平面惯性波三元共振不稳定性的三维性
Three-dimensionality of the triadic resonance instability of a plane inertial wave
摘要：
本文从理论和实验上分析了旋转流体中平面惯性波的三向共振不稳定性。建立在经典的三元螺旋模式之间的相互作用方程，我们通过数值积分，TRI的最大增长率被发现的二次波，不传播在同一个垂直平面的主波（旋转轴平行于垂直）。在无粘极限，我们证明了这一结果分析，在这种情况下，在水平传播方向的变化引起的TRI演变从$60^\circ$到$90^\circ$取决于频率的主要波。由于一个波发生器与一个大的空间延伸在水平方向上的不变性的强迫波，我们能够报告的实验证据表明，TRI的平面惯性波是三维的。由TRI产生的二次波的波矢示出匹配的最大增长率准则的基础上的理论预测。这些结果表明，惯性波之间的三元共振相互作用在垂直于旋转轴的水平面中重新分配能量是非常有效的。
英文摘要：
We analyze theoretically and experimentally the triadic resonance instability (TRI) of a plane inertial wave in a rotating fluid. Building on the classical triadic interaction equations between helical modes, we show by numerical integration that the maximum growth rate of the TRI is found for secondary waves that do not propagate in the same vertical plane as the primary wave (the rotation axis is parallel to the vertical). In the inviscid limit, we prove this result analytically, in which case the change in the horizontal propagation direction induced by the TRI evolves from $60^\circ$ to $90^\circ$ depending on the frequency of the primary wave. Thanks to a wave generator with a large spatial extension in the horizontal direction of invariance of the forced wave, we are able to report experimental evidence that the TRI of a plane inertial wave is three-dimensional. The wavevectors of the secondary waves produced by the TRI are shown to match the theoretical predictions based on the maximum growth rate criterion. These results reveal that the triadic resonant interactions between inertial waves are very efficient at redistributing energy in the horizontal plane, normal to the rotation axis.
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