In this simulation-based study, we investigate the surface roughness signature induced by internal solitary waves in oceans. We present the first-ever effort to directly capture the surface roughness signature with a deterministic two-layer model to avoid the singularity encountered in the traditional wave–current interaction theory. By capturing over four million wave components, the simulation resolves the surface wave and internal wave dynamics simultaneously. The surface signature characterized by a rough region followed by a smooth region travelling with an internal wave is quantified by the local wave geometry variation and the wave energy change. The surface wave dynamics are analysed in the wavenumber–frequency slope spectrum calculated in the frame moving with the internal wave. The asymmetric behaviours of right-moving and left-moving surface waves are found to contribute to the surface signature formation. Our results show that the formation of the surface signature is essentially an energy-conservative process and justify the use of the wave-phase-resolved two-layer model.

中文翻译：

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用确定性能量守恒模型直接模拟内波表面粗糙度特征

在这项基于模拟的研究中，我们研究了海洋中内部孤立波引起的表面粗糙度特征。我们首次尝试使用确定性的两层模型直接捕获表面粗糙度特征，以避免传统波流相互作用理论中遇到的奇点。通过捕获超过 400 万个波分量，模拟同时解析了表面波和内波动力学。以粗糙区域和平滑区域为特征的表面特征由内波传播，通过局部波几何变化和波能变化来量化。在随内波移动的坐标系中计算的波数-频率斜率谱中分析了表面波动力学。发现向右移动和向左移动的表面波的不对称行为有助于表面特征的形成。我们的结果表明，表面特征的形成本质上是一个能量守恒过程，并且证明了使用波相分辨两层模型是合理的。