论文标题
地球模式的近乎共鸣的不稳定：超越格林斯潘定理
Near-resonant instability of geostrophic modes: beyond Greenspan's theorem
论文作者
论文摘要
我们通过数值和理论分析探索了惯性波与旋转流体中的地质模式的近谐振相互作用。当施加单个惯性波时，我们发现某些地质模式基于波数和波浪振幅，不稳定的rossby数字$ kro $以上是不稳定的。我们表明，这种不稳定是由涉及两个惯性波和地质模式的三合会相互作用引起的，因此其本特征频率的总和不是零。我们得出了这种近乎共鸣不稳定的增长率的理论量表。按全球旋转速率扩展的增长率与$ $ kro $的$（kro）^2 $成正比，并过渡到$ kro $缩放的较大$ kro $。这些量表与直接数值模拟非常吻合。这种不稳定性可以解释对波浪驱动的地质不稳定性的最新实验观察。
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.
