A generalized stability criterion for resonant triad interactions
A generalized stability criterion for resonant triad interactions
复制标题
共振三元组相互作用的广义稳定性准则
DOI：
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发表时间：
1996
影响因子：
3.7
通讯作者：
H. Segur
中科院分区：
文献类型：
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作者：
Carson C. Chow;D. Henderson;H. Segur
众所周知，在任何允许共振三波相互作用的保守系统中，如果参与单个三波的均匀（测试）波列在三波中具有最高频率，则它是不稳定的，否则是中性稳定的。我们表明，这一结果的变化显着耦合的三合会的存在下：与耦合，测试波可以是不稳定的高频扰动。耦合将能量从（弱）高频源发送到特定的低频波中，即使它们最初的振幅为零，这些低频波也会增长。因此，该机制从可用于三元相互作用的低频波的频谱中选择这些低频波。此外，不稳定性持续存在的弱阻尼，提供的波幅超过两个阈值。首先，试验波列的初始振幅必须足够大，以使不稳定性控制阻尼。其次，高频扰动的（小的）初始振幅必须超过阈值，以便低频波增长到规定的振幅。
It is well known that in any conservative system that admits resonant triad interactions, a uniform (test) wavetrain that participates in a single triad is unstable if it has the highest frequency in the triad, and neutrally stable otherwise. We show that this result changes significantly in the presence of coupled triads: with coupling, the test wave can be unstable to a high-frequency perturbation. The coupling sends energy from the (weak) high-frequency source into particular low-frequency waves that grow even though they had zero amplitudes initially. This mechanism thereby selects these low-frequency waves from the spectrum of low-frequency waves available for triad interactions. Moreover, the instability persists in the presence of weak damping, provided the wave amplitudes exceed two thresholds. First, the initial amplitude of the test wavetrain must be large enough for the instability to dominate the damping. Secondly, the (small) initial amplitudes of the high-frequency perturbations must exceed a threshold in order for the low-frequency waves to grow to a prescribed amplitude.