The Lagrangian-mean motion of fluid particles induced by horizontally localized small-amplitude wavepackets of vertically trapped inertia–gravity waves is computed analytically, at second order in wave amplitude, and the results are supported by direct nonlinear numerical simulations. The leading-order motion is assumed to be inertia–gravity waves, which is applicable to oceanic mesoscale flows in regions where wave activity is as strong as or stronger than the balanced flow. The analytical computation is based on time-dependent asymptotic wave–mean interaction theory, and the numerical simulation uses a Galerkin-truncated $f$ -plane nonlinear hydrostatic Boussinesq model that retains the barotropic mode and two baroclinic modes (vertical wavenumbers 0, $m$ and $2m$ ), this being the minimal set on which consistent wave–mean interactions can take place. Two novel dynamical effects are revealed: First, we find that the barotropic component robustly dominates the Lagrangian-mean flow response, which is contrary to earlier findings for the same problem. Second, we discovered a new wavepacket regime in which the baroclinic mean-flow response consists of the persistent radiation of resonantly forced secondary internal waves. The latter effect occurs in an oceanically accessible parameter regime.

中文翻译：

---

垂直限制域中惯性-重力波引起的平均流动

由垂直捕获的惯性重力波的水平局部小振幅波包引起的流体粒子的拉格朗日平均运动在波幅的二阶进行解析计算，结果得到直接非线性数值模拟的支持。假设先导运动为惯性重力波，适用于波浪活动与平衡流一样强或强于平衡流的区域的海洋中尺度流。解析计算基于时间相关的渐近波-平均相互作用理论，数值模拟使用伽辽金截断的 $f$ 平面非线性流体静力 Boussinesq 模型，该模型保留了正压模式和两个斜压模式（垂直波数 0，$m美元和 200 万美元），这是可以发生一致波均值相互作用的最小集合。揭示了两个新的动力学效应：首先，我们发现正压分量在拉格朗日平均流量响应中占主导地位，这与同一问题的早期发现相反。其次，我们发现了一种新的波包机制，其中斜压平均流响应由共振强迫二次内波的持续辐射组成。后一种效应发生在海洋可及的参数范围内。我们发现了一种新的波包机制，其中斜压平均流量响应由共振强迫二次内波的持续辐射组成。后一种效应发生在海洋可及的参数范围内。我们发现了一种新的波包机制，其中斜压平均流量响应由共振强迫二次内波的持续辐射组成。后一种效应发生在海洋可及的参数范围内。