Numerical simulations of Rossby–Haurwitz waves

Simulations of Rossby–Haurwitz waves have been carried out using four different high‐resolution numerical shallow water models: a spectral model, two semi‐Langrangian models predicting wind components and potential vorticity respectively, and a finite‐volume model on a hexagonal–icosahedral grid. The simulations show that (i) unlike the nondivergent case, the shallow water Rossby–Haurwitz wave locally generates small‐scale features and so has a potential enstrophy cascade, and (ii) contrary to common belief, the zonal wavenumber 4 Rossby–Haurwitz wave is dynamically unstable and will eventually break down if initially perturbed. Implications of these results for the use of the Rossby–Haurwitz wave as a numerical model test case are discussed. The four models tested give very similar results, giving confidence in the accuracy and robustness of the results. The most noticeable difference between the models is that truncation errors in the hexagonal–icosahedral grid model excite the Rossby–Haurwitz wave instability, causing the wave to break down quickly, whereas for the other models in the configurations tested the instability is excited only by roundoff error at worst, and the Rossby–Haurwitz wave breaks down much more slowly or not at all.     

Generalized Haurwitz waves

Waves which propagate along a vertical wall lying in an arbitrary direction on aβ-plane are derived as a generalization of Haurwitz waves (Haurwitz, 1940) whose direction of propagation is restricted to the east-west direction. The waves are classified into two types. One consists of neutral waves, which correspond to a generalization of Haurwitz waves. The other consists of waves with complex wavenumber and without energy flux. The phase of the waves also propagates in the direction normal to the coast in an envelope except for the case in which the coast lies in the east-west direction.     

On the nonlinear interactions in triads of edge waves on the sea shelf

We study nonlinear three-wave interactions between edge waves propagating in the same direction over the shelf step. The conditions of synchronism are determined and the coefficient of interaction is computed for the cases where the waves of the five lowest modes participate in the interaction. The space-time dynamics is studied by analyzing, as an example, a single triad of edge waves. The possibility of interaction of edge waves in the regions with actual topography is demonstrated. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 3–19, May–June, 2008.     

半封闭海湾共振周期计算与研究

三门湾海域水波共振现象较为显著,容易引发海洋灾害。针对三门湾这一典型半封闭海湾,分别从理论推导和数值模拟两方面研究了三门湾的共振周期。研究发现:理论推导结果可以用于对海湾整体共振周期的粗略估计,数值模拟结果更加精确,也能充分反映海湾内不同水域的共振特征。数值模拟结果表明,三门湾内各水域普遍存在3~4个共振周期模态,湾内各水道第一模态和第三模态共振周期数值解与理论值较为接近,石浦水道与外海相联通,共振周期不显著。三门湾内各水域共振周期第一模态对应的振幅最大,然后依次递减,但湾顶的青山港、蛇蟠水道第二模态共振周期及对应的振幅值与第一模态相差较小,基本呈现双峰结构。共振振幅由湾外向三门湾顶部逐渐增加,尤其是湾顶处振幅增益比较显著。通过本研究可以为三门湾的防灾减灾提供科学依据。     

Bragg resonant reflection of carrier waves composing wave groups

Numerical analyses for the Bragg resonant reflection of carrier waves associated long waves due to sinusoidally varying seabeds are performed by using a set of coupled ordinary differential equations derived from the Boussinesq equations. The Boussinesq equations are firstly approximated with the Fourier decomposition. The coupled governing equations are then derived and used to simulate evolution of both short and long wave components. It is also found that wave groups are generated by two carrier waves with slightly different frequencies. The wave energy of the initial wave components is transferred to other harmonic components during propagation over a long distance. Evolution and reflection of both short and long waves were largely affected by nonlinearity.     

海洋含黏粒砂土共振柱试验研究

本文利用英国GDS公司生产的RCA共振柱系统测试海洋含黏粒砂土动剪切模量,同时对比纯砂样的动剪切模量,系统研究固结应力、初始密实度、黏粒含量等因素对砂土最大动剪切模量的影响。试验结果表明:最大动剪切模量随有效固结应力增大而增大;随初始密实度增大而增大;随黏粒含量的增加而降低。     

The resonant generation of shelf waves by a moving cyclone

The resonant generation of shelf waves by the local atmospheric disturbance displacing longshore is considered. The model, which is more precise compared with that in refs 3 and 4 owing to the consideration of dispersion of the trapped waves, was applied to the analysis. It is shown that comparatively low-frequency waves are generated most effectively when the cyclone displacement rate is close to the maximum phase velocity of a single shelf mode.Translated by Mikhail M. Trufanov.     

Stabilization of a linearly unstable wave participating in a three-wave resonant interaction

An analytical study of the influence of three-wave resonant interactions on the evolution of unstable wave disturbances is presented in the Kelvin-Helmholtz model. These results may be of interest in analyzing the dynamics of disturbances at the ocean-atmosphere interface and in two-layer flows which arise in the ocean and are characterized by large gradients of flow velocity at the boundary of layers. In the case under consideration, the instability arises when eigenfrequencies coincide in the framework of a single mode and the instability is algebraic. The amplitudes of the two other interacting stable waves are assumed to be small compared to the amplitude of the third, unstable, mode. The system of amplitude equations for this case is investigated using the WKB method. As a result, we obtain the formulas coupling the solutions for the time before and after a transition through a singular point, where the amplitude of the linearly unstable wave has a local minimum. These formulas give the rule of transformation of the parameter that characterizes a phase shift between fast and slow modes and determines the behavior of the system. It is shown that, in a transition through a singular point, this parameter changes randomly. As long as the parameter is positive, the amplitude of the linearly unstable wave remains limited and oscillates stochastically. In a transition of the parameter through zero, we exit the stabilization region and have an infinite growth of amplitude. The transition into the instability region is random. However, if the time interval where the amplitude remains limited is large enough, the scenario of the behavior of the system we have obtained can be treated as the partial stabilization of instability. The results make it possible for us to investigate the stochasticity caused by the nonlinear interaction of gravity-capillary waves in a two-layer model of a shear flow. These results are also of interest in analyzing secondary flows in laboratory facilities modeling the ocean and atmospheric processes.     

A study of resonant oscillations in the Split harbour (Adriatic Sea)

The study examines the occurrence of Proudman resonance in front of the Split harbour (Adriatic Sea). The dataset comprises air and sea pressure (sea level) data collected at the harbour entrance during August to October 2000 and is characterized by rather strong synoptic disturbances that took place over the harbour. The analyses encompass empirical tools, such as time-series analysis, high- and band-pass filtering, spectral and wavelet analyses, while the theoretical approach includes the conceptual model of the resonance. Resonance appears in front of the harbour and then propagates inward, covering periods between 7.7 and 28.5 min as a result of complex atmospheric gravity wave structure. Gain between sea level and air pressure equals 0.05–0.40 dbar/hPa (5–40 cm/hPa).     

Numerical evaluation of a subsea equipment installation method designed to avoid resonant responses

Several methods have been employed to install the different types of subsea equipment that are required for offshore oil and gas production systems. More recently, the increasing development of oil fields at remote, ultra-deepwater scenarios has been requiring heavier and more complex subsea equipment. In such scenarios the usual installation methods have been facing increasing challenges, including resonance effects associated to the dynamic behavior of the cable-equipment system. In this context, after presenting a review of the state-of-the-art of installation methods for subsea equipment, this work presents a methodology for the design and evaluation of an installation method based on the combination of steel wire and polyester ropes. The goal is to obtain a feasible and safe installation method that can avoid resonance effects along all phases of the lowering procedure, without the need of specialized devices such as heave compensators, and using only simpler installation vessels such as standard tugboats instead of more expensive and specialized vessels (such as drilling rigs). The method is evaluated by numerical simulations for case studies considering representative metocean data for Brazilian ultra-deepwater scenarios, following a methodology that considers the random characteristic of actual sea states by employing an irregular spectral representation. The results indicate that the method may indeed be feasible for the deepwater installation of heavier equipment, potentially being more cost-effective especially for remote locations where other more complex methods might become inefficient.     

Probabilistic analysis of offshore wind turbines under extreme resonant response: Application of environmental contour method

Offshore wind turbines can exhibit dynamic resonant behavior due to sea states with wave excitation frequencies coinciding with the structural eigenfrequencies. In addition to significant contributions to fatigue actions, dynamic load amplification can govern extreme wind turbine responses. However, current design requirements lack specifications for assessment of resonant loads, particularly during parked or idling conditions where aerodynamic damping contributions are significantly reduced. This study demonstrates a probabilistic approach for assessment of offshore wind turbines under extreme resonant responses during parked situations. Based on in-situ metocean observations on the North Sea, the environmental contour method is used to establish relevant design conditions. A case study on a feasible large monopile design showed that resonant loads can govern the design loads. The presented framework can be applied to assess the reliability of wave-sensitive offshore wind turbine structures for a given site-specific metocean conditions and support structure design.     

Numerical computations of resonant sloshing using the modified isoAdvector method and the buoyancy-modified turbulence closure model

Sloshing is an interfacial-flow phenomenon which brings two challenges on how to locate the position of the interface and avoid the unphysical motion of the interface. In order to locate the the position of the interface, a new geometric Volume-of-Fluid (VOF) method called isoAdvector is adopted to pursue a sharp interface. Aiming to make the isoAdvector method compatible with the dynamic mesh adopted to handle the tank motion, the motion-flux correction is introduced, and a moving-velocity correction for face-interface intersection line (FIIL) is proposed. An approximation formula is adopted to effectively reconstruct the moving-velocity field of the meshes at each cell center based on the motion fluxes on each cell face. In order to avoid the unphysical motion of the interface due to the excessive turbulence level in the transition region at the interface, the buoyancy-modified k − ω SST model is adopted. The numerical results of wave elevations and forces are compared with the experiments. The comparisons suggest that (i) the moving-velocity correction for FIIL is important to update the volume fraction; (ii) the modified isoAdvector method can capture the the position of the interface more accurately than the algebraic VOF method; (iii) the unphysical motion of the interface can be avoided by using the buoyancy-modified k − ω SST model in long-time simulations. In addition, a new post-processing approach is proposed to evaluate the interface thickness. The decrease of interface thickness improves the accuracies of wave elevations by using the modified isoAdvector method. The adoption of both the modified isoAdvector method and the buoyancy-modified k − ω SST model improves the computational accuracies of wave elevations and hydrodynamic loads in long-time simulations.     

The influence of quasi resonant internal waves on the radar imaging mechanism of shallow sea bottom topography

During previous field experiments in the North Sea it was often assumed that the water column in such shallow coastal tidal waters is vertically well mixed and stratification was neglected when discussing the Normalized Radar Cross Section modulation caused by the sea floor. In this paper the influence of quasi resonant internal waves with the sea bed on the radar imaging mechanism of submarine sand waves itself is investigated. In situ data of the tidal current velocity and several water quality parameters such as sea surface temperature, fluorescence, and beam transmittance were measured in the Southern Bight of the North Sea in April 1991. Simulations of the total NRCS modulation caused by sand waves and internal waves as a function of the current gradient or strain rate induced by the internal wave current field at the sea surface have been carried out using the quasi-steady approximation and linear internal wave theory. As a first approximation the strain rate depending on stratification was calculated using the two-layer model. These simulations demonstrate that at least a density difference between the two layers of the order of Δρ ≈ 1 kg m^–3 is necessary for a sinusoidal thermocline to effect the total NRCS modulation considerably. The NRCS modulation as a function of wind friction velocity has been calculated independently and is discussed with regard to the strain rate of the surface current field caused by the superimposed imaging mechanisms of sand waves and internal waves. It turned out that the existence of a surface roughness-wind stress feedback mechanism cannot be excluded.     

Second-order resonant heave,roll and pitch motions of a deep-draft semi-submersible: Theoretical and experimental results

Large volume semi-submersible units may present significant wave induced resonant motions in heave, roll and pitch. Evaluating the slow motions of such systems is important from the initial stages of their designs and therefore requires a model that is both accurate and expedite enough. In the present article, different options for modeling the second-order hydrodynamic forces and induced motions are discussed using as a case-study the PETROBRAS 52 unit—P-52. Computations of the low frequency forces are performed in the frequency domain by means of a commercial Boundary Element Method (BEM) code. Different hydrodynamic approximations are tested and evaluated by directly comparing the predicted responses with those measured in small-scale tests performed in a wave-basin. From the results obtained in theses comparisons, a methodology based on a white-noise approach of the force spectrum is proposed. The validity of such approximation is attributable to the typically low damping levels in heave, roll and pitch motions. Furthermore, results also indicate that the second order forces may be calculated disregarding the free-surface forcing components, an option that helps to reduce the computational burden even more, rendering the procedure suitable for preliminary design calculations.     

Propagating tsunami wave and subsequent resonant response signals detected by HF radar in the Kii Channel,Japan

Signals from the tsunami waves induced by the March 11, 2011 moment magnitude (M_w) 9.0 Tohoku-Oki earthquake and from subsequent resonances were detected as radial velocity variability by a high-frequency ocean surface radar (HF radar) installed on the eastern coast of the Kii Channel, at a range of about 1000 km from the epicenter along the eastern to southern coasts of Honshu Island. A time–distance diagram of band-passed (9–200 min) radial velocity along the beam reveals that the tsunami waves propagated from the continental shelf slope to the inner channel as progressive waves for the first three waves, and then natural oscillations were excited by the waves; and that the direction of the tsunami wave propagation and the axis of the natural oscillations differed from that of the radar beam. In addition, spectral analyses of the radial velocities and sea surface heights obtained in the channel and on the continental shelf slope suggest complex natural oscillation modes excited by the tsunami waves.     

厄尔尼诺/拉尼娜信号循环回路及其传播特性研究

基于1992～2001年卫星高度计资料分析了海面高度距平在厄尔尼诺/拉尼娜(El Niño/La Niña)现象中的演变过程,发现:(1)在El Niño过程中,海面高度正距平信号从西太平洋沿赤道海域向东传播至东海岸,然后分成南北两支,北支在10°N附近从东太平洋传回西太平洋的信号最强,到达西太沿岸海域再传回赤道,表明El Niño信号传播在北半球存在一明显循环回路.赤道以南循环圈不及赤道以北环路清晰.东太平洋的季节变化信号主要通过6°N,10°N和8°S附近的3个通道向西太平洋传播.La Niña信号主要从5°N和7°S向西传播;(2)在大洋海盆尺度快速传播信号背景下,存在波长700～800km的慢速传播信号,两类信号将信息在太平洋内传送.传播速度分析表明,慢速传播信号的相速与Rossby波相速相符,而快速传播信号应该是海洋对大气变异的响应.     

政府在我国海洋能产业发展中的角色定位

海洋能产业作为一项战略性新兴产业,其发展仍受到很多因素的制约,目前我国海洋能产业总体上仍处于发展初期,需要政府的积极引导和大力扶持。文章结合我国海洋能产业发展的现状,针对海洋能产业发展中存在的问题,明确了政府在我国海洋能产业发展中的角色地位,即战略规划的设计者、产业发展的激励者、市场环境的营造者、技术创新的推进者和生态环境的监管者。政府要扮演好自己在海洋能发展中的角色,真正促进我国海洋能产业的可持续发展。     

On the identification of ship coupled heave–pitch motions using neural networks

This paper outlines a procedure for the derivation of the differential equations describing the free response of a heaving and pitching ship from its stationary response to random waves. The coupled heave–pitch motion of a ship in random seas is modelled as a multi-dimensional Markov process. The partial differential equation describing the transition probability density function, known as the Fokker-Planck equation, for this process is derived. The Fokker-Planck equation is used to derive the random decrement equations for the coupled heave–pitch motion. The parameters in these equations are then identified using a neural network approach. The method is validated using numerical simulations and experimental results. The experimental data was obtained using an icebreaker ship model heaving and pitching in random waves. It is shown that the method produces good results when the system is lightly damped. An extension for using this method to identify couple heave–pitch motion in realistic seas is suggested.