In a linearly stratified fluid, two sets of resonant triads with one member in common, hence coupled, can arise for a wide range of wave numbers where all five waves travel in the same direction. The nonlinear dynamics is investigated by deriving the evolution equations of slowly varying wave packets. The dependence of the interaction coefficients on the channel depth and the buoyancy frequency are explicitly demonstrated. Coupling may produce instabilities with growth rates bigger than those displayed by either triad in isolation. Similar properties are expected for layered fluids with shear currents. By drawing on a recent link between modulation instability and the occurrence of rogue waves, surprisingly large displacements in the interior of the fluid are thus more likely. For applications to oceanography, the interaction coefficients of the evolution equations will affect the magnitude of the actual amplitude of an internal rogue wave. Computations indicate that displacements much larger than those of surface rogue waves are possible. From a more theoretical perspective of wave resonance through the Madelung representation, special ranges of dynamical phase angles are identified for the existence of time invariants. Finally, numerical simulations of a simplified system are performed to highlight the spontaneous generation of modes due to coupling.

中文翻译：

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内波动力学中的耦合三重轴：使用线性分层流体的案例研究

在线性分层的流体中，对于大范围的波数，所有五个波都沿相同方向传播，因此会出现两组共振三单元组，其中一个具有相同的成员，因此耦合在一起。通过推导缓慢变化的波包的演化方程来研究非线性动力学。相互作用系数对通道深度和浮力频率的依赖性得到了明确证明。耦合可能会产生不稳定性，其增长率会大于两个黑社会孤立显示的增长率。对于具有剪切电流的层状流体，期望具有类似的特性。通过利用调制不稳定性和流氓波的发生​​之间的最新联系，流体内部的大位移可能因此变得出乎意料。对于海洋学的应用，演化方程的相互作用系数将影响内部流氓波的实际振幅的大小。计算表明，比表面流浪大得多的位移是可能的。从通过马德隆表示法产生的共振的更理论的角度来看，可以确定存在时间不变性的动态相位角的特殊范围。最后，执行简化系统的数值模拟以突出由于耦合而自发产生的模式。对于时不变性的存在，确定了动态相位角的特殊范围。最后，执行简化系统的数值模拟以突出由于耦合而自发产生的模式。对于时不变性的存在，确定了动态相位角的特殊范围。最后，执行简化系统的数值模拟以突出由于耦合而自发产生的模式。