Rogue Wave Statistics from a Sparse Coherent Structure Decomposition

Abstract

While conventional rogue wave statistical models rely on linear or weakly nonlinear descriptions of random seas, we demonstrate experimentally that moderately or strongly nonlinear wave fields can be represented by sparse ensembles of coherent soliton-like packets. These packets exhibit log-normal amplitude distributions together with uniformly distributed phases and peak emergence times. This sparse coherent structure framework naturally leads to an extreme value description in which the probability of exceedance is governed by the tail of the coherent-structure amplitude distribution. The prediction is validated against laboratory hydrodynamic experiments across a variety of unidirectional sea states, showing good agreement with the experimental observations and comparing favourably with conventional statistical prediction models while retaining analytical simplicity. Our results provide a direct physics-based link between sparse coherent structures and rogue wave probabilities, with broader implications for nonlinear wave physics in optics, cold gases, and plasmas.