Most of the studies on extreme waves are focused on the systems with single-peak wave spectra. However, according to the statistics of occurrence, the bimodal spectral system is also frequent in real sea conditions. In order to summarize the statistics of extreme waves, irregular wave trains under single-peak and bimodal spectra for long durations are simulated in this paper, based on a two-dimensional High Order Spectral (HOS) numerical wave tank. A large number of configurations have been tested under unimodal and bimodal spectra. The investigation on the wave trains under single-peak spectrum indicates that although in conditions often referred as deep water (k_ph > π), the relative water depth has a significant influence on the probabilities of occurrence of extreme waves. A detailed analysis of the combined effect of Benjamin-Feir Index (BFI) and relative water depth is provided. However, the situation is more complex in real sea conditions, which may exhibit multimodal spectra. We focus in this study on long-crested bimodal spectra characterized by the same significant wave height H_s and mean zero-crossing period T_z of the sea states as the single-peak spectrum. The wave conditions under bimodal spectrum present milder extreme wave statistics than those under single-peak spectrum. In addition, mixed ocean systems with equivalent energy distribution (i.e., Sea-Swell Energy Ratio (SSER) is close to 1.0) and larger separation between partitions (i.e., Intermodal Distance (ID) > 0.10) are the less prominent to extreme waves appearance. The comparison of the mixed sea states and the corresponding single independent systems demonstrates that the complexity of the underlying physics of a given sea state (for instance the presence of modulational instability or other nonlinear process) cannot be deduced by an analysis limited to the statistical content of the combined sea state. The wave energy being distributed among frequencies plays a major role. Additionally, Gram-Charlier distribution can accurately predict the probability of large waves (1.5 < H/H_s < 2.0) compared to the MER distribution, but it underestimates the statistics of the wave height distribution when H/H_s is larger than 2.0 for both single-peak and bimodal states.

关于极限波的大多数研究都集中在具有单峰波谱的系统上。但是，根据发生的统计数据，双峰光谱系统在实际海况下也很常见。为了总结极端波的统计数据，本文基于二维高阶谱（HOS）数值波箱，模拟了单峰和双峰频谱下长时间的不规则波列。在单峰和双峰光谱下已经测试了许多构型。对单峰频谱下的波列的研究表明，尽管在通常被称为深水的条件下（k _p h  >  π），相对水深对出现极端波浪的可能性有重大影响。详细分析了本杰明·费尔指数（BFI）和相对水深的综合作用。但是，在实际海洋条件下情况更为复杂，可能会表现出多峰光谱。在本研究中，我们将重点放在长峰双峰光谱上，该光谱具有与单峰光谱相同的有效波高H _s和平均海底过零时间T _z。与单峰频谱相比，双峰频谱下的波况呈现出更温和的极端波统计数据。此外，具有相等能量分布（即海浪能量比）的混合海洋系统（SSER）接近1.0），并且分区之间的较大间隔（即联运距离（ID）> 0.10）对极端波浪的出现不太显着。对混合海态和相应的单个独立系统的比较表明，给定海态的基础物理学的复杂性（例如，调制不稳定性或其他非线性过程的存在）不能通过限于统计内容的分析来推断合并的海洋国家。在频率之间分布的波能起着主要作用。此外，克-夏利分布可准确预测大波的概率（1.5 <  H / H _s 与MER分布相比<2.0），但是对于单峰和双峰态，当H / H _s大于2.0时，它低估了波高分布的统计量。