Parametric rolling prediction in irregular seas using combination of deterministic ship dynamics and probabilistic wave theory

In recent years there have been reports of serious accidents of parametric rolling for modern container ships and car carriers. For avoiding such accidents, a prediction method of parametric rolling in irregular seas is required. Since parametric rolling is practically non-ergodic, repetitions of numerical simulations or experiments could be not feasible to ascertain the behaviour. Therefore, in this paper, a method combining a stochastic approach with a deterministic approach in order to estimate the probabilistic index without such simple repetitions is developed. The ship's response in regular seas is estimated by solving an averaged system of the original 1-DoF roll model, and random waves necessary for occurrence of parametric rolling is achieved by using Longuet-Higgins’s or Kimura’s wave group theory. As a result, a fast and robust computation method of the probabilistic index is established. Finally, it is concluded that the proposed method is considered to be one of the useful tools for discussing the new IMO Intact Stability Code.     

Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit

The chaos that appears in the ship roll equation in beam seas known as the escape equation has been intensively investigated because it is closely related to capsizing incidents. In particular, many applications of the Melnikov integral formula have been reported in the literature; however, in all the analytical works concerning the escape equation, the Melnikov integral is formulated utilizing a separatrix for the Hamiltonian part or a numerically obtained heteroclinic orbit for the non-Hamiltonian part of the original escape equation. To overcome such limitations, this article attempts to utilise an analytical expression for the non-Hamiltonian part. As a result, an analytical procedure is provided that makes use of a heteroclinic orbit of the non-Hamiltonian part within the framework of the Melnikov integral formula.     

Prediction methods for the surf-riding threshold and the wave-blocking threshold based on Melnikov’s method

A ship operating in following and/or quartering seas may be susceptible to broaching-to preceded by the surf-riding phenomenon. Therefore, for the safety assessment of fast vessels such as destroyers and patrol craft, the estimation of the surf-riding condition is important. As shown by previous research, there are two boundaries for ship motion in following and quartering seas. These are the surf-riding threshold and wave-blocking threshold. In this study, the theoretical methods to estimate both boundaries are obtained by making use of Melnikov’s method. In order to validate the formulae, free-running model experiments are conducted in the towing tank. Comparisons between the results obtained from calculations and experiments show good agreement. It is concluded that the formulae based on Melnikov’s method could be applicable to the safety assessment of surface ships.     

Fundamental research on resistance reduction of surface combatants due to stern flaps

It is well known that a decrease in ship resistance may be achieved due to the installation of a stern flap. Therefore, so far, a considerable amount of research on stern flaps has been conducted. Previous research has demonstrated that the primary mechanism by which a stern appendage reduces resistance is a change in the pressure distribution over the aft body of the hull, and secondly through effects on the running attitude, near and far field wave generation, and local transom flow among other phenomena. However, the change in pressure distribution is influenced by the other components. Hence, there is still room for argument about the relative contribution of each component to the pressure distribution. Therefore, as the first step of the research, by conducting the model experiment in towing tank and CFD (Computational Fluid Dynamics) analysis, we examined the effect of running attitudes and wave making at the after portion of the hull on resistance reduction. As a result, it is concluded that a flap affects a change in the wave generated at the transom part and it could lead to a decrease in wave-making resistance.     

DETECTION OF BCL-2 GENE MAJOR BREAKPOINTREGION REARRANGEMENT IN HUMAN B-CELL LYMPHOMAS

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Analytical formulae for predicting the surf-riding threshold for a ship in following seas

Making use of Melnikov’s method, a generalized formula for predicting the surf-riding threshold is developed as an extension to the applications of Kan and Spyrou. A new analytical formula for calculating the surf-riding threshold of a ship in following seas is also proposed in light of nonlinear dynamical system theory. By applying a continuous piecewise linear approximation to the wave-induced surge force, a heteroclinic bifurcation point is obtained analytically with an uncoupled surge equation. Results calculated using these formulae are presented, and they show good agreement with those obtained utilizing numerical bifurcation analysis. Further, it was confirmed that the surf-riding threshold obtained using the proposed formulae agrees reasonably well with that obtained experimentally for an unconventional vessel.     

Numerical prediction of the surf-riding threshold of a ship in stern quartering waves in the light of bifurcation theory

In order to develop design and operational criteria to be used at the International Maritime Organization (IMO), critical conditions for broaching are explored in the light of bifurcation analysis. Since surf-riding, which is a prerequisite to broaching, can be regarded as a heteroclinic bifurcation, one of global bifurcations, of a surge-sway-yaw-roll model in quartering waves, the relevant bifurcation condition is formulated with a rigorous mathematical background. Then an efficient numerical solution procedure suitable for tracing the surf-riding threshold hypersurface is presented with successful examples. This deals with all state and control variables in parallel, and excludes backward time integration and an orthogonal condition in the iteration process. The bifurcation conditions identified were compared with the results from a direct numerical simulation in the time domain. As a result, it was confirmed that the heteroclinic bifurcation provides a boundary between motions periodically overtaken by waves and nonperiodic motions such as surf-riding and broaching.     

Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit: analytic extension and numerical validation

In the research field of nonlinear dynamical system theory, it is well known that a homoclinic/heteroclinic point leads to unpredictable motions, such as chaos. Melnikov’s method enables us to judge whether the system has a homoclinic/heteroclinic orbit. Therefore, in order to assess a vessel's safety with respect to capsizing, Melnikov’s method has been applied for investigations of the chaos that appears in beam sea rolling. This is because chaos is closely related to capsizing incidents. In a previous paper (Maki et al. in J Mar Sci Technol 15:102–106, 2010), a formula to predict the capsizing boundary by applying Melnikov’s method to analytically obtain the non-Hamiltonian heteroclinic orbit was proposed. However, in that paper, only limited numerical investigation was carried out. Therefore, further comparative research between the analytical and numerical results is conducted, with the result being that the formula is validated.     

A new weather-routing system that accounts for ship stability based on a real-coded genetic algorithm

The operation schedule of an oceangoing vessel can be influenced by wave or wind disturbances, and is therefore weather routed. The weather-routing problem is considered to be a multimodal function problem. Therefore, in the present research, the real-coded genetic algorithm technique (an evolutionary calculation technique) is applied to globally search for the optimum route. Additionally, to avoid maritime accidents due to parametric rolling, this route optimization method takes into account the risk of parametric rolling as one of its objective functions. Numerical verification is carried out for three kinds of objective functions with different weight ratios between fuel efficiency and ship safety in parametric rolling. As a result, it is numerically confirmed that the relation between economics and ship safety is a trade-off, and the safer route is not necessarily the most economical. Considering its robustness, the proposed method appears to be a powerful practical tool by choosing the most appropriate weights for economics and ship safety.