2026/05/28 by Pieter B. Smit
Earth and Planetary Sciences · #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #Coastal and Marine Dynamics
paper · doi:10.1175/jpo-d-25-0254.1
Abstract Nonlinear deep-water gravity waves can be described by Stokes-type perturbation expansions, but these are not unique. Multiple formulations exist that differ in how the perturbation amplitude is defined. We introduce a parameterized family of solutions and examine how different choices affect key wave characteristics—wave height, action, energy, momentum, and variance—in both deterministic and stochastic frameworks. For the parameterized form that aligns with the limit of the Zakharov equation for a single free-wave component, fourth-order corrections vanish from action and momentum, yielding a form that generalizes naturally to irregular and wave fields interacting with the environment. We discuss why different formulations arise in the literature and argue that while in general application dependent, this generalization property makes this the preferred form when considering the interaction of waves with the environment.