Abstract—

The hydrodynamic system that admits the development of internal wave attractors under biharmonic forcing is investigated. It is shown that in the case of low amplitude of external forcing the wave pattern consists of two attractors that interact between themselves only slightly: the total energy of the system is equal to the sum of energies of the components with high accuracy. In the nonlinear case the attractors interact in the more complex way which leads to the development of a cascade of triad interactions generating a rich set of time scales. In the case of closely adjacent frequencies of the components of a biharmonic perturbation, the nonlinear “beating” regime develops, namely, the mean energy of the system of coupled attractors performs oscillations at a large time scale that corresponds to the beating period. It is found that the high-frequency energy fluctuations corresponding to the same mean energy can differ by an order of magnitude depending on whether the envelope of the mean value increases or decreases.

中文翻译：

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内引力波的双调和吸引子

摘要——

研究了在双调和力作用下允许内波吸引子发展的水动力系统。结果表明，在外力幅度较小的情况下，波形由两个吸引子组成，它们之间只有轻微的相互作用：系统的总能量等于高精度组件的能量总和。在非线性情况下，吸引子以更复杂的方式相互作用，这导致产生一系列丰富的时间尺度的三元相互作用级联的发展。在双谐波扰动分量的频率非常接近的情况下，非线性“搏动”状态发展，即耦合吸引子系统的平均能量在对应于搏动周期的大时间尺度上进行振荡。