Semi-Empirical Single Realization and Ensemble Crest Distributions of Long-Crest Nonlinear Waves

Abstract

In wave basin model test of an offshore structure, waves that represent the given sea states have to be generated, qualified and accepted for the model test. We normally accept waves in wave calibration tests if the significant wave height, spectral peak period and spectrum match the specified target values. However, for model tests where the responses depend highly on the local wave motions (wave elevation and kinematics) such as wave impact on hull, green water impact on deck and air gap tests, additional qualification checks may be required. For instance, we may need to check wave crest probability distributions to avoid unrealistic wave crest in the test. To date, acceptance criteria of wave crest distribution calibration tests of large and steep waves of three-hour duration (full scale) have not been established. Two purposes of the work presented in the paper are: 1. to define and clarify the wave crest probability distribution of single realization (PDSR) and the probability distribution of wave crest for an ensemble of realizations (PDER) of a given sea state in order to use them appropriately; and 2. to develop semi-empirical probability distributions of nonlinear waves for both PDSR and PDER for easy, practical use. We found that in current practice ensemble and single realization distributions have the potential to be misinterpreted and misused. Clear understanding of the two kinds of distributions will help appropriate offshore design and production unit performance assessments. The semi-empirical formulas proposed in this paper were developed through regression analysis of crest distributions from a large number of sea states and realizations. Wave time series from potential flow simulations, computational fluid dynamics (CFD) simulations and model test results were used to establish the probability distributions. The nonlinear wave simulations were performed for three-hour duration assuming that they were long-crested. The sea states are assumed to be represented by JONSWAP spectrum, where a wide range of significant wave height, peak period, spectral peak parameter, and water depth were considered. Coefficients of the proposed semi-empirical probability distribution formulas, comparisons among crest distributions from numerical simulations and the semi-empirical formulas are presented in this paper.

Qualification Criteria for the Verification of Numerical Waves – Part 1: Potential-Based Numerical Wave Tank (PNWT)

“…Forristall distribution from the 2 nd -order theory and Huang's distribution from physical and numerical wave tank data are also compared. The ±5% range from Huang's distribution [14] [17], which is suggested as a preliminary qualification criterion, is also shown. Both TPNWT and HAWASSI show very good agreement with Huang's distribution.…”

“…Note that if the size of the test domain is large, the height of the largest crests may decrease as the waves propagate because of dissipation due to breaking. The crest height distributions can also be compared to the formulas given in [14] and [17] for the mean, as well as the upper 99th and lower 99th percentiles. These formulas are based on a regression analysis of nonlinear numerical simulations with JONSWAP spectra and peak enhancement parameters γ between 1 and 4.…”

Validation of Numerical Wave Tank Simulations Using Reef3d With Jonswap Spectra in Intermediate Water Depth

“…The ensemble distribution of the crest heights is usually compared with the second-order Forristall distribution which is presented as a blue line in the diagrams of Figure 15. Huang & Zhang [31] give a formula defining the mean, the upper 99th and lower 99th percentiles of the wave crest heights. These formulae are based on a regression analysis of nonlinear numerical simulations with the JONSWAP spectrum with peak enchantment parameters γ between 1 and 4.…”

Representation of Breaking Wave Kinematics in the Fully Nonlinear Potential Flow Model REEF3D::FNPF

“…The ensemble distribution of the crest heights is usually compared with the second-order Forristall distribution which is presented as a blue line in the diagrams of Figure 7. Huang & Zhang [22] give a formula defining the mean, the upper 99th and lower 99th percentiles of the wave crest heights. These formulae are based on a regression analysis of nonlinear numerical simulations with the JONSWAP spectrum with peak enchantment parameters γ between 1 and 4.…”