A nonlinear model of parametric rolling stabilization by anti-roll tanks

The present paper describes a mathematical model in which the fluid motion inside a U-tank is nonlinearly coupled to the heave, roll and pitch motions of the ship. The main purpose of the investigation is centred on the control of roll motion in the case of parametric resonance in longitudinal waves. A transom stern small vessel, known to be quite prone to parametric amplification, is employed in the study. Four tank designs are employed in order to study the influence of tank mass, tank natural frequency and tank internal damping on the control of parametric rolling at different head seas conditions. Additionally, the influence of the vertical position of the tank is also investigated. The main results are presented in the form of limits of stability, with encounter frequency and wave amplitudes as parameters. Distinct dynamical characteristics are discussed and conclusions are drawn on the relevant parameters for the efficient control of the roll amplifications in head seas.     

Design of passive anti-roll tanks for roll stabilization in the nonlinear range

The best way of reducing roll motion is by increasing roll damping. Bilge keels are the most common devices for increasing roll damping. If more control is required, anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. Our objective is to develop design procedures for passive tanks for roll reduction in rough seas. This paper focuses on the design of passive U-tube tanks. The tank-liquid equation of motion is integrated simultaneously with the six-degree-of-freedom (6DOF) equations of the ship motion. The coupled set of equations is solved by using the Large Amplitude Motion Program ‘LAMP’, which is a three-dimensional time-domain simulation of the motion of ships in waves. The unstabilized and stabilized roll motions of a S60-70 ship with forward speed and beam waves have been analyzed. For high-amplitude waves, the unstabilized roll angle exhibits typical nonlinear phenomena: a shift in the resonance frequency, multi-valued responses, and jumps. The performance of a S60-70 ship with a passive tank is investigated in various sea states with different encounter wave directions. It is found that passive anti-roll tanks tuned in the linear or nonlinear ranges are very effective in reducing the roll motion in the nonlinear range. The effect of the tank damping, frequency, and mass on the tank performance is studied. Also, it is found that passive anti-roll tanks are very effective in reducing the roll motion for ships having a pitch frequency that is nearly twice the roll frequency in sea states 5 and 6.     

Roll stabilization by anti-roll passive tanks

Since the most severe roll motion occurs at resonance (known as synchronous rolling), the best way of reducing it is to increase the damping. The most common means of doing so is by the installation of bilge keels. If more control is required, both anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. The use of tanks with liquid free surfaces for reducing roll motion of ships is an old idea. Many researchers have studied the design of anti-roll tanks. However, most of the past effort has concentrated on studying the performance of anti-roll tanks in damping the roll motion of the ship. Little attention has been paid to the fluid motion inside the tank itself. Another important issue is the tank tuning. Proper tuning of the anti-roll tank, to match the ship's natural frequency, is very important in reducing the roll motion. This paper concentrates on the most familiar type, which is the U-tube passive tank as a mechanical absorber of roll motion. A detailed study, covering tank damping, mass, location relative to the ship CG, and tuning, is presented. New suggestions and observations are stated concerning tank damping and tuning.     

On the development of ship anti-roll tanks

This paper reviews the development of ship anti-roll tanks from the 1880s to the present day including their modelling and control strategies. Mention is also made of other ship roll stabilization systems and the application of the technology to stabilization of other structures. The potential for the use of roll stabilization tanks on modern, high speed multi-hull craft which also have a low speed operational requirement is also discussed.     

Control of ship roll using passive and active anti-roll tanks

We numerically studied the full (six degrees of freedom) motion of a cargo ship without roll stabilizers in rough (sea state 5) conditions for multiple heading angles ranging from 0° (follower seas) to 180° (head seas). We found that the ship exhibits excessive roll motion in quartering (45° off the stern), beam, and head seas. Therefore, roll damping is critical in these conditions. We then investigated the performance of passive and active anti-roll tank (ART) systems and compared their performance in each of the three sea conditions. Each ART consists of three identical tanks, distributed along the centerline of the ship, each of which consists of two vertical ducts connected at the bottom with a horizontal duct. A pump is located at the middle of the horizontal duct of each tank. The pumps are switched on for active ARTs but switched off for passive ones. The loads (forces and moments) exerted on the ship by the ARTs are added to the hydrodynamic loads (e.g., due to pressure and viscous effects) and the thrust in the governing equations of motion of the ship. Whereas both passive and active ARTs are able to reduce the excessive roll motion, active ARTs outperform the passive ones from three perspectives. First, they are more effective in reducing the roll motion. Second, they require much less working liquid. Third, their performance is insensitive to their natural frequencies and, hence, to their geometric design. In addition, we found that head seas are most responsive to ARTs, which suggests that they are effective in mitigating parametric roll.     

Estuarine salt conservation: a Lagrangian approach

Understanding tidal and mean flow transport mechanisms that maintain the estuarine salt balance against seaward transport by river flow is one of the fundamental questions of estuarine oceanography. Previous salt transport studies have failed to resolve this problem for two principal methodological reasons, in addition to the inherent variability of estuaries. First, salt transport expansions used to represent the salt balance have included a large number of terms that could not be related to any theory of estuarine circulation and whose physical meaning was thus unclear. Second, it has proven difficult to measure small mean velocities in the presence of much larger tidal variations. A new analysis method that expresses Lagrangian scalar property transport in terms of time and space variations of Eulerian variables is much simpler than expansions previously used and yields new insights into estuarine transport processes. This approach (like previous expansions) is valid for narrow systems in which cross-channel transport processes are weak and the ratio of tidal amplitude to mean depth is small. A surface boundary condition is used to eliminate one class of troublesome terms. The equivalence of the tidal-cycle average transport of tidal variations in salinity and the Stokes transport of mean salinity is then employed to show that the vertically integrated tidal flow plays no role in the overall salt balance. That is, seaward transport of salt caused by the river flow can only be balanced by landward transport resulting from correlations between shear and stratification in the mean, tidal and overtide flows. In a hypothetical inviscid estuary, tide and overtide flows would be vertically uniform, and outward fluvial salt transport could only be balanced by shear and stratification in the mean gravitational circulation. In a more realistic example with strong friction, the gravitational circulation would be severely damped, and inward transport could only be accomplished by correlations of shear and stratification in the tide and overtide flows.     

Interactions of nonlinear gravity waves and uniform current in Lagrangian system

The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an EulerLagrange transformation. The thirdorder asymptotic solution is a periodic bounded function of Lagrangian labels and time, which imply that the entire solution is uniformlyvalid. The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form. The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian. The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.     

An ecosystem modeling approach to predicting cod recruitment

The Norwegian Ecological Model (NORWECOM) biophysical model system implemented with the ROMS ocean circulation model has been run to simulate conditions over the last 25 years for the North Atlantic. Modeled time series of water volume fluxes, primary production, and drift of cod larvae through their modeled ambient temperature fields have been analyzed in conjunction with VPA estimated time series of 3-year-old cod recruits in the Barents Sea. Individual time series account for less than 50% of the recruitment variability; however, a combination of simulated flow of Atlantic water into the Barents Sea and local primary production accounts for 70% of the variability with a 3-year lead. The associated regression predicts increased recruitment between 2007 and 2008 from about 450–700 million individuals with a standard error of nearly 150 million.     

非线性波传播的新型数值模拟模型及其实验验证

以一种新型的Boussinesq型方程为控制方程组,采用五阶Runge-Kutta-England格式离散时间积分,采用七点差分格式离散空间导数,并通过采用恰当的出流边界条件,从而建立了非线性波传播的新型数值模拟模型.通过对均匀水深水域内波浪传播的数值模拟说明,模型能较好地模拟大水深水域和强非线性波的传播.通过设置不同的入射波参数来进行潜堤地形上波浪传播的物理模型实验,并将数值解与物理模型实验结果进行了比较.     

Feature modeling approach to simulating Loop Current Frontal Eddies

Loop Current Frontal Eddies (LCFE) in the Gulf of Mexico are simulated with a regional configuration of the Princeton Ocean Model using a feature-oriented initialization technique. The initialization procedure is based on a prior investigation of stability characteristics of the Loop Current (LC). Zonal channel experiments conducted with a multi-layer intermediate equations model allowed to identify conditions necessary for formation and growth of frontal eddies. The simulations were able to reproduce key features of LCFE-topography interaction in the DeSoto Canyon region observed during the “Eddy Intrusion” study.     

Estuary/ocean exchange and tidal mixing in a Gulf of Maine Estuary: A Lagrangian modeling study

A Lagrangian particle method embedded within a 2-D finite element code, is used to study the transport and ocean–estuary exchange processes in the well-mixed Great Bay Estuarine System in New Hampshire, USA. The 2-D finite element model, driven by residual, semi-diurnal and diurnal tidal constituents, includes the effects of wetting and drying of estuarine mud flats through the use of a porous medium transport module. The particle method includes tidal advection, plus a random walk model in the horizontal that simulates sub-grid scale turbulent transport processes. Our approach involves instantaneous, massive [O(500,000)] particle releases that enable the quantification of ocean–estuary and inter-bay exchanges in a Markovian framework. The effects of the release time, spring–neap cycle, riverine discharge and diffusion strength on the intra-estuary and estuary–ocean exchange are also investigated.The results show a rather dynamic interaction between the ocean and the estuary with a fraction of the exiting particles being caught up in the Gulf of Maine Coastal Current and swept away. Three somewhat different estimates of estuarine residence time are calculated to provide complementary views of estuary flushing. Maps of residence time versus release location uncover a strong spatial dependency of residence time within the estuary that has very important ramifications for local water quality. Simulations with and without the turbulent random walk show that the combined effect of advective shear and turbulent diffusion is very effective at spreading particles throughout the estuary relatively quickly, even at low (1 m²/s) diffusivity. The results presented here show that a first-order Markov Chain approach has applicability and a high potential for improving our understanding of the mixing processes in estuaries.     

Numerical modeling of nonlinear elastic components of mooring systems

This paper deals with the finite-element analysis of compliant structures containing nonlinear elastic components and subjected to loading by waves and currents. An efficient procedure to model such components is developed and implemented in a computer program. It can be applied to analyze nonlinear elastic ropes, rubber tethers, risers, and hoses. The elastic modulus is assumed to depend on the amount of strain in a component. The Newton-Raphson iteration scheme is modified to account for the change of elastic properties on each step of time integration procedure. The approach is applied to develop feed buoy mooring systems for the University of New Hampshire Open Ocean Aquaculture site. The complex nonlinear and viscoelastic load-elongation behavior of suitable high stretch mooring elements for this application is modeled to obtain realistic numerical predictions at sea conditions. Various designs and environmental loading scenarios are considered. Numerical simulations provide predictions of the overall dynamics of the system and maximum values of tensions in critical components.     

Use of genetic algorithm in new approach to modeling of flood routing

The hydrological models and simpli?ed methods of Saint-venant equations are used extensively in hydrological modeling, in particular for the simulation of the ?ood routing. These models require speci?c and extensive data that usually makes the study of ?ood propagation an arduous practice. We present in this work a new model, based on a transfer function, this function is a function of parametric probability density, having a physical meaning with respect to the propagation of a hydrological signal. The inversion of the model is carried out by an optimization technique called Genetic Algorithm. It consists of evolving a population of parameters based primarily on genetic recombination operators and natural selection to?nd the minimum of an objective function that measures the distance between observed and simulated data. The precision of the simulations of the proposed model is compared with the response of the Hayami model and the applicability of the model is tested on a real case, the N'Fis basin river, located in the High Atlas Occidental, which presents elements that appear favorable to the study of the propagation. The results obtained are very satisfactory and the simulation of the proposed model is very close to the response of the Hayami model.     

极值波高建模中不确定性的模糊量化方法

A non-traditional fuzzy quantification method is presented in the modeling of an extreme significant wave height. First, a set of parametric models are selected to fit time series data for the significant wave height and the extrapolation for extremes are obtained based on high quantile estimations. The quality of these results is compared and discussed. Then, the proposed fuzzy model, which combines Poisson process and generalized Pareto distribution(GPD) model, is applied to characterizing the wave extremes in the time series data. The estimations for a long-term return value are considered as time-varying as a threshold is regarded as non-stationary. The estimated intervals coupled with the fuzzy theory are then introduced to construct the probability bounds for the return values. This nontraditional model is analyzed in comparison with the traditional model in the degree of conservatism for the long-term estimate. The impact on the fuzzy bounds of extreme estimations from the non stationary effect in the proposed model is also investigated.     

非线性波传播的新型数值模拟模型及其实验验证引入变换速度变量

以一种新型的含变换速度变量的Boussinesq型方程为控制方程组,采用五阶Runge-Kutta-England格式离散时间积分,采用七点差分格式离散空间导数,并采用恰当的出流边界条件,从而建立了非线性波传播的新型数值模拟模型.对均匀水深水域内波浪传播的数值模拟,说明在引入变换速度后进一步增大了模型的水深适用范围.对潜堤地形上波浪传播的数值模拟说明,在引入变换速度后进一步提高了模型的数值模拟精度.     

Numerical modeling of nonlinear water waves over heterogeneous porous beds

The transformation of nonlinear water waves over porous beds is studied by applying a numerical model based on Chen's [2006. Fully nonlinear Boussinesq-type equations for waves and currents over porous beds. Journal of Engineering Mechanics, 132:2, 220–230] Boussinesq-type equations for highly nonlinear waves on permeable beds. The numerical model uses a high-order time-marching solution and fourth-order finite-difference schemes for discretization of first-order spatial derivatives to obtain a computational accuracy consistent with the model equations. By forcing the wave celerity and spatial porous-damping rate of the linearized model to match the exact linear theory for horizontal porous bed over a prescribed range of relative depths, the values of the model parameters are optimally determined. Numerical simulations of the damped wave propagation over finite-thickness porous layer demonstrate the accuracy of both the numerical model and governing equations, which have been shown by prior theoretical analyses to be accurate for both nominal and thick porous layers. These simulations also elucidate on the significance of the higher-order porous-damping terms and the influence of the hydraulic parameters. Application of the model to the simulation of the wave field around a laboratory-scale submerged porous mound provides a measure of its capability, as well as useful insight into the scaling of the porous-resistance coefficients. For application to heterogeneous porous beds, the assumption of weak spatial variation of the porous resistance is examined using truncated forms of the governing equations. The results indicate that the complete set of Boussinesq-type equations is applicable to porous beds of nonhomogeneous makeup.     

Stochastic inverse modeling of nonlinear roll damping moment of a ship

This work presents an application of stochastic inverse method for the determination of nonlinear roll damping moment of a ship at zero forward speed. Nonlinear roll damping moment was estimated from the measured dynamic responses through stochastic inverse model. It is shown that this method enables nonlinear characteristic of the roll damping to be estimated without any assumption on its form of nonlinearity, including its confidence intervals given noisy data. The accuracy and practicability were assessed with laboratory tests related to both free-decay and forced rolling motions. The estimation results of the nonlinear damping moment show good agreement in all cases.     

Inverse modeling of discrete interaction approximations for nonlinear interactions in wind waves

In the last two decades, the Discrete Interaction Approximation (DIA) has been the only economically feasible parameterization for nonlinear wave–wave interactions in operational wind wave models. Its major drawback is its limited accuracy. Several improvements to the DIA have been suggested recently. The present study summarizes these improvements and suggests some new modifications to the DIA. Using inverse modeling techniques, where the potential of various DIAs is assessed by optimal fitting to exact solutions, a comprehensive comparison of the potential of several such improvements is made. An in depth analysis of the behavior of DIAs in full wave models will be the subject of a second study, to be reported elsewhere. The major findings of this study are that: (i) An expanded definition of the representative quadruplet with additional degrees of freedom is necessary for an accurate representation of the exact interactions; (ii) Slowly varying the free parameters in such a DIA as a function of the spectral frequency f results in a (mostly qualitative) improvement; (iii) A DIA with expanded quadruplet definition and with four representative quadruplets is found to reproduce the exact source term accurately; (iv) Adding additional tunable constants to the equation for the strength of the interactions has little impact on the quality of the DIA.     

Formation Control of Marine Surface Craft: A Lagrangian Approach

This paper presents a method for formation control of marine surface craft inspired by Lagrangian mechanics. The desired formation configuration and response of the marine surface craft are given as a set of constraint functions. The functions are treated according to constraints in analytical mechanics. Thus, constraint forces arise and feedback from the constraint functions keeps the formation assembled. Since the constraint functions are designed for a desired effect, the forces can be interpreted as control laws. Examples of constraint functions that maintain a formation are presented. Furthermore, the same approach has been applied with no major modification to position control purposes for a single vessel. An extension to underactuated vessels is given. Simulations with nonlinear models of tugboats illustrate the proposed method versatility and its robustness with respect to environmental disturbances and time delays     

A Lagrangian model for wind- and wave-induced near-surface currents

A theory is outlined for time-dependent currents induced near the sea surface in deep water, away from coastal boundaries, by a variable wind stress and deep-water wave field. It is based on the theory of Weber (1983) which uses a second-order perturbation expansion of the Navier-Stokes equations in Lagrangian coordinates and includes the Coriolis effect. It uses an eddy viscosity formulation for both wave dissipation and momentum transfer within the current field: the eddy viscosity ν may be allowed to vary with depth. The wind stress may be time-varying and the wave field may vary in both space and time.For the case of a constant ν, the results agree with those of Ursell (1950), Hasselmann (1970) and Pollard (1970) in the limit ν→0, and the steady-state results agree with those of Weber. For a particular case of depth-varying ν, results (obtained from numerical simulations) are in better general agreement with observations of wind-induced surface drift than when a constant ν is used.An outline is given of the application of the theory to the case of a random sea state. There are good prospects for using output data from numerical wave prediction models to drive the equations of this near-surface current model.