STABILITY OF STEADY MULTI-WAVE CONFIGURATIONS FOR THE FULL EULER EQUATIONS OF COMPRESSIBLE FLUID FLOW

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the Riemann problem in the flow direction, consisting of two shocks, one vortex sheet, and one entropy wave, which is one of the core multi-wave configurations for the two-dimensional Euler equations. It is proved that such steady four-wave configurations in supersonic flow are stable in structure globally, even under the BV perturbation of the incoming flow in the flow direction. In order to achieve this, we first formulate the problem as the Cauchy problem （initial value problem） in the flow direction, and then develop a modified Glimm difference scheme and identify a Glimm-type functional to obtain the required BV estimates by tracing the interactions not only between the strong shocks and weak waves, but also between the strong vortex sheet/entropy wave and weak waves. The key feature of the Euler equations is that the reflection coefficient is always less than 1, when a weak wave of different family interacts with the strong vortex sheet/entropy wave or the shock wave, which is crucial to guarantee that the Glimm functional is decreasing. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution, close to the background solution of steady four-wave configuration.

Joint Distribution of Wave Heights and Wavelengths and Distribution of Wave Steepness

A joint probability density is derived for wavelengths and wave heights. It is asymmetric and depends only on the spectral bandwidth epsilon defined by Cartwright and Longuet-Higgins (1956). After that a theoretical probability density for wave steepness is obtained. It tends to Rayleigh distribution as epsilon --> 0. A comparison between theoretical steepness distribution and laboratory experiment result shows good agreement.

A Comparative Study of Numerical Models for Wave Propagation and Setup on Steep Coral Reefs

Complex factors including steep slopes, intense wave breaking, large bottom friction and remarkable wave setup should be considered while studying wave propagation over coral reefs, and how to simulate wave propagation and setup on coral reefs efficiently has become a primary focus. Several wave models can be used on coral reefs as have been published, but further testing and comparison of the reliability and applicability of these models are needed. A comparative study of four numerical wave models (i.e., FUNWAVE-TVD, Coulwave, NHWAVE and ZZL18) is carried out in this paper. These models’ governing equations and numerical methods are compared and analyzed firstly to obtain their differences and connections;then the simulation effects of the four wave models are tested in four representative laboratory experiments. The results show that all four models can reasonably predict the spectrum transformation. Coulwave, NHWAVE and ZZL18 can predict the wave height variation more accurately;Coulwave and FUNWAVE-TVD tend to underestimate wave setup on the reef top induced by spilling breaker, while NHWAVE and ZZL18 can predict wave setup relatively accurately for all types of breakers;NHWAVE and ZZL18 can predict wave reflection by steep reef slope more accurately. This study can provide evidence for choosing suitable models for practical engineering or establishing new models.

Numerical Investigation of Run-ups on Cylinder in Steep Regular Wave

The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylinder by solving the Navier-Stokes equations. A numerical wave tank is established based on the open-source package to simulate the wave scattering induced by a vertical cylinder. The VOF method is applied to capture the large deformation and breaking of the free surface. The numerical model is validated by experimental results. The relative wave run-ups on the front face and the back face along the centerline of a cylinder are analyzed. The changes of the relative run-ups with the wave steepness, the relative diameter and the relative depth are studied. It is found that the relative run-ups on the front face and the back face of the cylinder depend mainly on the wave steepness and the relative diameter, while the dependence on the relative depth is weak. The empirical formulae are proposed to calculate the relative run-ups in terms of the wave steepness of incident regular waves and the relative diameter of a cylinder.

Dependence of Wave Height Distribution on Spectral Width and Wave Steepness

In this paper experimental wind wave data are analyzed. It is found that differences in spectral width will give rise to differences in wave height distribution. The effect of spectral width on the distribution is mainly in the high wave range. The effect of wave steepness is in low, medium and high wave ranges. In the high wave range the effect of spectral width is comparable to that of wave steepness. Differences in spectral width in the observations may give rise to discrepancies in the result when wave steepness is the only parameter in the distribution.

Nonlinear Numerical Analysis of Vortex-Induced Vibration of A Three-Dimensional Deepwater Steep Wave Riser with Large Deformation Features

The cross-flow(CF)vortex-induced vibration(VIV)of a deepwater steep wave riser(SWR)subjected to uniform or shear flow loads is investigated numerically.The model is based on a three-dimensional(3D)nonlinear elastic rod theory coupled with a wake oscillator model.In this numerical simulation,the nonlinear motion equations of the riser with large deformation features are established in a global coordinate system to avoid the transformation between global and local coordinate systems,and are discretized with the time-domain finite element method(FEM).A wakeoscillator model is employed to study the vortex shedding,and the lift force generated by the wake flow is described in a van der Pol equation.A Newmark-βiterative scheme is used to solve their coupling equation for the VIV response of the SWR.The developed model is validated against the existing experimental results for the VIV response of the top-tension riser(TTR).Then,the numerical simulations are executed to determine VIV characteristics of the SWR.The effects of both flow velocity and the spanwise length of the flow field on the drag coefficient in the inline(IL)direction and the lift coefficient in the CF direction are investigated systematically.The results indicate that compared with TTR,the low frequency and multi-modal vibration are the main components of the SWR due to the large deformation and flexible characteristics.For shear flow,the multi-frequency resonance dominates the VIV response of the SWR,especially at the hang-off segment.

Relationship between wave steepness and wave age in the course of wind wave growth

It is traditionally assumed that the relationship between wave steepness and wave age is inde- pendent of the wind wave growth state. In fact, the traditional relationship can not describe the whole course of wind wave growth. This paper assumes that the relationship between wave steepness and wave age changes with the variety of dimensionless fetch. Based on the relationship proposed by Hou and Wen (1990), a new relation- ship in the course of wind wave growth is revealed. Comparisons between the present study and other previous relationships show that this new relationship explains better the observations than the other existing relationships. In the case of small fetch, wave age value increases more quickly than other models while it is in opposition to that in the case of large fetch. The result in present paper can clearly reflect the whole course of wind wave growth, it is an improvement for traditional results.Key words: wave steepness, wave age, relationship between wave steepness and wave

基于悬链线理论的Lazy-wave和Steep-Wave立管形态确定方法

作为改良型的钢质悬链线立管(Steel Catenary Riser,SCR),懒波型立管(Lazy Wave Riser, LWR)和陡波型立管(Steep-Wave Riser,SWR)在深水油气开发中的应用越来越广泛。LWR和SWR的立管形态在其设计中至关重要,并且在海流作用下,LWR和SWR的立管形态会发生相当大的变化。文章将悬链线理论推广到深水LWR和SWR简化了立管形态确定方法,实现了工程设计初期快速确定立管形态的需求,减少了工程设计工作量。

Nonlinear Dynamic Analysis and Fatigue Study of Steep Wave Risers Under Irregular Loads

As a reliable alternative option for traditional steel catenary risers(SCRs),steep wave risers(SWRs)have been widely applied to deepwater oil and gas production.However,the nonlinear dynamic analysis of SWRs is more complicated than that of traditional SCRs due to their special configuration and significant geometric nonlinearity.Moreover,SWRs are highly susceptible to fatigue failure under the combined excitation of irregular waves and top floater motions(TFMs).In this study,considering irregular waves and TFMs,a numerical SWR model with an internal flow is constructed based on the slender rod model and finite element method.The Newmark-βmethod is adopted to solve the dynamic behavior of SWR.Moreover,the Palmgren-Miner rule,a specified S-N curve,and rainflow counting method are applied to estimate the fatigue damage.An efficient numerical computation procedure,i.e.,DRSWR,is programmed with MATLAB in this study.Calculation results are compared with those of OrcaFlex to verify the accuracy of the DRSWR.The nonlinear dynamic response and fatigue damage of an SWR under the combined excitation of irregular waves and TFMs are obtained,and a comprehensive parametric analysis is then conducted.The analysis results show that the buoyancy section undergoes the highest level of stress and fatigue damage under the combined excitation of irregular waves and TFMs.An internal flow with high velocity and high density produces a high level of fatigue damage.The buoyancy factor and length of the buoyancy section should be set moderately to reconcile the reduction of the top tension with increased fatigue life.These results are expected to provide some reference significance for the engineering design of SWR.

Time-Domain Nonlinear Wave-Current Interaction with A Steep Wave Riser Considering Internal Flow Effect

The nonlinear dynamic response induced by the wave-current interaction on a deepwater steep wave riser(SWR)is numerically investigated based on a three-dimensional(3 D)time-domain finite element method(FEM).The governing equation considering internal flow is established in the global coordinate system.The whole SWR consists of three segments:the decline segment,buoyancy segment and hang-off segment,in which the buoyancy segment is wrapped by several buoyancy modules in the middle section,leading to the arch bend and sag bend.A Newmark-β iterative scheme is adopted for the accurate analysis to solve the governing equation and update the dynamic response at each time step.The proposed method is verified through the published results for the dynamic response of steel catenary riser(SCR)and static configuration of steel lazy wave riser(SLWR).Simulations are executed to study the influence of wave height,current velocity/direction,internal flow density/velocity and top-end pressure on the tension,configuration and bending moment of the SWR.The results indicate that the influence of the current on the configuration and mechanical behavior of the SWR is greater than that of the wave,especially in the middle section.With increasing current velocity,the suspending height of the middle section drops,meanwhile,its bending moment decreases accordingly,but the tension increases significantly.For a fixed external load,the increasing internal flow density induces the amplification of the tension at the hang-off segment and the mitigation at the decline segment,while the opposite trend occurs at the bending moment.

Nonlinear Analysis of Bidirectional Vortex-Induced Vibration of A Deepwater Steep Wave Riser Subjected to Oblique Currents

An improved three-dimensional(3D)time-domain couple model is established in this paper to simulate the bidirectional vortex-induced vibration(VIV)of a deepwater steep wave riser(SWR)subjected to oblique currents.In this model,the nonlinear motion equations of the riser are established in the global coordinate system based on the slender rod theory with the finite element method.Van der Pol equations are used to describe the lift forces induced by the x-and y-direction current components,respectively.The coupled equations at each time step are solved by a Newmark-βiterative scheme for the SWR VIV.The present model is verified by comparison with the published experimental results for a top-tension riser.Then,a series of simulations are executed to determine the influences of the oblique angle/velocity of the current,different top-end positions and the length of the buoyancy segment on the VIV displacement,oscillating frequency as well as hydrodynamic coefficients of the SWR.The results demonstrate that there exists a coupled resonant VIV corresponding to x-direction and y-direction,respectively.However,the effective frequency is almost identical between the vibrations at the hang-off segment along x and y directions.The addition of the buoyancy modules in the middle of the SWR has a beneficial impact on the lift force of three segments and simultaneously limits the VIV response,especially at the decline segment and the hang-off segments.Additionally,the incident current direction significantly affects the motion trajectory of the SWR which mainly includes the fusiform and rectangle shapes.

Numerical method for wave height distribution within the artificial harbor with water depth of steep variation

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A New Probability Distribution Function of Wave Steepness

Wave steepness is an important characteristic describing the severity of sea state in ocean engineering. In the existing theoretical and experimental studies,wave steepness is often substituted by some related quantities. In this paper,a new probability density function(pdf) of steepness,which is a pdf of the steepness in its original definition,is obtained for narrowband Gaussian processes. The drawback inherent in the previous theoretical pdfs of steepness,that is,the probability density at zero steepness is nonzero,has been eliminated. Laboratory experiments were conducted in a wind-wave flume to measure the wave steepness distribution. Comparisons among laboratory measurements and some theoretical pdfs of steepness show that the new pdf generally fits the data better than the one proposed by Zheng et al.(1999) .

A relationship between wave steepness and wave age for wind waves in deep water

Studying the relationship between wave steepness and wave age is important for describing wind wave growth with energy balance equation of significant waves. After invoking the dispersion rela- tion of surface gravity wave in deep water, a new relationship between wave steepness and wave age is revealed based on the “3/2-power law” (Toba, 1972), in which wave steepness is a function of wave age with a drag coefficient as a parameter. With a given wave age, a larger drag coefficient would lead to larger wave steepness. This could be interpreted as the result of interaction between wind and waves. Comparing with previous relationships, the newly proposed one is more consistent with observational data in field and laboratory.

WAVEWATCHⅢ第三代海浪数值模式在中国东海的应用和改进

利用东海的浮标观测数据,比较了WAVEWATCHⅢ第三代海浪数值模式的ST2、ST4和ST6三种源函数方案在东海的适用性。结果表明,三种源函数方案在波高小于3 m中低风速情形下,模拟波高与观测波高符合的很好,而在波高大于3 m的高风速情形下,模拟波高偏大。在此基础上,提出了以波龄和波陡为参数的海面粗糙度参数化公式,以此来计算拖曳系数。该方案可以自动满足拖曳系数在临界风速达到饱和的观测事实,将上述拖曳系数计算方案应用于最新的ST6源函数方案,在保持中低风速时的模拟精度的同时,可有效地改善高风速时模拟波高偏大问题,而且可使模拟周期与浮标观测结果更为一致。

Wave steepness retrieved from scatterometer data in a genetic algorithm

Wave steepness is an important characteristic of a high sea state, and is widely applied on wave propagations at ports, ships, offshore platforms, and CO2 circulation in the ocean. Obtaining wave steepness is a difficult task that depends heavily on theoretical research on wavelength distribution and direct observations. Development of remote-sensing techniques provides new opportunities to study wave steepness. At present, two formulas are proposed to estimate wave steepness from QuikSCAT and ERS-1/2 scatterometer data. We found that wave steepness retrieving is not affected by radar band, and polarization method, and that relationship of wave steepness with radar backscattering cross section is similar to that with wind. Therefore, we adopted and modified a genetic algorithm for relating wave steepness with radar backscattering cross section. Results show that the root-mean-square error of the wave steepness retrieved is 0.005 in two cases from ERS-1/2 scatterometer data and from QuikSCAT scatterometer data.

Mathematical simulation of steep waves at a focus point

Mathematical models simulating steep waves at a focus point are presented in this paper. Simulations of extreme waves in a model basin were used to determine the loads on floating structures induced by the waves. Based on a new wave theory, numerical test results show that the simulation procedure is effective and the induced motion of water particles in the front of waves is an important factor influencing impact loads on floating bodies.

基于分布式联邦学习的毫米波通信系统波束配置方法

针对超密集组网中毫米波通信系统复杂的波束配置问题,该文提出一种基于分布式联邦学习(DFL)的波束配置算法(BMDFL),旨在利用有限的波束资源实现用户覆盖率最大化。考虑到传统集中式学习存在用户数据安全问题,基于分布式联邦学习框架构建系统模型,从而减少用户隐私信息的泄露。为了实现波束的智能化配置,引入双深度Q学习算法(DDQN)训练系统模型,并通过马尔可夫决策过程将长期的动态优化问题转化为相应的数学模型进行求解。仿真结果从系统的网络吞吐量和用户覆盖率方面验证了该方法的有效性和鲁棒性。

矿山高陡岩石边坡生态修复技术研究进展

高陡岩石边坡生态修复是矿山生态修复领域中的重难点之一。通过中国期刊全文数据库和Web of Science核心合集数据库,对2003-2022年发表的关于高陡岩石边坡的文献进行检索与综述分析。本研究分析了高陡岩石边坡的年度发文量和研究热点,从边坡稳定性、植生环境构造、植被配置等方面对高陡岩石边坡生态修复现状进行探讨,以期为今后该领域的研究提供参考方向。

陡倾角单斜地层地震勘探观测系统设计及其应用

我国西部地区煤层倾角大于30°的煤炭资源相当可观。为了提高陡倾角煤田地震勘探采集资料品质,通过研究分析倾斜地层地震反射波时距曲线特征,建立陡倾角单斜地质模型并进行3种不同观测系统(中点放炮、下倾方向放炮上倾方向接收和上倾方向放炮下倾方向接收)设计,同时采用射线追踪方法进行地震波场正演模拟。通过对比分析3种不同观测系统对应地震波场和叠加时间剖面特征,总结出适合陡倾角单斜地层地震勘探观测系统设计方法。将适合陡倾斜地层的地震勘探观测系统设计方法应用到实际地震勘探资料采集工作中,取得了较为理想的地震资料。