A nonlinear wave profile correction of the diffraction of a wave by a long breakwater: Fixed point approach

The authors of the present paper have suggested an iterative scheme to calculate the nonlinear wave profiles [Jang and Kwon, 2005. Application of nonlinear iteration scheme to the nonlinear water wave problem: Stokes wave. Ocean Engineering 32, 1862–1872]. The scheme was shown to be good for estimating nonlinear wave profiles. In the study, the iterative scheme is applied to the wave-diffraction problem by a long breakwater to calculate a diffracted wave by the breakwater. The iterative solution of diffraction was compared with the linear solution of Sommerfeld, 1896. [Mathematische Theoried der Diffraction. Mathematical Annals 47, 317–374]. For a small wave slope, the two solutions were in good agreement. However, the scheme enabled us to observe the nonlinear behaviors of a beating phenomenon and of wave profile such as Stokes’ wave for a relatively large wave slope: as the wave slope becomes larger, we can examine the nonlinear wave characteristics of the actual shapes of waves, i.e., the crests are steeper and the troughs are flatter.     

Fast spin up of Ocean biogeochemical models using matrix-free Newton–Krylov

A novel computational approach is introduced for the efficient computation of equilibrium solutions of seasonally forced ocean biogeochemical models. The essential idea is to formulate the problem as a large system of nonlinear algebraic equations to be solved with a class of methods known as matrix-free Newton–Krylov (MFNK). MFNK is a combination of Newton-type methods for superlinearly convergent solution of nonlinear equations, and Krylov subspace methods for solving the Newton correction equations. The basic link between the two methods is the Jacobian-vector product, which may be probed approximately without forming and storing the elements of the true Jacobian. To render this approach practical for global models with O(10⁶) degrees of freedom, a flexible preconditioning strategy is developed. The result is an essentially “black-box” numerical scheme than can be applied to most existing biogeochemical models. The method is illustrated by applying it to find the equilibrium solutions of two realistic biogeochemical problems. Compared with the conventional approach of direct time integration, the preconditioned-MFNK scheme is shown to be roughly two orders of magnitude more efficient. Several potential refinements of the basic algorithm that may yield further performance gains are discussed. The numerical scheme described here addresses a fundamental challenge to using ocean biogeochemical models more effectively.     

Modeling hurricane waves and storm surge using integrally-coupled,scalable computations

The unstructured-mesh SWAN spectral wave model and the ADCIRC shallow-water circulation model have been integrated into a tightly-coupled SWAN + ADCIRC model. The model components are applied to an identical, unstructured mesh; share parallel computing infrastructure; and run sequentially in time. Wind speeds, water levels, currents and radiation stress gradients are vertex-based, and therefore can be passed through memory or cache to each model component. Parallel simulations based on domain decomposition utilize identical sub-meshes, and the communication is highly localized. Inter-model communication is intra-core, while intra-model communication is inter-core but is local and efficient because it is solely on adjacent sub-mesh edges. The resulting integrated SWAN + ADCIRC system is highly scalable and allows for localized increases in resolution without the complexity or cost of nested meshes or global interpolation between heterogeneous meshes. Hurricane waves and storm surge are validated for Hurricanes Katrina and Rita, demonstrating the importance of inclusion of the wave-circulation interactions, and efficient performance is demonstrated to 3062 computational cores.     

一类海洋遥感反演问题的迭代格式

对于海洋遥感反演中常见的一类非线性反演问题,构造迭代格式进行近似求解。通过给出适当的条件,对格式产生迭代解的收敛性进行证明,并给出迭代的终止原则和步骤。结果表明格式产生的迭代解在适当的光滑性条件下,收敛于原问题的精确解,并且迭代格式在终止原则下是一种正则化的方法。     

On an improvement of a nonlinear iterative scheme for nonlinear wave profile prediction

The authors of the present paper present an iterative scheme to calculate the nonlinear wave profiles [Jang, T.S., Kwon, S.H., 2005. Application of nonlinear iteration scheme to the nonlinear water wave problem: Stokian wave. Ocean Engineering, in press]. The nonlinear operator was constructed from the dynamic boundary condition of the free surface. The initial input of the iterative process was linear potential. The linear dispersion relation was utilized. The authors of the present paper suggest an improved scheme in terms of accuracy and speed of convergence by utilizing the nonlinear dispersion relation. The existence and uniqueness of the improved scheme are illustrated in this paper. The calculation results together with Fast Fourier transform revealed that the improved scheme made it possible to predict higher-order nonlinear characteristics of the Stokes’ wave.     

Reversed responses within a segmented detached breakwater, the Tuscany coast Italy—a case study

A multiple detached breakwater system was designed to protect an extended length of shoreline in front of the presidential villa located in the Gombo region, Tuscany, Italy. The purpose of this empirical field study was to examine the impact of the surface-piercing segmented breakwater on the subaqueous morphology and to follow the effect of the breakwaters on the beach.Shoreline mapping was performed on rectified, stereo-plotted air photos and was also based on topographic field surveying. Bathymetric mapping was based on interpolation of profile lines extending to 10 m water depth.Building the breakwaters in a downstream order caused the trapping of the longshore-driven sediments mainly at the southernmost breakwaters that faced the longshore sediment supply. The longshore down-current direction controlled the hierarchy of the beach response. Two relatively coherent behavioral domains were found to exist: (1) the “permanent tombolo stage” of segments 1–3 and (2) the “no sinuosity” response of the beach opposite the northern segment no. 5. The segment no.4, in-between, did not exhibit a coherent behaviour, indicating a drastic reversal in the sedimentary regime.The three southernmost tombolos facing the longshore current became the main sediment trap, causing a lee-side erosional effect to emerge within the protection scheme of the segmented detached breakwaters. The oblique incident waves enter through the gaps and maintain in the inshore the depleted longshore drift, causing the shoreline configuration in the lee of the northern breakwaters to develop into a prograding log-spiral bay.     

Total (practical) stability of ships

In this paper the “total (practical) stability” concept is introduced to nonlinear forced rolling motion of a ship. This is achieved by employing “boundedness” and “Lyapunov's function” approach. In this respect two new theorems are proved and conditions and domain of Practical Stability are evaluated. The Paper also contains a critical review of the present status of international intact ship stability regulations. A qualitative discussion of oscillatory rolling motion and the capsizing phenomena is presented.     

The discrete methods for free vibration analyses of an immersed beam carrying an eccentric tip mass with rotary inertia

In this paper, a beam without contact with water is called the “dry” beam and the one in contact with water is called the “wet” beam. For a partially (or completely) immersed uniform beam carrying an eccentric tip mass possessing rotary inertia, the conventional analytical (closed-form) solution is achieved by considering the inertial forces and moments of the tip mass and rotary inertia as the boundary conditions at the tip end of the beam. However, it has been found that the approximate solution for the last problem may be achieved by two techniques: Method 1 and Method 2. In Method 1, the basic concept is the same as the conventional analytical method; but in Method 2, the tip end of the beam is considered as a free end, while the inertial forces and moments induced by the tip mass and rotary inertia are considered as the external loads applied at the tip end of the beam. The main differences between the formulation of Method 1 and that of Method 2 are: In Method 1, the “normal” shapes of the “dry” beam are functions of the frequency-dependent boundary conditions but the external loads at the tip end are equal to zero; On the contrary, in Method 2, the “normal” mode shapes of the “dry” beam are determined based on the zero boundary conditions at the tip end of the beam but the external loads at the tip end due to the inertial effects of the tip mass and rotary inertia must be taken into consideration for the free vibration analysis of the “wet” beam. Numerical results reveal that the approximate solution obtained from Method 2 are very close to that from Method 1 if the tip mass moment of inertia is negligible. Besides, the two approximate solutions are also very close to the associated analytical (closed-form) solution or the finite element solution. In general, it is hoped that there exist several methods for tackling the same problem so that one may have more choices to incorporate with the specified cases. It is believed that the two approximate methods presented in this paper will be significant from this point of view.     

The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: A comparison study using a nonlinear reduced gravity ocean model

This paper compares contending advanced data assimilation algorithms using the same dynamical model and measurements. Assimilation experiments use the ensemble Kalman filter (EnKF), the ensemble Kalman smoother (EnKS) and the representer method involving a nonlinear model and synthetic measurements of a mesoscale eddy. Twin model experiments provide the “truth” and assimilated state. The difference between truth and assimilation state is a mispositioning of an eddy in the initial state affected by a temporal shift. The systems are constructed to represent the dynamics, error covariances and data density as similarly as possible, though because of the differing assumptions in the system derivations subtle differences do occur. The results reflect some of these differences in the tangent linear assumption made in the representer adjoint and the temporal covariance of the EnKF, which does not correct initial condition errors. These differences are assessed through the accuracy of each method as a function of measurement density. Results indicate that these methods are comparably accurate for sufficiently dense measurement networks; and each is able to correct the position of a purposefully misplaced mesoscale eddy. As measurement density is decreased, the EnKS and the representer method retain accuracy longer than the EnKF. While the representer method is more accurate than the sequential methods within the time period covered by the observations (particularly during the first part of the assimilation time), the representer method is less accurate during later times and during the forecast time period for sparse networks as the tangent linear assumption becomes less accurate. Furthermore, the representer method proves to be significantly more costly (2–4 times) than the EnKS and EnKF even with only a few outer iterations of the iterated indirect representer method.     

Efficient higher-order finite-difference schemes for parabolic models

Implicit finite-difference schemes for use in parabolic equation models are developed. Like the familiar Crank-Nicolson scheme, which has hitherto been used almost exclusively for the solution of these equations, these schemes are unconditionally stable and use a computational molecule of only six points on two “time” levels. However, they are accurate to a higher order than the Crank-Nicolson scheme, thus allowing the solution grid to be coarser and the solution time to be (approximately) halved. Examples of computations on constant depth are shown, in which significant reductions in time and grid-point density are achieved, for two different parabolic models. The schemes are then extended to refraction and diffraction, and are shown to have a similar effect in this more general case too. It is recommended that finite-difference schemes based on these higher-order (or Hermitian) methods replace the more commonly used Crank-Nicolson scheme in all physical domain parabolic equation models, but especially in minimax (wide-angle) equation models.     

A flexible-segment-model-based dynamics calculation method for free hanging marine risers in re-entry

In re-entry,the drilling riser hanging to the holding vessel takes on a free hanging state,waiting to be moved from the initial random position to the wellhead.For the re-entry,dynamics calculation is often done to predict the riser motion or evaluate the structural safety.A dynamics calculation method based on Flexible Segment Model(FSM) is proposed for free hanging marine risers.In FSM,a riser is discretized into a series of flexible segments.For each flexible segment,its deflection feature and external forces are analyzed independently.For the whole riser,the nonlinear governing equations are listed according to the moment equilibrium at nodes.For the solution of the nonlinear equations,a linearization iteration scheme is provided in the paper.Owing to its flexibility,each segment can match a long part of the riser body,which enables that good results can be obtained even with a small number of segments.Moreover,the linearization iteration scheme can avoid widely used Newton-Rapson iteration scheme in which the calculation stability is influenced by the initial points.The FSM-based dynamics calculation is timesaving and stable,so suitable for the shape prediction or real-time control of free hanging marine risers.     

An efficient algorithm for strapdown accelerometer-based motion measurement

The paper is concerned with the measurement of motion of free floating bodies using accelerometers strapped to a cross-arm mounted on the body. The measurement system has been studied with the help of a formulation involving a set of coupled nonlinear initial-value equations involving the angular acceleration components. A PC-based software using the Bulirsch-Stoer technique has been developed to solve the initial-value problem so as to deduce the body motions from the measured accelerations. Suitable filtering strategy has been employed at every stage of numerical integration. The reliability of the strapdown accelerometer system together with software developed has been validated using a “dry” test. Typical motion measurements have been done in all the six degrees of freedom of a tug model in a wave flume. The method is deemed to be an efficient and cost-effective technique suitable for free floating bodies and for large motions.     

Static and dynamic aspects of a capsize phenomenon

Capsizing of ships constitutes a primary group of casualties that leads to loss of life and money. Unfortunately, its mechanism has yet to be fully resolved due to underlying complex dynamics and parameters. Upon studying the causes in more detail, designing safer ships against capsizing may become a reality. In the present study, a relatively different approach called “reserve of stability” or “stability margins” which utilizes both statical and nonlinear dynamical aspects of stability is employed to analyze ship hydrodynamics. For this purpose a nonlinear roll model in beam waves has been implemented. In order to apply the theory, a capsized vessel is chosen to be analyzed in terms of stability. The necessary data about the vessel at the time of capsizing were collected from the published work found in the naval architecture literature. Suggestions are made based on the results of the analysis to improve ship stability qualities in a seaway.     

基于非结构网格的波流耦合数值模式研究

本文采用ADCIRC模型和SWAN模型, 建立了一个基于非结构化网格的波流耦合数值模式, 风浪计算和潮汐风暴潮计算均采用同一套三角网格, 对复杂岸线和建筑物布置均有较好的描述, 且避免了模型插值, 提高了计算效率和精度。利用该模型对渤海湾西南海域几次强风过程中的风浪和潮汐风暴潮进行了研究, 通过实测资料对该模型进行了验证, 结果表明该模式具有较高的精度, 能较好地描述风浪、潮汐风暴潮的传播演变及其相互作用, 可应用于风浪与潮汐风暴潮的模拟计算。     

Propulsion of single-screw ships

On the basis of the little clause in the “Outline Specification” for a new ship: “Trial speed at a load draught of … with the engine at maximum continuous rating has to be …” some aspects regarding propulsion of single-screw ships are discussed, especially the problem of how to combine the hull form, the propeller and the machinery for propulsion in such a way that an optimal solution is obtained.In order to limit the problem, only ships provided with a single conventional propeller for propulsion are considered.A parameter study of a single-screw vessel has been done in order to get some concrete information on the interaction between ship, engine and propeller, and to investigate how the ship propeller power curve should be placed in relation to the engine operation area and to investigate changes in this relationship when the conditions change.     

The marine ecosystem off Peru: What are the secrets of its fishery productivity and what might its future hold?

The marine ecosystem located off the coast of central and northern Peru has stood as the “world’s champion” producer, by far, of exploitable fish biomass, generally yielding more than 20 times the tonnage of fishery landings produced by other comparable regional large marine ecosystems of the world’s oceans that operate under similar dynamic contexts and are characterized by comparable, or even greater, basic primary production. Two potentially contributing aspects are discussed from a framework of interregional comparative pattern recognition: (1) the advantageous low-latitude situation that combines strong upwelling-based nutrient enrichment with low wind-induced turbulence generation and relatively extended mean “residence times” within the favorable upwelling-conditioned near-coastal habitat and (2) the cyclic “re-setting” of the system by ENSO perturbations that may tend to interrupt malignant growth of adverse self-amplifying feedback loops within the nonlinear biological dynamics of the ecosystem.There is a developing scientific consensus that one of the more probable consequences of impending global climate changes will be a general slowing of the equatorial Pacific Walker Circulation and a consequent weakening of the Pacific trade wind system. Since the upwelling-favorable winds off Peru tend to flow directly into the Pacific southeast trade winds, a question arises as to the likely effect on the upwelling-producing winds that power the productivity of the regional coastal ecosystems of the Peru–Humboldt Current zone. It is argued that the effects will in fact be decoupled to the extent that upwelling-favorable winds will actually tend to increase off Peru. Data demonstrative of this decoupling are presented. A tendency for less intense El Niño episodes in the future is also suggested. These conclusions provide a framework for posing certain imponderables as to the future character of the Peruvian marine ecosystem and of the fisheries it supports.     

Wave propagation in a fully nonlinear numerical wave tank: A desingularized method

The problem of wave propagation in a fully nonlinear numerical wave tank is studied using desingularized boundary integral equation method coupled with mixed Eulerian–Lagrangian formulation. The present method is employed to solve the potential flow boundary value problem at each time step. The fourth-order predictor–corrector Adams–Bashforth–Moulton scheme is used for the time-stepping integration of the free surface boundary conditions. A damping layer near the end-wall of wave tank is added to absorb the outgoing waves with as little wave reflection back into the wave tank as possible. The saw-tooth instability is overcome via a five-point Chebyshev smoothing scheme. The model is applied to several wave propagations including solitary, irregular and random incident waves.     

Diffusion reduction in an arbitrary scale third generation wind wave model

The numerical schemes for the geographic propagation of random, short-crested, wind-generated waves in third-generation wave models are either unconditionally stable or only conditionally stable. Having an unconditionally stable scheme gives greater freedom in choosing the time step (for given space steps). The third-generation wave model SWAN (“Simulated WAves Nearshore”, Booij et al., 1999) has been implemented with this type of scheme. This model uses a first order, upwind, implicit numerical scheme for geographic propagation. The scheme can be employed for both stationary (typically small scale) and nonstationary (i.e. time-stepping) computations. Though robust, this first order scheme is very diffusive. This degrades the accuracy of the model in a number of situations, including most model applications at larger scales. The authors reduce the diffusiveness of the model by replacing the existing numerical scheme with two alternative higher order schemes, a scheme that is intended for stationary, small-scale computations, and a scheme that is most appropriate for nonstationary computations. Examples representative of both large-scale and small-scale applications are presented. The alternative schemes are shown to be much less diffusive than the original scheme while retaining the implicit character of the particular SWAN set-up. The additional computational burden of the stationary alternative scheme is negligible, and the expense of the nonstationary alternative scheme is comparable to those used by other third generation wave models. To further accommodate large-scale applications of SWAN, the model is reformulated in terms of spherical coordinates rather than the original Cartesian coordinates. Thus the modified model can calculate wave energy propagation accurately and efficiently at any scale varying from laboratory dimensions (spatial scale O(10 m) with resolution O(0.1 m)), to near-shore coastal dimension (spatial scale O(10 km) with resolution O(100 m)) to oceanic dimensions (spatial scale O(10 000 km) with resolution O(100 km).     

Adaptive output feedback control based on DRFNN for AUV

The tracking control problem of AUV in six degrees-of-freedom (DOF) is addressed in this paper. In general, the velocities of the vehicles are very difficult to be accurately measured, which causes full state feedback scheme to be not feasible. Hence, an adaptive output feedback controller based on dynamic recurrent fuzzy neural network (DRFNN) is proposed, in which the location information is only needed for controller design. The DRFNN is used to online estimate the dynamic uncertain nonlinear mapping. Compared to the conventional neural network, DRFNN can clearly improve the tracking performance of AUV due to its less inputs and stronger memory features. The restricting condition for the estimation of the external disturbances and network's approximation errors, which is often given in the existing literatures, is broken in this paper. The stability analysis is given by Lyapunov theorem. Simulations illustrate the effectiveness of the proposed control scheme.     

Path following control system for a tanker ship model

A two-dimensional path following control system for autonomous marine surface vessels is presented. The guidance system is obtained through a way-point guidance scheme based on line-of-sight projection algorithm and the speed controller is achieved through state feedback linearization. A new approach concerning the calculation of a dynamic line-of-sight vector norm is presented which main idea is to improve the speed of the convergence of the vehicle to the desired path. The results obtained are compared with the traditional line-of-sight scheme. It is intended that the complete system will be tested and implemented in a model of the “Esso Osaka” tanker. The results of simulations are presented here showing the effectiveness of the system aiming in to be robust enough to perform tests either in tanks or lakes.