1077 Coherent Phase-space Structures Governing Surge Dynamics in Astern Seas Ioannis Kontolefas, National Technical University of Athens, ikon@central.ntua.gr Kostas J. Spyrou, National Technical University of Athens, spyrou@deslab.ntua.gr ABSTRACT Consideration of a steep multi-chromatic wave field greatly increases the complexity of ship surge dynamics as it renders the underlying strongly nonlinear system also time-dependent. Conse- quently, conventional concepts used for the analysis of stationary phase-space flows are no longer sufficient to support an in-depth investigation of ship dynamics. To overcome this hindrance, the concept of hyperbolic Lagrangian Coherent Structures (LCSs) is employed. These phase-space ob- jects can be regarded as finite-time generalizations of the stable and unstable manifolds of hyperbol- ic trajectories defined in dynamical systems with special (such as periodic or quasiperiodic) time dependencies. LCSs represent, locally, the strongest repelling or attracting material surfaces (curves in the case of 2-dimensional systems) advected with the phase flow. We identify hyperbolic LCSs that are intrinsic to the phase flow associated with the surge motion of a ship in astern seas. To the global approach of LCSs is incorporated a scheme aiming to track in space-time “local features” of the flow. The emerging new toolset can enhance substantially current efforts towards a rigorous as- sessment of ship dynamic stability in steep following seas. Keywords: Surf-riding, Multi-frequency Waves, Lagrangian Coherent Structures 1. INTRODUCTION The mechanisms generating surf-riding for a ship in regular seas have been extensively studied in the past (Kan 1990; Spyrou 1996). However, gaining understanding beyond the context of harmonic waves has been con- sidered as a daunting task, till recently. The consideration of a multi-frequency wave field brings in new concepts accruing from the time- dependent nature of the problem. For the regular sea scenario, it is well known that surf-riding can be identified as an equilibrium solution of the surge equation of motion. The consideration, though, of more general wave forms introduces profound com- plications. For an irregular seaway, this key definition needs to be revised, since stationary states are not likely to exist; i.e., one cannot assume that the underlying non-autonomous dynamical system will admit constant solu- tions. Therefore, a broader definition of surf- riding needs to be sought. These difficulties have been recognized and a phenomenological approach to surf-riding in irregular seas has been proposed, expanding upon the notion of wave celerity and its role in signaling the capture to surf-riding (Spyrou et al. 2012, 2014a). In particular, definition and methods for the calculation of wave celeri- ty for an irregular seaway were proposed and their relevance to the problem of surf-riding Proceedings of the 12 th International Conference on the Stability of Ships and Ocean Vehicles, 14-19 June 2015, Glasgow, UK.