On diffraction and oblique interactions of horizontally two-dimensional internal solitary waves
On diffraction and oblique interactions of horizontally two-dimensional internal solitary waves
复制标题
DOI：
10.1017/jfm.2022.60
复制
发表时间：
2022-02
影响因子：
3.7
通讯作者：
C. Yuan;Zhan Wang
中科院分区：
文献类型：
--
作者：
C. Yuan;Zhan Wang
摘要在三维海洋内波的背景下，考虑地形的影响，提出了一个修正的Benney-Luke方程来描述倾斜海底上的内波-波相互作用。导出的方程的特点是各向同性和双向传播，这是缺乏广泛使用的Kadomtsev-Petviashvili方程。事实上，这些差异证实了截断的内部孤立波的衍射和部分弯曲的孤立波的演变的数值结果。然而，修正的Benney-Luke方程的数值结果与原始方程的数值结果之间的良好的一致性证实了我们的简化模型的有效性。由于在一个现实的海洋环境中的分层通常是连续的，在这里使用的尖锐的密度不连续的假设相反，以保持运动学上的等效性，分层方案，用于确定从连续分层的每一层的密度和厚度。此外，偶尔观察到的，但很少检查X形的内部波-波相互作用的特征新颖的波图案，地形效应调制的传播速度，振幅和波形。
Abstract In the context of three-dimensional oceanic internal waves, taking topographic effects into account, a modified Benney–Luke equation is proposed for describing internal wave–wave interactions on a sloping bottom. The derived equation is characterised by isotropy and bi-directional propagation, which are absent in the widely used Kadomtsev–Petviashvili equation. Indeed, these disparities are confirmed by numerical results of the diffraction of a truncated internal solitary wave and the evolution of a partially bent solitary wave. However, a good agreement between the numerical results of the modified Benney–Luke equation and those of the primitive equations confirms the validity of our simplified model. Because the stratification in a realistic ocean environment is usually continuous, in contrast to the assumption of a sharp density discontinuity used here, to maintain the kinematical equivalence, a layering scheme for determining the density and thickness of each layer from a continuous stratification is proposed. In addition, the occasionally observed but rarely examined X-shaped internal wave–wave interactions are shown to feature novel wave patterns, where topographic effects modulate the propagation speed, amplitude and waveform.