地转模的近共振不稳定性：超越格林斯潘定理
Near-resonant instability of geostrophic modes: beyond Greenspan's theorem
摘要：
通过数值和理论分析，探讨了旋转流体中惯性波与地转模的近共振相互作用。当单一惯性波作用时，我们发现某些地转模态在Rossby数$kRo$的阈值以上是不稳定的。我们表明，这种不稳定性所造成的三元相互作用，涉及两个惯性波和地转模式，使其本征频率的总和是非零的。我们推导出这种近共振不稳定性的增长率的理论比例。在低$kRo$下，由全局旋转速率缩放的增长速率与$(kRo)^2$成比例，并且对于较大的$kRo$，转变为$kRo$缩放。这些缩放与直接数值模拟非常一致。这种不稳定性可以解释最近由波驱动的地转不稳定性的实验观测。
英文摘要：
We explore the near-resonant interaction of inertial waves with geostrophic modes in rotating fluids via numerical and theoretical analysis. When a single inertial wave is imposed, we find that some geostrophic modes are unstable above a threshold value of the Rossby number $kRo$ based on the wavenumber and wave amplitude. We show this instability to be caused by triadic interaction involving two inertial waves and a geostrophic mode such that the sum of their eigen frequencies is non-zero. We derive theoretical scalings for the growth rate of this near-resonant instability. The growth rate scaled by the global rotation rate is proportional to $(kRo)^2$ at low $kRo$ and transitions to a $kRo$ scaling for larger $kRo$. These scalings are in excellent agreement with direct numerical simulations. This instability could explain recent experimental observations of geostrophic instability driven by waves.
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