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.     

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.     

Capsizing Probability of Dead Ship Stability in Beam Wind and Wave for Damaged Ship

The International Maritime Organization has developed the second-generation intact stability criteria. Thus, damage stability criteria can be established in the future. In order to identity the capsizing probability of damaged ship under dead ship condition, this paper investigates two methods that can be used to research the capsizing probability in time domain, which mainly focus on the nonlinear righting lever GZ curve solution. One method subjects the influence of damaged tanks on the hull shape down to the wind and wave, and the other method is consistent with the real-time calculation of the GZ curve. On the basis of one degree of freedom rolling equation, the solution is Monte Carlo method, and a damaged fishery bureau vessel is taken as a sample ship. In addition, the results of the time-domain capsizing probability under different loading conditions are compared and analyzed. The relation of GM and heeling angle with the capsizing probability is investigated, and its possible reason is analyzed. On the basis of combining the time-domain flooding process with the capsizing probability calculation, this research aims to lay the foundation for the study of capsizing probability in time domain under dead ship condition, as well as provide technical support for capsizing mechanism of dead ship stability and damage stability criteria establishment in waves.     

“Batfish” a depth controllable towed body for collecting oceanographic data

“Batfish” is a streamlined vehicle developed to house fast-responding oceanographic sensors. It is towed behind a ship or small vessel and its depth is controlled from the vessel by a manually or automatically produced command signal. Variable-angle wings permit the vehicle to be lowered and a novel control surface, which eliminates the need for heavy ballast, assures lateral stability. There are two models: the standard and the wide-wing Batfish. The standard Batfish has collected temperature and conductivity data at depths of up to 200 m when towed at 10–25 km/hr, and the wide-wing Batfish at depths to 400 m when towed at 10–16km/hr.     

A rational approach to intact ship stability assessment

In this study, asymptotic and total stability of the non-linear free and forced pure rolling motions of a ship are investigated. A ship performing a rolling motion is taken as a dynamical system. Lyapunov's direct method is employed in the analysis. By generating a time-invariant Lyapunov function, conditions and the domain of asymptotic stability are obtained for free rolling motion. Results of the work on “boundedness” and “uniform boundedness” of the solutions of the equation of forced rolling motion, done by Özkan (1977), that is, conditions of total (practical) stability and its domain in the phase-plane are given and illustrated.     

Alternative placement technique for antifer blocks used on breakwaters

In this study, a placement technique named as “alternative placement technique” was developed for antifer blocks and the results of its application to a breakwater model were presented. This placement technique was compared with the existing techniques such as the “regular placement technique”, the “irregular placement technique” and the “sloped wall placement technique” by experiments. The comparison was carried out considering armor layer stability, prototype placement, clarity of the placement technique’s definition, armor layer cost, and wave runup. As a result of this investigation the “alternative placement technique” was found to be superior to the other existing placement techniques.     

Solution of the nonlinear roll model by a generalized asymptotic method

Mathematical modeling of the nonlinear roll motion of ships is one subject widely dealt with in nonlinear ship dynamics. This paper investigates setting up a form of nonlinear roll motion model and developing its periodic solution by the generalized Krylov–Bogoliubov asymptotic method in the time domain. In this model, nonlinearities are introduced through damping and restoring terms. The restoring term is approximated as a third-order odd polynomial whereas the quadratic term is favored to represent the nonlinear damping. The ship is assumed to be under the influence of a sinusoidal exciting force. Although the method is expressible to contain any order of the perturbing term, a single degree is chosen to avoid cumbersome mathematical complexity. In order to improve the solution a first-order correction term is also included. Moreover, a numerical example is carried out for a small vessel in order to validate the solution scheme.     

Numerical simulation of ship stability for dynamic environment

The prediction of ship stability during the early stages of design is very important from the point of vessel’s safety. Out of the six motions of a ship, the critical motion leading to capsize of a vessel is the rolling motion. In the present study, particular attention is paid to the performance of a ship in beam sea. The linear ship response in waves is evaluated using strip theory. Critical condition in the rolling motion of a ship is when it is subjected to synchronous beam waves. In this paper, a nonlinear approach has been tried to predict the roll response of a vessel. Various representations of damping and restoring terms found in the literature are investigated. A parametric investigation is undertaken to identify the effect of a number of key parameters like wave amplitude, wave frequency, metacentric height, etc.     

Calculation of a capsizing rate of a ship in stochastic beam seas

This study introduces a method of calculating a capsizing rate of a ship. The phenomenon ‘capsizing’ is described as a jump of local equilibrium point from that near the upright position of a ship to what describes the upside-down attitude of the capsized ship; the rate of occurrence of such jumps was calculated. The potential function corresponding to the roll restoring moment have two potential wells located at the roll displacement angle 0 and 180°, respectively. A nonlinear Fokker–Planck equation for the joint probability density function of roll angle and velocity was solved. The excitation to the ship was assumed to be a combination of a regular harmonic wave and a white noise process.     

Stability and capsizing analysis of nonlinear ship rolling in wind and stochastic beam seas

Considering the actual seaway condition, stability and capsizing of nonlinear ship rolling system in stochastic beam seas is of significant importance for voyage safety. Safe zone are defined in the phase space plan of the unperturbed Hamilton system to qualitatively distinguish ship motions as capsize and noncapsize. Capsize events are defined by solutions passing out of the safe zone. The probability of such an occurrence is studied by virtue of the random Melnikov function and the concept of phase space flux. In this paper, besides conventional wave excitation, the effect of wind load is also taken into account. The introduction of wind load will lead to asymmetry, in other words, it transforms the symmetric heteroclinic orbits into asymmetric homoclinic orbits. For asymmetric dynamical system, the orbital analytic solutions and its power spectrum are not readily available, and the technique of discrete time Fourier transformation (DTFT) is used. In the end, as verification of theoretical critical significant wave height, capsizing probability contour diagram is generated by means of numerical simulation. The contour diagram shows that these analytical methods provide reliable and predictive results about the likelihood of a vessel capsizing in a given seaway condition.     

Estimation of survival probability for a ship in beam seas using the safe basin

The purpose of this paper is to analyze the nonlinear ship roll motion equation and the main parameters that induce ship capsizing in beam seas, estimate the survival probability of a ferry in random seas and to find out a risk assessment method for the ship’s intact stability. A single degree of freedom (1-DOF) dynamic system of ship rolling in beam seas is investigated and the nonlinear differential equation is solved in the time domain by the fourth order Runge-Kutta algorithm. The survival probability of a ferry in beam seas is investigated using the theory of “safe basin”. The survival probability is calculated by estimating erosion of “safe basin” during ship rolling motion by Monte Carlo simulations. From the results it can be concluded that the survival probability of a ship in beam sea condition can be predicted by combining Monte Carlo simulations and the theory of “safe basin”.     

A review of intact ship stability research and criteria

An investigation on capsizing of a vessel in a seaway is of paramount importance from the point of view of safety of life at sea. The present paper analyzes the major research efforts made throughout the world regarding intact stability and the establishment of stability criteria. Attempts have been made by the authors to draw conclusions from this analysis and to provide guidelines for future research efforts in the field of intact stability of ships.     

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 BCI criterion for the initiation of breaking process in Boussinesq-type equations wave models

The Breaking Celerity Index (BCI) is proposed as a new wave breaking criterion for Boussinesq-type equations wave propagation models (BTE).The BCI effectiveness in determining the breaking initiation location has been verified against data from different experimental investigations conducted with incident regular and irregular waves propagating along uniform slope [Utku, M. (1999). “The Relative Trough Froude Number. A New Criteria for Wave Breaking”. Ph.D. Dissertation, Dept. of Civil and Enviromental Engineering, Old Dominion University, Norfolk, VA; Gonsalves Veloso dos Reis, M.T.L. (1992). “Characteristics of waves in the surf zone”. MS Thesis, Department of Civil Engineering, University of Liverpool., Liverpool; Lara, J.L., Losada, I.J., and Liu, P.L.-F. (2006). “Breaking waves over a mild gravel slope: experimental and numerical analysis”. Journal of Geophysical Research, VOL 111, C11019] and barred beaches [Tomasicchio, G.R., and Sancho, F. (2002). “On wave induced undertow at a barred beach”. Proceedings of 28th International Conference on Coastal Engineering, ASCE, New York, 557–569]. The considered experiments were carried out in small-scale and large-scale facilities. In addition, one set of data has been obtained by the use of the COBRAS model based upon the Reynolds Averaged Navier Stokes (RANS) equations [Liu, P.L.-F., Lin, P., Hsu, T., Chang, K., Losada, I.J., Vidal, C., and Sakakiyama, T. (2000). “A Reynolds averaged Navier–Stokes equation model for nonlinear water wave and structure interactions”. Proceedings of Coastal Structures ‘99, Balkema, Rotterdam, 169–174; Losada, I.J., Lara, J.L., and Liu, P.L.-F. (2005). “Numerical simulation based on a RANS model of wave groups on an impermeable slope”. Proceedings of Fifth International Symposium WAVES 2005, Madrid].Numerical simulations have been performed with the 1D-FUNWAVE model [Kirby, J.T., Wei, G., Chen, Q., Kennedy, A.B., and Dalrymple, R.A. (1998). “FUNWAVE 1.0 Fully Nonlinear Boussinesq Wave Model Documentation and User's Manual”. Research Report No CACR-98-06, Center for Applied Coastal Research, University of Delaware, Newark]. With regard to the adopted experimental conditions, the breaking location has been calculated for different trigger mechanisms [Zelt, J.A. (1991). “The run-up of nonbreaking and breaking solitary waves”. Coastal Engineering, 15, 205–246; Kennedy, A.B., Chen, Q., Kirby, J.T., and Dalrymple, R.A. (2000). “Boussinesq modeling of wave transformation, breaking and run-up. I: 1D”. Journal of Waterway, Port, Coastal and Ocean Engineering, 126, 39–47; Utku, M., and Basco, D.R. (2002). “A new criteria for wave breaking based on the Relative Trough Froude Number”. Proceedings of 28th International Conference on Coastal Engineering, ASCE, New York, 258–268] including the proposed BCI.The calculations have shown that BCI gives a better agreement with the physical data with respect to the other trigger criteria, both for spilling and plunging breaking events, with a not negligible reduction of the calculation time.     

Water levels in a dual-basin harbour in response to infragravity and edge waves

Seiche modes in a compound harbour (an “Outer Harbour” connected both to the sea and to an “Inner Harbour”) were studied using water level data and a numerical model. A variety of harbour oscillations are present, with periods up to 67 min. Periods longer than 25 min exceed resonant modes of the harbour. This paper addresses the characteristics and causes of the open-basin modes. The dual harbour open-basin mode is modified by constriction at the connection between harbours, by partial reflection at the antinode, and by the geometry of the entrance. The single-harbour open-basin mode excites the dual harbour closed-basin mode, which has nearly the same period. This forcing moves the closed-basin antinode and slightly changes the modal period, but the coupling permits the amplitude to increase through the closed-basin resonance. The water level response to wind stress is weak, but significant residual currents can occur, which take the form of clockwise gyres in each basin. Energetic peaks in the water level spectrum at 26, 35, and 67 min are shown to correspond to possible edge waves on the local shelf. The work has practical implications to port design, e.g. towards minimisation of ship ranging while at anchor.     

Transient effects in wave-current boundary layer flow

Previous studies of combined wave and current bottom boundary layer flow have concentrated on the final converged state of the flow following the addition of waves to a current. While this final state is of primary interest to modellers and engineers, it pre-supposes that such a state is actually attained in reality, and this may not always be the case. In addition, it overlooks the interesting and complicated transient effects which occur as a wave-current flow evolves from one state to another. The present study concentrates attention on the transient effects predicted by a “one-equation” turbulence closure model. Results of case studies are presented in which waves are superimposed co-linearly on a current (“forward problem”), and are then removed from the converged wave-current flow (“backward problem”). Two formulations of the “forward” and “backward” problems are discussed. In the first the steady component of the pressure gradient driving the mean flow is held constant throughout, and in the second the steady component of the mass flux is held constant. In each case the detailed evolution of the profiles of mean velocity, turbulent energy, mixing length, eddy viscosity and shear stress are discussed. More generally, the question of the convergence timescale of a combined wave-current flow is considered, and a convergence criterion is proposed.     

An experimental method for determining the frequency-dependent added mass and added mass moment of inertia for a floating body in heave and pitch motions

Most of the existing relevant materials have been obtained from experiments, in which evaluating the added mass at the resonant frequency corresponding to the peak of a frequency-response curve obtained from the “forced” vibration analysis is the most popular technique. In this paper, a simple experimental method was presented where the “free” vibration responses instead of the “forced” ones were used to determine the values of m_ah and I_ap. The main part of the experimental system is composed of a floating body (model) and a spring–shaft shaker. The “free” vibration of this main part was induced by imposing on it an initial displacement (and/or an initial velocity), and from the time histories of displacements information such as the “damped” natural frequencies, damping ratios, sectional added mass coefficients (C_V and C_P) were obtained. Since the displacements of the spring–shaft shaker are “translational” and those of the floating body due to pitch motions are “angular”, a technique for the transformation between the associated parameters of the two components of the main part was presented.     

Stochastic inversion for the roll gyradius second moment mass property in ships at full-scale and model-scale

In current Naval Architecture practice, employing static considerations is an important and necessary step in assessing ship stability and seakeeping properties (e.g. inclining experiments, load line regulations, range of stability calculations). However, damaged vessels and vessels operating in heavy weather or in conditions where topside icing is a concern may require an additional assessment of stability that considers dynamic effects. Within such contexts, the actual (i.e. current) second moment properties of the vessel mass become very important in the associated equations of motion for a given ship. One such critical second mass moment property is the roll gyradius, as it is closely related to the occurrence of capsizing. The present paper furnishes a means for reckoning the actual roll gyradius of a given ship operating within a seaway. The approach hinges on the formulation and solution of a stochastic inverse problem that leverages existing seakeeping software against the shipboard inertial measurement unit (IMU) telemetry. The method is demonstrated at full-scale and validated at model scale.     

Tracking the last sea-level cycle: seafloor morphology and shallow stratigraphy of the latest Quaternary New Jersey middle continental shelf

Seafloor geomorphology and surficial stratigraphy of the New Jersey middle continental shelf provide a detailed record of sea-level change during the last advance and retreat of the Laurentide ice sheet (120 kyr B.P. to Present). A NW–SE-oriented corridor on the middle shelf between water depths of 40 m (the mid-shelf “paleo-shore”) and 100 m (the Franklin “paleo-shore”) encompasses 500 line-km of 2D Huntec boomer profiles (500–3500 Hz), an embedded 4.6 km² 3D volume, and a 490 km² swath bathymetry map. We use these data to develop a relative stratigraphy. Core samples from published studies also provide some chronological and sedimentological constraints on the upper <5 m of the stratigraphic succession.The following stratigraphic units and surfaces occur (from bottom to top): (1) “R”, a high-amplitude reflection that separates sediment >46.5 kyr old (by AMS ¹⁴C dating) from overlying sediment wedges; (2) the outer shelf wedge, a marine unit up to 50 m thick that onlaps “R”; (3) “Channels”, a reflection sub-parallel to the seafloor that incises “R”, and appears as a dendritic system of channels in map view; (4) “Channels” fill, the upper portion of which is sampled and known to represent deepening-upward marine sediments 12.3 kyr in age; (5) the “T” horizon, a seismically discontinuous surface that caps “Channels” fill; (6) oblique ridge deposits, coarse-grained shelly units comprised of km-scale, shallow shelf bedforms; and (7) ribbon-floored swales, bathymetric depressions parallel to modern shelf currents that truncate the oblique ridges and cut into surficial deposits.We interpret this succession of features in light of a global eustatic sea-level curve and the consequent migration of the coastline across the middle shelf during the last 120 kyr. The morphology of the New Jersey middle shelf shows a discrete sequence of stratigraphic elements, and reflects the pulsed episodicity of the last sea-level cycle. “R” is a complicated marine/non-marine erosional surface formed during the last regression, while the outer shelf wedge represents a shelf wedge emplaced during a minor glacial retreat before maximum Wisconsin lowstand (i.e., marine oxygen isotope stage 3.1). “Channels” is a widespread fluvial subarial erosion surface formed at the late Wisconsin glacial maximum 22 kyr B.P. The shoreline migrated back across the mid-shelf corridor non-uniformly during the period represented by “Channels” fill. Oblique ridges are relict features on the New Jersey middle shelf, while the ribbon-floored swales represent modern shelf erosion. There is no systematic relationship between modern seafloor morphology and the very shallowly buried stratigraphic succession.