Comparison of Temporal and Spatial Statistics of Nonlinear Waves

Abstract

In the past, it was most common to derive wave parameters and their statistics from time series of wave elevation. The duration of the wave records has been usually restricted to 20 or 30 minutes. Recently, increasing attention has started to be given to spatial wave data and wave statistics, particularly due to introduction in oceanography of stereo camera systems for collecting space–time ensemble of sea surface elevation. Using numerical linear, 2nd and 3rd order simulations this study compares temporal and spatial statistics of wave parameters. The 3rd order wave data are simulated by a numerical solver based on the Higher Order Spectral Method (HOSM) which includes the leading order nonlinear dynamical effects, accounting for the effect of modulational instability. The Pierson-Moskowitz and the JONSWAP spectrum with different gamma parameters are used in the analysis. Sea states with wave steepness where rogue waves were recorded in nature are considered. Consequences of using temporal contra spatial statistics are discussed in perspective of marine structures’ design. Functional dependency between wave parameters characterizing occurrence of rogue waves in unidirectional wave field is proposed.