Advances in Statistical and Deterministic Modeling of Wind-Driven Seas

Abstract : The long-term goal of this research is the development of accurate, fast, and advanced statistical and dynamical nonlinear models of ocean surface waves based on first physical principles. These wave models will improve both long-term ocean surface wave forecasts and the prediction of strongly coherent events, such as freak waves, tsunamis, and wave breaking. The objectives of this project are as follows: (1) finding a physically correct wind input term for the Hasselmann equation, (2) understanding the balance of source terms in the Hasselmann equation, (3) investigating the interaction of different scales on the ocean surface (sea and swell), and (4) developing new water surface analytical models and methods. The approach employed advanced analytical techniques, including Hamiltonian formalism, self-similar solutions, analytical solutions of integral equations, numerical methods for the solution of integral and pseudo-differential equations, and the comparison of analytical and numerical results with experimental data. We found the new wind input term through experimental, theoretical, and numerical approaches. We also found the following: (1) that S(sub nl) has a leading role in the energy balance of wind-driven seas within the Hasselmann equation; (2) global visual observations are a useful tool for discriminating sea swells and wind-driven seas; (3) a new method for solving the exact S(sub nl) in the energy balance equation; and (4) a new canonical equation for one-dimensional surface waves.