The stability and overturning of fully three-dimensional internal gravity wave packets is examined for a rotating, uniformly stratified Boussinesq fluid that is stationary in the absence of waves. We derive through perturbation theory an integral expression for the mean flow induced by upward-propagating fully localized wave packets subject to Coriolis forces. This induced Bretherton flow manifests as a dipolelike recirculation about the wave packet in the horizontal plane. We perform numerical simulations of fully localized wave packets with the predicted Bretherton flow superimposed, for a range of initial amplitudes, wave-packet aspect ratios, and relative vertical wave numbers spanning the hydrostatic and nonhydrostatic regimes. Results are compared with predictions based on linear theory of wave breaking due to overturning, convection, self-acceleration, and shear instability. We find that nonhydrostatic wave packets tend to destabilize due to self-acceleration, eventually overturning although the initial amplitude is well below the overturning amplitude predicted by linear theory. Strongly hydrostatic waves, propagating almost entirely in the horizontal, are found not to attain amplitudes sufficient to become shear unstable, overturning instead due to localized steepening of isopycnals. Results are discussed in the broader context of previous studies of one- and two-dimensional wave packets overturning and recent observations of oceanic internal waves.

中文翻译：

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具有旋转的三维Boussinesq波包的传播和倾覆

对于旋转的，均匀分层的Boussinesq流体，检查了完整三维内部重力波包的稳定性和倾覆性，该流体在没有波的情况下是静止的。我们通过微扰理论推导了受科里奥利力作用的向上传播的完全局域波包所引起的平均流量的积分表达式。这种引起的布雷瑟顿流表现为围绕水平面中波包的偶极子状再循环。对于覆盖整个静水力和非静水力状态的一系列初始振幅，波包纵横比和相对垂直波数，我们对带有预测的布雷瑟顿流量的全局部波包进行了数值模拟。将结果与基于基于倾覆，对流的波浪破碎的线性理论的预测进行比较，自加速和剪切不稳定。我们发现非静水波包由于自身加速而趋于不稳定，尽管初始振幅远低于线性理论预测的倾覆振幅，但最终会倾覆。人们发现几乎完全在水平方向传播的强静水波的振幅不足以使剪切变得不稳定，而是由于等渗管的局部变陡而倾覆。在先前对一维和二维波包倾覆的研究以及最近对海洋内波的观测中，对结果进行了更广泛的讨论。尽管初始幅度远低于线性理论预测的翻转幅度，但最终还是会翻转。人们发现几乎完全在水平方向传播的强静水波的振幅不足以使剪切变得不稳定，而是由于等位面的局部变陡而倾覆。在先前对一维和二维波包倾覆的研究以及最近对海洋内波的观测中，对结果进行了更广泛的讨论。尽管初始幅度远低于线性理论预测的翻转幅度，但最终还是会翻转。人们发现几乎完全在水平方向传播的强静水波的振幅不足以使剪切变得不稳定，而是由于等渗管的局部变陡而倾覆。在先前对一维和二维波包倾覆的研究以及最近对海洋内波的观测中，对结果进行了更广泛的讨论。