A weakly nonlinear time-dependent theory for the evolution of superharmonics generated by the nonlinear self-interaction of a mode-1 internal tide in non-uniform stratification is developed and compared to numerical simulations. The forcing by the internal tide is found to excite near-pure mode-1 superharmonics whose natural frequency is moderately different from twice the internal tide frequency. Consequently, the superharmonics undergo a slow periodic growth and decay that is comparable to an acoustic ‘beat’. At low latitudes the beat frequency is smaller and the superharmonics can grow to larger amplitude, allowing for the possibility of a superharmonic cascade.

中文翻译：

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非均匀分层中内部潮汐激发的超谐波演化

开发了一种弱非线性时间相关理论，用于非均匀分层中模式 1 内部潮汐的非线性自相互作用产生的超谐波演化，并与数值模拟进行比较。发现内部潮汐的强迫激发了近纯模式 1 超谐波，其固有频率与内部潮汐频率的两倍略有不同。因此，超谐波经历了缓慢的周期性增长和衰减，类似于声学“节拍”。在低纬度地区，拍频更小，超谐波可以增长到更大的幅度，从而产生超谐波级联的可能性。