A clustering scheme has been applied for capturing qualitatively different surge motion patterns in the phase space. The scheme enables the identification of "high-run" incidents as soon as such motions are triggered and while their phenomenology has not yet been well developed. A "high run" is a surf-riding-like behavior, appearing in irregular following seas. The concept of finite-time coherent sets is exploited for deriving estimates of the probability of high-runs. The method is verified by identifying independently the corresponding hyperbolic Lagrangian coherent structures; then, consistency is sought between the two approaches. An important feature of the method is that it does not rely on the use of some empirical criterion for the high-run threshold, such as one based on the exceedance of an arbitrary high-speed level. Despite its computational burden, the proposed scheme offers "objective" statistical information on a ship's high-run tendency that can be used for benchmarking simpler (approximative) probability calculation schemes.

1. Introduction

Current efforts to assess a ship's tendency for abnormal behavior in extreme seas are still limited from our inadequate grasp of the full variety of nonlinear ship motion phenomena that could be realized in an irregular seaway. A classification of these motion patterns would provide a sound basis for developing probabilistic calculation methods of ship operability and safety in extreme seas. A few recent research efforts in our group have been related to this target. In one case, it was endeavored to distinguish ship high-runs from ordinary surging, by engaging the concept of instantaneous wave celerity (Spyrou et al. 2014). In another, the derivation of a practical metric for the probability of high-run was pursued (Belenky et al. 2016). Also, high-run and broaching-to statistics were produced through a direct approach based on assigning prescriptive exceedance thresholds (Spyrou et al. 2016b). Moreover, the theory of surf-riding was extended for bichromatic waves, revealing some rather unexpected types of motion (Spyrou et al. 2018). Even richer phenomena could be conjectured for a multifrequency environment.

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