Kostas Spyrou

In the current paper we are extending our earlier work on the assessment of a ship’s tendency to capsize due to broaching-to in a stochastic seaway. Capturing, in a probabilistic context, interferences between different phenomena occurring during ship operation in extreme seas is a challenging task. Estimates of statistical correlations are deduced between high-run events, broaching-to and capsize. A phenomenological approach is adopted in this study for the classification of the targeted motions. Large scale simulations and a direct counting scheme are applied on the basis of a 4 degrees of freedom (4DOF) mathematical model for the coupled surge–sway–yaw–roll (and rudder) motions. Comparison with the results obtained from a previously used 3DOF model for the same scenarios is carried out in order to investigate the effect of roll on high-run’s correlation with broaching-to. Additionally, sensitivity studies are carried out in order to examine the effect of the commanded heading ang...

The dynamic stability of ships encountering large regular waves from astern is analyzed, with focus on delineating the specific conditions leading to the uncontrolled turn identified as broaching. The problem's formulation takes into account motions of the actively steered or controls-fixed vessel in surge-sway-yaw-roll with consideration of Froude-Krylov and diffraction wave excitation. Dynamical analysis of surf-riding is carried out for the general case of quartering waves, exploring the route periodic motions—surf riding, loss of stationary stability, turn, capsize. Steady-state and transient analysis is carried out in the system's multidimensional state-space in order to identify all existing limit sets and locate attracting domains. Broaching from periodic motions is also a part of the investigation.

A method to identify the law of roll motion decay from extreme angles is presented based on perturbations of the elliptic-type solutions of the corresponding Hamiltonian system. Restoring polynomials up to the 7th order are considered. It is shown that the decay law can be expressed in closed form for up to quintic restoring. The method should be especially useful for deriving linear and nonlinear roll damping coefficients in the context of ship capsize investigations where the large amplitude behavior, near to the angle of vanishing stability, needs to be taken into account.

Continuation analysis is performed for the coupled surge, heave, and pitch motions of a ship in steep following seas. The focus of the work is on the efficient elicitation of system dynamics related to the phenomena of nonlinear surging and surf-riding. Background material with several references can be found in Spyrou (1996a, 1996b, 1997, 2006). Main novel features of the current work are the inclusion of fluid memory effects within the framework of continuation analysis and the successful implementation of continuation for the periodic motions that correspond to the "overtaking waves" scenario. The entailed steps for realizing these goals are discussed in detail. Application is presented for a well-known ITTC ship.

An integrated numerical environment for the exploration and assessment of nonlinear ship dynamics has been developed. The potential is demonstrated through an investigation of controllability of a modern Ro-Pax in steady wind. An improved windloading module is coupled to a standard maneuvering model, and the combination is put through "continuation analysis" in order to determine the branching behavior and specific bifurcations governing system responses. The analysis unveils a complex dynamical structure that dictates the limits of the ship's course-keeping capability. The topology, in state-parameter space of self-excited yawing in head wind, the occurrence of which had been established from earlier research, is now clarified. Interesting interactions between stationary and periodic responses are reported. The effectiveness of active control in removing undesirable responses is also part of the analysis.

In earlier studies we have analyzed the phenomena which can generate loss of ship controllability in astern seas. In this paper we examine how the yaw instability associated with broaching can lead to roll instability and ship capsize. The dynamic effects responsible for capsize during the forced turn of broaching do not have their origin in the customary roll equation but are the result of interactions with other motions of the ship. Stability studies based solely on the roll equation are thus clearly inappropriate for this case where a multidimensional approach is deemed necessary. After presenting the theoretical background we set out a multi-degree method of global analysis which is based on transient maps. We apply this method to clarify how capsize occurs during the escape from surf-riding and also during transients from arbitrary initial condition of the ship. Our study establishes the connection between speed, heading, automatic control parameters and capsize. The proposed m...

ABSTRACT From investigations with ship models tested in steep periodic following waves, it has been conjectured in the past that, if the speed is observed reaching (in transient) the celerity value, attraction toward the condition commonly identified as “surf-riding” is already in progress. The nonlinear dynamics of this phenomenon has been investigated in depth also theoretically; however, it is unknown whether the stated simple phenomenological detection rule is meaningful also for more natural sea wave profiles. A practical question that prompted the current investigation is whether the duration of attraction to surf-riding could be properly quantified as a percentage of the total time of exposure to a specified wave environment, so that a probability of surf-riding could be eventually calculated. Celerity is defined in the current work as the velocity of propagation of a suitable local property of the wave profile, such as a certain value of slope. For irregular seas, this leads to the concept of instantaneous celerity. Unfortunately, instantaneous celerity, in general, is not a smooth and bounded curve in time. An alternative definition of celerity fitting to the problem of surf-riding is thus investigated, where the propagated points of the profiles are those with the locally maximum slope. Simultaneous treatment of the “wave” and “ship” processes is implemented, and the potential of a condition based on local celerity for surf-riding prediction is examined. Various patterns of behavior before and into surf-riding are observed and discussed. The paper is a step in the direction of developing a probabilistic method of assessment for the dangerous phenomenon of surf-riding and indirectly, for the evaluation of the class of cross-disciplinary phenomena that obey similar nonlinear dynamics.