a free surface

A model problem of the flow under an air-cushion vessel is studied. Two different numerical techniques are used to determine the solution of the free-surface elevation and the wave resistance for a range of Froude number, Reynolds number, value of the pressure applied in the cushion, and depth of the water. The first numerical technique uses a velocity potential that satisfies linearized free-surface boundary conditions, whereas the second employs a finite-volume method to find a solution that satisfies the fully nonlinear free-surface boundary conditions. The results clearly show that for high Froude number and practical values of the cushion pressure, the linear-theory solution is in excellent agreement with the more exact nonlinear prediction. For lower Froude number the solution becomes unsteady, and the disagreement between the two methods is larger.     

Theoretical analysis on the transverse motion of a buoy by surface wave

The theoretical analysis on the transverse motion of a buoy is reported here. The analysis has been done by linear differential equation, and its conclusion shows that the transverse motion occurs when the parameters of surface wave and buoy system are related by Mathieu's instability condition. This analysis can be applied to the pole structure which has the equal flexibility in all directions.     

地球流体中的非线性Rossby波

Rossby波是由行星涡度随纬度变化引起的一种波动,它是地球流体中大尺度运动的主要波动之一.     

Non-linear surface waves in the layer of fluid on a porous base

Non-linear and solitary surface waves represent one of the most intriguing and thoroughly investigated phenomena in ocean dynamics. Up to now, a considerable number of results have been obtained, which are related to the study of solitary waves in the coastal shelf zone, and their propagation and transformation under the effect of various factors. In the majority of such studies, the sea bottom surface was assumed to be impervious to fluid. Only some of them, e.g. refs 1–4, considered the propagation of waves in the limited layers of fluids on the pervious (porous) bases. At the same time, Shepard [5] and Nikolaevsky [6] pointed out that the bottom surface structure on the shelf is often porous. In this case, the pervious layer represents a porous matrix (possibly deformable) completely filled with fluid. Its density is different from the free fluid density.Translated by Mikhail M. Trufanov. UDK 532.59.     

Dynamics of gravity-capillary waves on the surface of a nonuniformly heated fluid

The method of slowly varying amplitudes is used to determine the reflection of surface gravity-capillary waves from regions of regular surface convection in the approximation of an ideal and homogeneous viscous fluid. A model of a quasi-steady distribution of temperature is employed. The conditions of both weak (nonresonant) interaction, when the wave passes almost completely through the convective zone, and strong resonant interaction are revealed. When interaction is strong, standing waves form in front of the convective region and the spectral composition of the wave packet changes. Viscosity and the accompanying boundary layers lead to the broadening of forbidden zones.     

基于PS-VF-TBD的地波雷达船只目标航迹起始方法

针对地波雷达低信噪比目标信号"闪烁"导致的航迹起始困难问题,本文提出了一种基于PS-VF-TBD的航迹起始方法.该方法综合利用了地波雷达回波谱中目标信号的展宽特征和运动特性,利用PS-VF-TBD方法对运动目标能量有效积累的特点,提高对疑似目标多帧信号间的关联概率,进而提高对真实目标的搜索概率和航迹起始成功率.通过地波...     

Irrotational,progressive surface gravity waves near the limiting height

Numerical solutions of irrotational, progressive surface gravity waves in water of a constant depth are obtained by means of an iterative method. Our results suggest that waves with the surface slope angle greater than/6 may exist. The calculated phase velocity of deep water waves near the wave steepness 0.14 is significantly smaller than the value given by the Stokes' fourth approximation.In order to check our method, we apply it to the problem proposed byDavies (1951), which is hypothetical but similar to the present problem, and for which the exact solution is known. In this case our results show good agreement with the exact solution.     

两层流体中多个圆柱浮体波浪力的解析方法

采用解析方法研究了线性入射波作用下两层流体中多个圆柱形淹没浮体的渡浪力特性.首先基于多极子展开方法,建立了散射势函数的解析表达式,并进一步得到浮体散射渡浪力的计算公式,然后利用边界元方法验证了本文的解析解,最后分析了不同参数的变化对双圆柱形浮体结构波浪力的特有影响.     

波面位移非对称性对风浪成长状态的依赖性

以二阶随机波动理论为基础，研究了刻画波面位移非对称性的偏度参量λ3对风浪成长参量(反波龄ω和无因次风区χ)的依赖性，得到了λ3与ω和λ3与χ的近似解析关系式，并利用实验室水槽风浪成长实验的实测数据对这些关系式进行了检验。     

Characterizing random wave surface elevation data

The definition and subsequent use of dimensional and dimensionless parameters to characterize various nonlinear aspects of ocean surface waves has again become a matter of great interest to the offshore community. The desire to ascertain whether laboratory simulations are adequately representing the surface waves found in the oceans and the concern over the mechanisms behind platform response phenomena, like ringing, has driven this resurgence of interest. This paper presents a depth independent characterization of single design waves, from which improved estimates of localized wave crest front and back slopes follow that are consistent with discrete time series analysis. Characterization of the nature of the entire wave data recorded requires a combination of spectral parameters and probabilistic models in addition to those used in the design wave characterization. A new expression for the direct evaluation of the kurtosis from knowledge of the spectral bandwidth, the relationship between some of the common spectral parameters, and some modified spectral parameters are presented and discussed. Three illustrative examples are presented. The first example provides a detailed examination of wave data measured from a series of random amplitude and random phase tests in a large model basin. The second presents estimates of the various parameters for the Pierson-Moskowitz and Wallops wave spectrum models. The third example investigates the use of the spectral peakedness ratio for comparing data with selected wave spectrum models. The examples illustrate how the formulae can provide a comprehensive local and global parametric characterization of surface wave elevation data.     

Characterizing random wave surface elevation data

The definition and subsequent use of dimensional and dimensionless parameters to characterize various nonlinear aspects of ocean surface waves has again become a matter of great interest to the offshore community. The desire to ascertain whether laboratory simulations are adequately representing the surface waves found in the oceans and the concern over the mechanisms behind platform response phenomena, like ringing, has driven this resurgence of interest. This paper presents a depth independent characterization of single design waves, from which improved estimates of localized wave crest front and back slopes follow that are consistent with discrete time series analysis. Characterization of the nature of the entire wave data recorded requires a combination of spectral parameters and probabilistic models in addition to those used in the design wave characterization. A new expression for the direct evaluation of the kurtosis from knowledge of the spectral bandwidth, the relationship between some of the common spectral parameters, and some modified spectral parameters are presented and discussed. Three illustrative examples are presented. The first example provides a detailed examination of wave data measured from a series of random amplitude and random phase tests in a large model basin. The second presents estimates of the various parameters for the Pierson-Moskowitz and Wallops wave spectrum models. The third example investigates the use of the spectral peakedness ratio for comparing data with selected wave spectrum models. The examples illustrate how the formulae can provide a comprehensive local and global parametric characterization of surface wave elevation data.     

Acoustic plane-wave reflection from a rough surface over a random fluid half-space

Plane-wave reflection from a rough surface overlying a fluid half-space, with a sound speed distribution subject to a small and random perturbation, is considered. A theory based upon a boundary perturbation method in conjunction with a formulation derived from Green's function for the coherent field in the random medium have been applied to a typical oceanic environment to study their effects on the plane-wave reflection. By considering the coherent field itself, the plane-wave reflection may be obtained straightforwardly through a procedure consistent with the formalisms currently employed in rough surface scattering. The results show that both the rough surface and medium inhomogenieties may reduce the plane-wave reflection, however, the characteristics of the curves representing their effects are different, enabling us to identify the dominant scattering mechanism. The results for the coherent reflection due to the individual scattering mechanism are compatible with those found in the existing literature.     

Acoustic plane-wave scattering from a rough surface over a random fluid medium

Acoustic plane-wave scattering from a rough surface overlying a fluid half-space with a sound-speed distribution subject to a small random variation is considered. Under the assumption that the surface roughness and medium randomness are statistically independent, the scattered field may be derived by first solving for the mean field in the medium, and then incorporating with boundary-perturbation method to obtain the total mean field and the power spectral density of the scattered field. The employed algorithm is compatible to the analysis available in the existing literature so that the formulations are conveniently integrated. The results for the power spectral density have shown that the effects of medium inhomogeneities on the rough surface scattering are limited in a spectral regime where the scattered components have shallow grazing angles. The distribution of the power spectral density over the space is primarily governed by the power spectrum and correlation lengths of the rough surface.     

Comparisons of internal solitary wave and surface wave actions on marine structures and their responses

In this paper, a time-domain numerical model is established for computing the action of internal solitary wave on marine structures and structure motion responses. For a cylindrical structure, its side and bottom are discretized by pole and surface elements, respectively. The drag and inertial forces in the perpendicular direction of the structure are computed by the Morison equation from the pole elements, and the Froude–Krylov force in the axial direction of the structure due to internal wave motion is computed by integration of the dynamic pressure over the surface elements. The catenary theory is used to analyze the reaction force due to mooring lines, and the motion equation of the marine structure is solved by the fourth-order Runge–Kutta method in the time domain. The model is used to calculate the interaction of the internal solitary wave with a Spar platform with mooring system, and the surface wave action with the platform has also been computed by a frequency-domain boundary element method for comparison. Through the comparison based on a practical internal wave and surface wave states, it can be concluded that the internal wave force on the structure is only 9% of the one due to surface waves. However, the motion response due to the internal wave is much greater than the one due to the surface waves. It shows that the low-frequency effect of internal solitary waves is a great threat to the safety of marine structures.     

Towing dynamics of a liferaft and fast rescue craft in a surface wave

The equations of motion for the coupled dynamics of a small liferaft and fast rescue craft in a surface wave are formulated in two dimensions using the methods of Kane and Levinson [1985. Dynamics: Theory and Applications. McGraw-Hill Inc., New York]. It is assumed that the motion normal to the wave surface is small and can be neglected, i.e. the bodies move along the propagating wave profile. The bodies are small so that wave diffraction and reflection are negligible. A Stokes second order wave is used and the wave forces are applied using Morison's equation for a body in accelerated flow. Wind loads are similarly modelled using drag coefficients. The equations are solved numerically using the Runge–Kutta routine “ode45” of MATLAB^®. The numerical model provides guidelines for predicting the tow loads and motions of small craft in severe sea states.     

Stochastization of the propagation of a surface wave packet in the field of an internal wave packet

The trapping of a surface wave packet by a packet of internal waves is discussed in this paper. Applying the criterion for non-linear resonance overlap, we have obtained a sufficient condition for stochasticity of the surface wave packet.Translated by Vladimir A. Puchkin.