Designing against parametric instability in following seas

We investigate the characteristics of parametric instability when very large variations of restoring between the wave trough and the wave crest are taking place, creating a restoring that is alternating between negative (or nearly negative) and strongly positive values. The possible ways to consider the nonlinearities in damping and in restoring are discussed in detail. The boundary separating parametric instability from pure-loss is identified. In depth studies are carried out to ascertain the practical relevance of the parametric mechanism. Instability regions are identified in terms of transient motions, rather than in terms of the customary asymptotic stability chart associated with Mathieu's equation. A basis for comparing parametric roll behavior for different representations of restoring is established. Asymmetric variation laws and bi-chromatic waves are considered.     

在平台振荡条件下TLP张力腿的涡激非线性响应

给出了预测张力腿涡激横向振动的时域分析,考虑了波浪、海流、张力腿平台的横漂与垂荡诸因素.张力腿平台的垂荡引起张力周期性变化,对张力腿的涡激横向振动起参数激励的作用,使其动力响应更为复杂.讨论了参数激励下涡激响应的共振条件;以尾流振子模型为基础,发展了分析张力腿在动张力作用下的涡激振动的工程方法,并分析了一座TLP实例,给出了在横漂周期内张力腿上质点的相对位移、弯矩、剪力幅值的时间历程.结果表明,平台垂荡使张力腿的涡激响应幅值升高、高频成分增加,因此它对张力腿的疲劳设计是重要的.     

Parametric vibration of submerged floating tunnel tether under random excitation

For the study of the parametric vibration response of submerged floating tunnel tether under random excitation,a nonlinear random parametric vibration equation of coupled tether and tube of submerged floating tunnel is set up.Subsequently,vibration response of tether in the tether-tube system is analyzed by Monte Carlo method.It may be concluded that when the tube is subjected to zero-mean Gaussian white noise random excitation,the displacement and velocity root mean square responses of tether reach the peak if the circular frequency of tube doubles that of tether;the displacement and velocity root mean square responses of tether increase as the random excitation root mean square increases;owing to the damping force of water,the displacement and velocity root mean square responses of tether decrease rapidly compared with tether in air;increasing the damping of the tether or tube reduces the displacement and velocity root mean square responses of tether;the large-amplitude vibration of tether may be avoided by locating dampers on the tether or tube.     

Bounded and unbounded coupled transverse response of parametrically excited vertical marine risers and tensioned cable legs for marine applications

The paper deals with the non-linear dynamic response in the transverse direction of vertical marine risers or a tensioned cable legs subjected to parametric excitation at the top of the structure. The dynamic model contains both elastic and bending effects. The analytical approach reveals that the dynamic lateral response is governed by effects originated from the coupling of modes in transverse direction. The mathematical model is being treated numerically by retaining a sufficient number of transverse modes. Numerical results are given for specific case studies and refer both to the time histories of the lateral response for all modes of motion, and to the corresponding power spectral densities obtained through FFT. The numerical predictions are suitably plotted and discussed. The calculations concern both the undamped and the damped dynamic system. The damping in the system is a non-linear Morison type term, which describes the effect of the hydrodynamic drag. Both coupled and uncoupled equations are treated and points as well as regions of coupled and uncoupled stability and instability are defined. It is shown that the impacts originated from the coupling, evaluate new instabilities for the respective undamped system. The numerical results obtained through FFT of the time histories, provide qualitative conclusions for the features of the dynamic response for the modes of motions considered. Special attention has been paid to the effect of the hydrodynamic drag for the parametric excitation frequencies that guide the dynamic system to lie within a region of coupled instability.     

A parametric design study for a semi/SCR system in Northern North Sea

In recent years, offshore reservoirs have been developed in deeper and deeper water environments. Steel catenary risers (SCRs) are being considered in deepwater development such as Northern North Sea. SCRs used in conjunction with a semi-submersible or floating production, storage and offloading (FPSO) in deepwater harsh environments present significant design challenges. The large vertical motions at the semi or FPSO induce severe riser response, which results in difficulty meeting strength and fatigue criteria at the hang off and touch down point locations. To improve the understanding of SCR behaviour and increase the confidence in the design of such systems in deepwater harsh environments, a parametric study on a SCR connected to a semi-submersible was carried out in this paper to deal with the factors that mainly influence the loading condition and fatigue life of the riser. Weight-optimized configurations were applied during the course of riser design. Riflex combined with DeepC was the primary analysis tool used for the long-term response of the nonlinear SCR structure simulations, which requires a large amount of computer time. Hence, the parameters affecting the efficiency and accuracy of the simulations have also been studied during the analysis process.     

Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincaré map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term.     

涡激致顶张力立管双频参量共振研究

研究了涡激力作用导致顶张力立管基于双频激励的参量共振机理。随着海洋油气开发走向深水,参量共振成为深海立管设计面临的挑战之一。立管系统一旦发生参量共振,将因应力过大或疲劳损伤而发生破坏,造成油气泄漏从而带来环境污染和重大经济损失。顶张力立管受涡激力作用产生横向运动,引起轴向张力波动,满足一定条件时,立管将发生参量共振。目前研究多以单频外激励探讨立管的马修不稳定性,而实际激励为多频叠加,因此双频外激励被提出并被应用于对立管参量稳定性的探讨。研究建立了顶张力立管非线性耦合的运动方程,并推导了多频激励马修方程,采用布勃诺夫-伽辽金法求解有阻尼马修方程,对比分析了单频和双频激励对顶张力立管参量稳定性的影响,探讨了双频激励马修方程设计深海顶张力立管参量稳定性的应用。研究表明:涡激致顶张力立管产生轴向应力波动,进而导致立管系统发生参量共振的现象值得设计人员关注;此外,实际工程设计中激励函数的选取,对被研究系统参量稳定性特性以及阻尼特性的预测具有决定性影响。     

On the parametric excitation of vertical elastic slender structures and the effect of damping in marine applications

The dynamic behaviour of vertical slender structures for marine applications under parametric excitation is considered. The governing equations are treated using two different numerical schemes. The effect of parametric excitation is examined in cases where the excitation frequency lies in the vicinity of nonlinear resonances. First, the un-damped case is considered and the features of the dynamic response are properly identified and discussed. For explaining the particulars of the un-damped behaviour, the governing equations are treated analytically by applying the method of normal forms. The effect of damping is examined through comparative numerical computations of the system's behaviour. It is shown that the inclusion of hydrodynamic drag in the describing model eliminates the impacts of internal resonances excited due to the parametrically imposed motions. Finally, the paper demonstrates the significance of the terms that describe the coupling between the longitudinal and transverse vibrations.     

Theoretical and experimental analysis of tethered buoy instability in gravity waves

The motion of a tethered spherical buoy subjected to incident regular waves was measured in a wave tank. Transverse instability was observed when the period of the wave generated was close to one-half of the natural period of the buoy. The transverse instability confirmed as Mathieu type was predominant at the surface but diminished with increase in the depth of submergence. The stable and unstable zones were determined on the Mathieu's instability diagram. Experimental results were in agreement with the predicted zone of instability for a two degree of freedom oscillation problem of Mathieu type which has a periodically varying spring constant.     

Improved representation of breaking wave energy dissipation in parametric wave transformation models

An improved formulation to describe breaking wave energy dissipation is presented and incorporated into a previous parametric cross-shore wave transformation model [Baldock, T.E., Holmes, P., Bunker, S., Van Weert, P., 1998. Cross-shore hydrodynamics within an unsaturated surf zone. Coastal Engineering 34, 173–196]. The new formulation accounts for a term in the bore dissipation equation neglected in some previous modelling, but which is shown to be important in the inner surf zone. The only free model parameter remains the choice of γ, the ratio of wave height to water depth at initial breaking, and a well-established standard parameter is used for all model runs. The proposed model is compared to three sets of experimental data and a previous version of the model which was extensively calibrated against field and laboratory data. The model is also compared to the widely used model presented by Thornton and Guza (1983) [Thornton, E.B., Guza, R.T., 1983. Transformation of wave height distribution. Journal of Geophysical Research 88 (No.C10), 5925–5938].     

Assessment of uncertainty in environmental contours due to parametric uncertainty in models of the dependence structure between metocean variables

A key factor for computing environmental contours is the appropriate modeling of the dependence structure among the environmental variables. It is known that all the information on the dependence structure of a set of random variables is contained in the copulas that define their multivariate probability distribution. Provided that copula parameters are estimated by means of statistical inference using observations, recordings, numerical or historical data, uncertainty is unavoidably introduced in their estimates. Parametric uncertainty in the copulas parameters then introduces uncertainty in the environmental contours. This study deals with the assessment of uncertainty in environmental contours due to parametric uncertainty in the copula models that define the dependence structure of the environmental variables. A point estimation approach is adopted to estimate the statistics of the uncertain coordinates of the environmental contours considering they are given in terms of inverse functions of conditional copulas. A case study is reported using copulas models estimated from storm hindcast data for the Gulf of Mexico. Uncertainty in environmental contours of significant wave height, peak period and wind speed is assessed. The accuracy of the point estimation of the mean and variance of the contour coordinates is validated based on Monte Carlo simulations. A parametric study shows the manner in which greater parametric uncertainty induces larger variability in the environmental contours. The influence of parametric uncertainty for different degrees of association is also analyzed. The results indicate that variability between contours considering parametric uncertainty can be meaningful.     

Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents

Local scour around a submerged vertical circular cylinder in steady currents was studied both experimentally and numerically. The physical experiments were conducted for two different cylinder diameters with a range of cylinder height-to-diameter ratios. Transient scour depth at the stagnation point (upstream edge) of the cylinder was measured using the so-called conductivity scour probes. Three-dimensional (3D) seabed topography around each model cylinder was measured using a laser profiler. The effect of the height-to-diameter ratio on the scour depth was investigated. The experimental results show that the scour depth at the stagnation point is independent on cylinder height-to-diameter ratio when the later is smaller than 2. The increase rate of equilibrium scour depth with cylinder height increases with an increase in Shields parameter.     

Parametric study of geometrical effects on the degree of bending (DoB) in offshore tubular K-joints under out-of-plane bending loads

In this paper, results of comprehensive finite element (FE) analyses carried out on 81 generated models of tubular K-joints are presented. Results of FE models were verified against experimental data and parametric equations. The fatigue life of a tubular joint, which is commonly found in offshore industry, is not only dependent on the value of hot-spot stress (HSS), but is also significantly influenced by the through-the-thickness stress distribution characterized by the degree of bending (DoB). Data extracted from FE analyses was used to study the effects of geometrical parameters on the DoB values in tubular K-joints subjected to two types of out-of-plane bending (OPB) moment loads. The determination of DoB values in a tubular joint is essential for improving the accuracy of fatigue life estimation using the stress-life (S–N) method and particularly for predicting the fatigue crack growth based on the fracture mechanics (FM) approach. Geometrically parametric investigation was followed by a set of nonlinear regression analyses to develop DoB parametric formulas for the fatigue analysis of K-joints under OPB loadings.     

Theoretical, numerical and experimental study on the problem of ergodicity and ‘practical ergodicity’ with an application to parametric roll in longitudinal long crested irregular sea

This paper addresses the problem of ergodicity of stochastic processes starting from a theoretical point of view, with the aim of obtaining a deeper understanding for practical applications. The problem is tackled bearing in mind the concept of ‘practical ergodicity’, that is, the possibility of obtaining reliable information about ensemble averages by using temporal averages. Some general analytical tools are given to address the problem of accuracy of temporal averages and an example of their use in a possible design of experiments is given. A series of Monte Carlo numerical simulations are performed by means of an analytical non-linear 1.5-DOF model of parametrically excited roll motion. The outcomes of such simulations are analysed to show the effect of ship speed and sea spectrum shape. The effect of wave grouping phenomenon is discussed with particular attention to the Doppler effect. Qualitative indications given by the numerical simulations are then compared with experimental tests showing a good agreement. Practical ergodicity of generated sea in towing tank is also briefly addressed.     

分层流体中内孤立波在潜浮式竖直薄板上透射和反射

采用边缘层理论研究了两层流体系统中内孤立波在潜浮式竖直薄板上的透射和反射问题,提出了非线性演化方程的“初值”条件,分析了内孤立波与薄板非线性相互作用的效应。研究表明:流体层的密度比以及薄板伸入上下层的深度对于反射和透射波结构具有显著的影响,薄板伸入下层越深、密度差越小,则薄板阻碍孤立波透射的效率越高;透射波通常演化为单峰孤立波和迅速衰减的尾波,反射波演化为缓慢衰减的尾波列;对于具有小密度差的跃层结构,内孤立波在潜浮式竖直薄板上的透射及其演化近乎是无障碍的。     

Factors determining the vertical profile of dimethylsulfide in the Sargasso Sea during summer

The major source of reduced sulfur in the remote marine atmosphere is the biogenic compound dimethylsulfide (DMS), which is ubiquitous in the world's oceans and released through food web interactions. Relevant fluxes and concentrations of DMS, its phytoplankton-produced precursor, dimethylsulfoniopropionate (DMSP) and related parameters were measured during an intensive Lagrangian field study in two mesoscale eddies in the Sargasso Sea during July–August 2004, a period characterized by high mixed-layer DMS and low chlorophyll—the so-called ‘DMS summer paradox’. We used a 1-D vertically variable DMS production model forced with output from a 1-D vertical mixing model to evaluate the extent to which the simulated vertical structure in DMS and DMSP was consistent with changes expected from field-determined rate measurements of individual processes, such as photolysis, microbial DMS and dissolved DMSP turnover, and air–sea gas exchange. Model numerical experiments and related parametric sensitivity analyses suggested that the vertical structure of the DMS profile in the upper 60 m was determined mainly by the interplay of the two depth-variable processes—vertical mixing and photolysis—and less by biological consumption of DMS. A key finding from the model calibration was the need to increase the DMS(P) algal exudation rate constant, which includes the effects of cell rupture due to grazing and cell lysis, to significantly higher values than previously used in other regions. This was consistent with the small algal cell size and therefore high surface area-to-volume ratio of the dominant DMSP-producing group—the picoeukaryotes.     

2010年马卡罗夫海盆冰站观测期间垂向热通量时间变化研究

Based on hydrographic data obtained at an ice camp deployed in the Makarov Basin by the 4th Chinese Arctic Research Expedition in August of 2010, temporal variability of vertical heat flux in the upper ocean of the Makarov Basin is investigated together with its impacts on sea ice melt and evolution of heat content in the remnant of winter mixed layer(r WML). The upper ocean of the Makarov Basin under sea ice is vertically stratified. Oceanic heat flux from mixed layer(ML) to ice evolves in three stages as a response to air temperature changes, fluctuating from 12.4 W/m2 to the maximum 43.6 W/m2. The heat transferred upward from ML can support(0.7±0.3) cm/d ice melt rate on average, and daily variability of melt rate agrees well with the observed results. Downward heat flux from ML across the base of ML is much less, only 0.87 W/m2, due to enhanced stratification in the seasonal halocline under ML caused by sea ice melt, indicating that increasing solar heat entering summer ML is mainly used to melt sea ice, with a small proportion transferred downward and stored in the r WML. Heat flux from ML into r WML changes in two phases caused by abrupt air cooling with a day lag. Meanwhile, upward heat flux from Atlantic water(AW) across the base of r WML, even though obstructed by the cold halocline layer(CHL), reaches0.18 W/m2 on average with no obvious changing pattern and is also trapped by the r WML. Upward heat flux from deep AW is higher than generally supposed value near 0, as the existence of r WML enlarges the temperature gradient between surface water and CHL. Acting as a reservoir of heat transferred from both ML and AW, the increasing heat content of r WML can delay the onset of sea ice freezing.     

2012年夏季楚科奇海浮游动物垂直迁移及上升流对其生物量的影响

The diel vertical migration(DVM) of zooplankton and the influence of upwelling on zooplankton biomass were examined using water column data of current velocity and mean volume backscattering strength(MVBS)collected by moored acoustic Doppler current profilers(ADCPs) deployed in the southeastern Chukchi Sea during the 5th Chinese National Arctic Research Expedition(CHINARE) in summer 2012, combined with the satellite observational data such as sea surface temperature(SST), wind, and chlorophyll a(Chl a). Hourly acoustic data were continuously collected for 49-d in the mooring site. Spectral analysis indicated that there were different migrating patterns of zooplankton, even though precisely classifying the zooplankton taxa was not available. The prevailing 24-h cycle corresponded to the normal DVM with zooplankton swimming upwards at sunrise and returning to deep waters at sunset. There was a clear DVM in the upper 17 m of the water column during the period with distinct day-night cycles, and no active DVM throughout the water column when the sun above the horizon(polar day), suggesting that light intensity was the trigger for DVM. Also there was a second migrating pattern with 12-h cycle. The upwelling event occurring in the northwest of Alaskan coastal area had important influence on zooplankton biomass at the mooring site. During the upwelling, the SST close to the mooring site dropped significantly from maximal 6.35°C to minimal 1.31°C within five days. Simultaneously, there was a rapid increase in the MVBS and Chl a level, suggesting the aggregation of zooplankton related to upwelling.