A study of the angle dependence of roll damping moment

The angle dependence of the roll damping moment is investigated by analysing experimentally obtained free roll decay records. Two ship models were used with and without bilge keels, also results with forward speed were obtained. The analysis indicate strong angle dependence and explains why the quadratic and cubic velocity dependent damping moments are successful in many cases.     

Roll damping characteristics of a small fishing vessel with a central wing

The roll damping characteristics of three models of a 3-ton class fishing vessel representing the bare hull, hull with bilge keels, and hull with bilge keels and a central wing are investigated by the free roll decay tests in calm water and also in uniform head waves in a towing tank. Speed and roll initial angle and OG (distance between the centers of gravity and roll) are varied to check their dependence on roll damping. The experimental results are compared with the numerical results of mathematical modeling by the energy method and the energy dissipation patterns are also compared for these three models. The bilge keel contributes significantly to the increment of the roll damping for zero speed but as speed increases, the lift generated by the central wing contributes significantly to the roll damping increase. In addition, it is shown that the roll damping is more or less influenced by the regular head waves.     

Full scale decay test of a tanker: field data and theoretical analysis

This paper presents results from a full scale decay test made with a tanker in a relatively protected area in the Brazilian coast. In at least two tests the environmental loads (wind, waves and current) were very small and the time history of the surge motion was well behaved, making it possible to check some proposed models for the damping in the hull and mooring lines. Field data seem to confirm that the damping is indeed of the fluid viscosity type and the theoretical models are able to recover roughly 75% of the observed damping, the energy dissipation in the mooring lines being, by far, the major contribution. The remaining 25% are likely due to non modeled effects, such as the environment influence, which although small and not measured certainly exists, and to the friction between the mooring lines and the seabed.     

Full scale decay test of a tanker: field data and theoretical analysis

This paper presents results from a full scale decay test made with a tanker in a relatively protected area in the Brazilian coast. In at least two tests the environmental loads (wind, waves and current) were very small and the time history of the surge motion was well behaved, making it possible to check some proposed models for the damping in the hull and mooring lines. Field data seem to confirm that the damping is indeed of the fluid viscosity type and the theoretical models are able to recover roughly 75% of the observed damping, the energy dissipation in the mooring lines being, by far, the major contribution. The remaining 25% are likely due to non modeled effects, such as the environment influence, which although small and not measured certainly exists, and to the friction between the mooring lines and the seabed.     

Laboratory investigation of damping of gravity-capillary waves on the surface of turbulized liquid

Investigation of damping of gravity-capillary waves (GCWs) in the presence of turbulence is a classical hydrodynamic problem which has important geophysical applications, one of which is related with the problem of forming a radar and optical image of a ship wake on wavy water surface. In this work a new method for the laboratory study of surface wave damping in turbulized liquid is described and the results are presented. The damping of standing GCWs by turbulence on the water surface in a tank mounted on a vibration table is studied. GCWs and turbulence are excited using a two-frequency mode of vibration table oscillations. A high-frequency small amplitude signal is used for parametric GCW excitation; a low-frequency large amplitude signal is used for generating turbulence due to water flowing through a fixed perforated grid submerged into the tank. The coefficient of GCW damping is determined by measured threshold of parametric excitation of the waves; turbulence characteristics are determined by the PIV and PTV techniques. Dependences of GCW damping coefficients on their frequency at different turbulence intensities are obtained, estimates for turbulent viscosity are presented, and a comparison with empirical models proposed earlier is performed.     

Weakly non-linear free oscillations in a basin of variable depth

Weakly non-linear free oscillations in a basin of variable depth filled with non-viscous fluid are investigated in terms of the long waves theory using the perturbation technique. Solutions to the initial two approximations for the horizontal velocity component and free surface departure are numerically derived. An attempt is made to determine the area of applicability of the linear theory by applying a parabolic bottom profile to the basin.Translated by V. Puchkin.     

Application of advanced system identification technique to extract roll damping from model tests in order to accurately predict roll motions

In this paper our previously developed advanced system identification technique [1] has been applied to extract the frequency dependent roll damping from a series of model tests run in irregular (random) waves. It is shown that this methodology accurately models the roll damping which can then be used to produce accurate predictions of the ships roll motion. These roll motion predictions are not only more accurate than the potential flow predictions but more accurate than potential flow models corrected using either empirical prediction methods [2] and even those corrected using roll damping obtained from free decay sallying experiments. This methodology has the potential to significantly improve roll motion prediction during full scale at sea trails of vessels in order to dramatically improve safety of critical operations such as helicopter landing or ship to ship cargo transfer.     

Numerical simulation of non-linear regular and focused waves in an infinite water-depth

Inviscid three-dimensional free surface wave motions are simulated using a novel quadratic higher order boundary element model (HOBEM) based on potential theory for irrotational, incompressible fluid flow in an infinite water-depth. The free surface boundary conditions are fully non-linear. Based on the use of images, a channel Green function is developed and applied to the present model so that two lateral surfaces of an infinite-depth wave tank can be excluded from the calculation domain. In order to generate incident waves and dissipate outgoing waves, a non-reflective wave generator, composed of a series of vertically aligned point sources in the computational domain, is used in conjunction with upstream and downstream damping layers. Numerical experiments are carried out, with linear and fully non-linear, regular and focused waves. It can be seen from the results that the present approach is effective in generating a specified wave profile in an infinite water-depth without reflection at the open boundaries, and fully non-linear numerical simulations compare well with theoretical solutions. The present numerical technique is aimed at efficient modelling of the non-linear wave interactions with ocean structures in deep water.     

Weakly non-linear waves forced by atmospheric disturbances in a confined basin of variable depth

Forced weakly non-linear oscillations of a homogeneous non-viscous fluid in a confined basin of variable depth are considered in a long-wave approximation. Fluid oscillations are caused by time-periodic fluctuations of the atmospheric pressure, whose spatial distribution corresponds to the first mode of free linear waves.Translated by V. Puchkin.     

On the hydrodynamics of bobbing cones

The paper describes an experimental investigation into the hydrodynamics of a right circular cone undergoing transient forced vertical oscillations in otherwise still water. Attention is given to the vertical fluid force and the relative vertical motion between the cone and its intersection with the adjacent free water surface. Comparisons are made between linear theory and experimental results extracted from paired response time histories obtained with input displacements of opposite sign. Comparisons are also made with the predictions obtained from fully non-linear numerical models. A slowly varying setup is observed in the measured relative vertical motion and a new second order term is identified in order to formulate a theoretical explanation.     

Non-linear propagation of unidirectional wave fields over varying topography

The present study aims at investigating the non-linear triad interaction process affecting shoaling surface gravity wave fields. The triad interaction phenomenon being enhanced towards the shore, the domain of study is extended up to the surf zone. Three 1D non-linear wave models (one phase-resolving and two phase-averaged spectral models) have been implemented and compared to laboratory experiments performed in a wave flume. This set of models includes two existing models and a new one which has been developed in the frame of this work. The models include a breaking dissipation term based on the parametrical model of Battjes and Janssen [Battjes, J.A., Janssen, P.A.E.M., 1978. Energy loss and set-up due to breaking of random waves. Proc. 16th Int. Conf. Coastal Eng. (ASCE), Vol. 1, pp. 569–587.]. The investigations concern the evolution of variance spectra, spectral significant wave height and mean period over a barred bathymetric profile. In addition, the performances of the different models are analysed by computing the spectral source term for triad interactions. We found that all models are able to reproduce the main features of non-linear mechanisms affecting a wave field in the near-shore zone. The phase-resolving model gives the most accurate results for non-breaking situations. It correctly reproduces the non-linear coupling effect in decreasing water depths due to wave–wave interactions, as well as the harmonic release after a bar. However, the model is computationally time-consuming. The CPU time is considerably reduced using phase-averaged models. They give satisfactorily results on harmonic generation. However, they do not reproduce the release of harmonics as water depth increases. In breaking conditions, the variance spectra undergo significant changes under the combined effects of non-linear energy transfers and dissipation. The depth-induced wave breaking model included in the equations provides a good estimate of the energy decay in the surf zone.     

Experimental Study and System Identification of Hydrodynamic Force Acting on Heave Damping Plate

Although Morison equation is often applied for simulating hydrodynamic force of marine structure, it may give poor results when non-linear behavior is severe or random wave is encountered. This leads to some modifications of Morison equation or other methods for predicting hydrodynamic force. One of them is the system identification technique. In this paper, NARMAX model theory is firstly used to identify the hydrodynamic system of heave damping plates, which are commonly installed on spar platform. Both linear and non-linear models are obtained. The comparisons between the predieted results and measured data indicate that NARMAX model can predict hydrodynamic force of a heave damping plate very well. The measured data for identification originate from forced oscillation tests, which are random records with given spectrum. The forced oscillation forms in experiment also contain simple harmonic, multi-frequency ones.     

On resonant Rossby–Haurwitz triads

The dynamics of non-divergent flow on a rotating sphere are described by the conservation of absolute vorticity. The analytical study of the non-linear barotropic vorticity equation is greatly facilitated by the expansion of the solution in spherical harmonics and truncation at low order. The normal modes are the well-known Rossby–Haurwitz (RH) waves, which represent the natural oscillations of the system. Triads of RH waves, which satisfy conditions for resonance, are of critical importance for the distribution of energy in the atmosphere.
We show how non-linear interactions of resonant RH triads may result in dynamic instability of large-scale components. We also demonstrate a mathematical equivalence between the equations for an orographically forced triad and a simple mechanical system, the forced-damped swinging spring. This equivalence yields insight concerning the bounded response to a constant forcing in the absence of damping. An examination of triad interactions in atmospheric reanalysis data would be of great interest.     

Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank

A time-independent finite-difference method and a fifth-order Runge–Kutta–Felhberg scheme were used to analyze the dynamic responses of sea-wave-induced fully non-linear sloshing fluid in a floating tank. The interaction effect between the fully non-linear sloshing fluid and the floating tank associated with coupled surge, heave and pitch motions of the tank are analyzed for the first time in the present pilot study. For the analysis of fluid motion in the tank, the coordinate system is moving (translating and rotating) with tank motion. The time-dependent water surface of the sloshing fluid is transformed to a horizontal plane and the flow field is mapped on to a rectangular region. The Euler equations as well as the fully non-linear kinematic free surface condition were used in the analysis of the sloshing fluid. The strip theory for linearized harmonic sea-wave loading was adopted to evaluate the regular encounter wave force. In addition, the dynamic coefficients used in the dynamic equations of tank motion were also derived based on strip theory and a harmonic motion of the tank. The characteristics of free and forced tank motions with and without the sloshing effect are studied. By the damping effect, the response of free oscillation will damp out and that of forced oscillation will approach a steady state. Without sea-wave action, the contribution of the sloshing load would enlarge the angular response of tank motion as well as the rise of free surface and the sloshing effect will delay the damping effect on angular displacement. On the contrary, under sea-wave action, the sloshing effect will decrease the dynamic response of tank motion and rise of free surface. The interaction, sloshing and coupling effects are found to be significant and should be considered in the analysis and design of floating tanks.     

Study of the generation of non-stationary non-linear long waves by atmospheric pressure disturbances

In a non-linear statement, this paper considers the generation of long waves by periodic atmospheric pressure disturbances in a confined basin of variable depth filled with homogeneous fluids. The study is conducted using a non-stationary finite-difference model. The contribution of dissipative forces to the development and stabilization of fluid oscillations is analysed. The paper also considers how the growth of the amplitude of atmospheric pressure disturbances may enhance the non-linearity of the wave process. It is shown that as the pressure amplitude becomes larger, the number of significant harmonics with multiple frequencies in the spectrum of sea level elevations increases. For the weakly non-linear case, wave velocities and free surface elevations, with oscillations stabilized, are compared with their counterparts derived through the perturbation technique.Translated by Vladimir A. Puchkin.     

Bow impact loading on FPSOs 2—Theoretical investigation

Steep wave impact pressures and the structural dynamic response of FPSO bows are studied using 1:80 scale instrumented models and time domain simulation. Comparisons are made between experimental and calculated impacts and associated pressures. A simple time history simulation method for bow loading in (non-linear) random seas is developed. Simplified design rules for curved bows are proposed. The rules account for the effect of the size of the loaded area on the average pressure, the rise and decay times of the pressure and the dynamic amplification of the response.     

Adriatic seiche decay and energy loss to the Mediterranean

A salient feature of sea level records from the Adriatic Sea is the frequent occurrence of energetic seiches of period about 21 h. Once excited by a sudden wind event, such seiches often persist for days. They lose energy either to friction within the Adriatic, or by radiation through Otranto Strait into the Mediterranean.The free decay time of the dominant (lowest mode) seiche was determined from envelopes of handpassed sea level residuals from three locations (Bakar, Split and Dubrovnik) along the Croatian coast during twelve seiche episodes between 1963 and 1986 by taking into consideration only time intervals when the envelopes decreased exponentially in time, when the modelled effects of along-basin winds were smaller than the error of estimation of decay time from the envelopes and when across-basin winds were small. The free decay time thus obtained was 3.2±0.5 d. This value is consonant with the observed width of the spectral peak.The decay caused by both bottom friction and radiation was included in a one dimensional variable cross section shallow water model of the Adriatic. Bottom friction is parameterized by the coefficient k appearing in the linearized bottom stress term _ρ0u (where u is the along-basin velocity and ρ₀ the fluid density). The coefficient k is constrained by values obtained from linearization of the quadratic bottom stress law using estimates of near bottom currents associated with the seiche, with wind driven currents, with tides and with wind waves. Radiation is parameterized by the coefficient f appearing in the open strait boundary condition ζ =auh/c (where ζ is sea level, h is depth and c is phase speed). This parameterization of radiation provides results comparable to allowing the Adriatic to radiate into an unbounded half plane ocean. Repeated runs of the model delineate the dependence of model free seiche decay time on k and a, and these plus the estimates of k allow estimation of a.The principle conclusions of this work are as follows.

1. (1) Exponential decay of seiche amplitude with time does not necessarily guarantee that the observed decay is free of wind influence.

2. (2) Winds blowing across the Adriatic may be of comparable importance to winds blowing along the Adriatic in influencing apparent decay of seiches; across-basin winds are probably coupled to the longitudinal seiche on account of the strong along-basin variability of across-basin winds forced by Croatian coastal orography.

3. (3) The free decay time of the 21.2 h Adriatic seiche is 3.2±0.5 d.

4. (4) A one dimensional shallow water model of the seiche damped by bottom stress represented by Godin's (1988) approximation to the quadratic bottom friction law ρ₀C_Du|u| using the commonly accepted drag coefficient C_D = 0.0015 and quantitative estimates of bottom currents associated with wind driven currents, tides and wind waves, as well as with the seiche itself with no radiation gives a damping time of 9.46 d; radiation sufficient to give the observed damping time must then account for 66% of the energy loss per period. But independent estimates of bottom friction for Adriatic wind driven currents and inertial oscillations, as well as comparisons between quadratic law bottom stress and directly measured bottom stress, all suggest that the quadratic law with C_D=0.0015 substantially underestimates the bottom stress. Based on these studies, a more appropriate value of the drag coefficient is at least C_D=0. In this case, bottom friction with no radiation leads to a damping time of 4.73 d, radiation sufficient to give the observed damping time then accounts for 32% of the energy loss per period.

     

新型圆筒型FPSO垂荡抑制结构优化设计

针对传统圆筒型FPSO垂荡运动剧烈的特点,提出一种带有垂荡抑制结构的圆筒型FPSO。采用1∶77.8的缩尺比制作模型,进行垂荡纵摇衰减试验,得到带有不同垂荡抑制结构模型的固有周期和无因次阻尼系数,进而选取最优的垂荡抑制结构型式。之后计算并对比传统圆筒型FPSO和新型圆筒型FPSO垂荡纵摇运动的固有周期和幅频响应函数。在此基础上,结合我国南海海洋环境条件,设计新型圆筒型FPSO的系泊系统,计算分析自存工况下的耦合动力响应,并与传统圆筒型FPSO进行对比。结果表明,文中提出的垂荡抑制结构可以有效增大系统垂荡纵摇运动的固有周期,改善运动性能,提高系泊的安全性。     

Modelling the long-term time series of significant wave height with non-linear threshold models

Linear autoregressive models and non-linear threshold autoregressive (TAR) models are used in the present work to describe the time series of the significant wave height of sea-states at Figueira da Foz, located in the Portuguese coast. The seasonal components of this series are identified and a TAR model with two regimes is proposed. A simulation study was carried out with the purpose of verifying if both the non-linear and linear models are suited to describe the probabilistic structure of the process. It is shown that both methods are adequate to describe the lower statistical moments of the original data, but the non-linear model represents better the skewness and the kurtosis of the data.