Nonlinear phase-resolved reconstruction of irregular water waves. (25th January 2018) - Qi, Yusheng; Wu, Guangyu; Liu, Yuming; Kim, Moo-Hyun; Yue, Dick K. P.
Abstract : We develop and validate a high-order reconstruction (HOR) method for the phase-resolved reconstruction of a nonlinear wave field given a set of wave measurements. HOR optimizes the amplitude and phase ofL free wave components of the wave field, accounting for nonlinear wave interactions up to orderM in the evolution, to obtain a wave field that minimizes the reconstruction error between the reconstructed wave field and the given measurements. For a given reconstruction tolerance, L andM are provided in the HOR scheme itself. To demonstrate the validity and efficacy of HOR, we perform extensive tests of general two- and three-dimensional wave fields specified by theoretical Stokes waves, nonlinear simulations and physical wave fields in tank experiments which we conduct. The necessaryL, for general broad-banded wave fields, is shown to be substantially less than the free and locked modes needed for the nonlinear evolution. We find that, even for relatively small wave steepness, the inclusion of high-order effects in HOR is important for prediction of wave kinematics not in the measurements. For all the cases we consider, HOR converges to the underlying wave field within a nonlinear spatial-temporal predictable zoneP_NL which depends on the measurements and wave nonlinearity. For infinitesimal waves, P_NL matches the linear predictable zoneP_L, verifying the analytic solution presented in Qi et al. ( Wave Motion, vol.77, 2018, pp. 195–213). With increasing wave nonlinearity, we find thatP_NL contains and is generally greater thanP_L . ThusP_L provides a (conservative) estimate ofP_NL when the underlying wave field is not known.