Wave dynamics and surface statistics in the framework of the weak‐turbulence theory

Most traditional notions concerned with equilibrium sea have been prompted (in the 1960s and 1970s) by field and laboratory observations characterized by a relatively low degree of sea development (wave age ξ = C₀/U is well below unity, where C₀ is the phase speed of waves corresponding to the spectral peak and U is the mean wind speed well above the surface). In contrast, in the case of open‐ocean waves, it is more typical that ξ > 1. Consequently, some of the common notions, for instance, wave groups, fully‐developed sea state (the Pierson‐Moscowitz model), energy dissipation rate, sea surface skewness, and other non‐Guassian statistics, etc., need considerable revision, as they acquire a very different physical meaning as well as different quantitative ratings. Based on the weak‐turbulence theory for equilibrium sea (due largely to V. Zakharov), which is appropriate for ξ⩾1, the corresponding revisions are proposed and their implications for statistical geometry of the sea surface are demonstrated. The results include a fairly complete statistical description of the field of steep and breaking waves related to intermittent whitecaps and bubble clouds. Various data products yielded by satellite altimeter, scatterometer, and microwave radiometer at different ξ, as well as some recent field measurements of open ocean waves, appear to support the theory. It is hoped that additional data might be inferred from acoustical measurements.