Abstract
The survivability, safe operation, and design of marine vehicles and wave energy converters are highly dependent on accurate characterization and estimation of the energy content of the ocean wave field. In this study, analytical solutions of the nonlinear Schrödinger equation (NLS) using periodic inverse scattering transformation (IST) and its associated Riemann spectrum are employed to obtain the nonlinear wave modes (eigen functions of the nonlinear equation consisting of multiple phase-locked harmonic components). These nonlinear wave modes are used in two approaches to develop a more accurate definition of the energy content. First, in an ad hoc approach, the amplitudes of the nonlinear wave modes are used with a linear energy calculation resulting in a semi-linear energy estimate. Next, a novel, mathematically exact definition of the energy content taking into account the nonlinear effects up to fifth order is introduced in combination with the nonlinear wave modes, the exact energy content of the wave field is computed. Experimental results and numerical simulations were used to compute and analyze the linear, ad hoc, and exact energy contents of the wave field, using both linear and nonlinear spectra. The ratio of the ad hoc and exact energy estimates to the linear energy content were computed to examine the effect of nonlinearity on the energy content. In general, an increasing energy ratio was observed for increasing nonlinearity of the wave field, with larger contributions from higher-order harmonic terms. It was confirmed that the significant increase in nonlinear energy content with respect to its linear counterpart is due to the increase in the number of nonlinear phase-locked (bound wave) modes.
On Hokusai's
Great wave off Kanagawa
: localization, linearity and a rogue wave in sub-Antarctic waters