A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow
A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow
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DOI：
10.1017/jfm.2015.251
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发表时间：
2014-11
影响因子：
3.7
通讯作者：
Jin-Han Xie;J. Vanneste
中科院分区：
文献类型：
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作者：
Jin-Han Xie;J. Vanneste
海洋的风力作用产生了惯性重力波的频谱，在当地惯性（或科里奥利）频率附近急剧达到峰值。相应的近惯性波（NIWs）是高能量的，在海洋缓慢的大尺度动力学中起着重要作用。为了分析这一作用，我们建立了NIWs与平衡运动之间非耗散相互作用的新模型。该模型是使用广义拉格朗日均值（GLM）框架（特别是Soward & Roberts， J.流体力学的“GLM”变体）推导出来的。， vol. 661, 2010, pp. 45-72)，利用两种类型运动之间的时间尺度分离来平均短NIW期间。我们结合萨尔蒙的（J.流体机械）。基于Whitham平均的GLM变分公式，以获得控制NIWs和平均流量联合演化的方程组。假设平均流是地转平衡的，将这个系统简化为一个简单的模型，将Young和Ben Jelloul的NIWs方程（J. Mar. Res., vol. 55, 1997, pp. 735-766）与一个修正的准地转（QG）方程耦合在一起。在该耦合模式中，平均气流通过平流和折射作用影响低场气旋；相反，NIWs通过二次波项修正位涡（PV）反演（平流PV与平流平均速度之间的关系）来影响平均流动，这与b<s:1> hler & McIntyre （J.流体力学）的GLM结果一致。，第354卷，1998，第301-343页)。耦合模型是哈密顿的，其守恒定律，特别是波浪作用和能量，证明了启动性：在此基础上，我们确定了一种新的相互作用机制，即在大尺度上被迫的NIWs从平衡流中提取能量，因为它们的水平尺度被微分平流和折射减小，从而使它们的势能增加。粗略估计，这种机制可以为中尺度运动提供一个重要的能量汇，并在海洋的全球能量学中发挥作用。推导了理想的二维模型，并进行了数值模拟，以深入了解niw -平均流量相互作用过程。对一维正压急流的模拟演示了在风的作用下，NIWs如何在向海洋内部传播时减慢急流的速度。一个假设垂直方向上的平面移动NIWs的模拟显示了涡旋偶极子是如何被NIWs偏转的，说明了相互作用的不可逆性质。在这两种模拟中，能量都是从平均流转移到小流。
Wind forcing of the ocean generates a spectrum of inertia–gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) are highly energetic and play a significant role in the slow, large-scale dynamics of the ocean. To analyse this role, we develop a new model of the non-dissipative interactions between NIWs and balanced motion. The model is derived using the generalised-Lagrangian-mean (GLM) framework (specifically, the ‘glm’ variant of Soward & Roberts, J. Fluid Mech., vol. 661, 2010, pp. 45–72), taking advantage of the time-scale separation between the two types of motion to average over the short NIW period. We combine Salmon’s (J. Fluid Mech., vol. 719, 2013, pp. 165–182) variational formulation of GLM with Whitham averaging to obtain a system of equations governing the joint evolution of NIWs and mean flow. Assuming that the mean flow is geostrophically balanced reduces this system to a simple model coupling Young & Ben Jelloul’s (J. Mar. Res., vol. 55, 1997, pp. 735–766) equation for NIWs with a modified quasi-geostrophic (QG) equation. In this coupled model, the mean flow affects the NIWs through advection and refraction; conversely, the NIWs affect the mean flow by modifying the potential-vorticity (PV) inversion – the relation between advected PV and advecting mean velocity – through a quadratic wave term, consistent with the GLM results of Bühler & McIntyre (J. Fluid Mech., vol. 354, 1998, pp. 301–343). The coupled model is Hamiltonian and its conservation laws, for wave action and energy in particular, prove illuminating: on their basis, we identify a new interaction mechanism whereby NIWs forced at large scales extract energy from the balanced flow as their horizontal scale is reduced by differential advection and refraction so that their potential energy increases. A rough estimate suggests that this mechanism could provide a significant sink of energy for mesoscale motion and play a part in the global energetics of the ocean. Idealised two-dimensional models are derived and simulated numerically to gain insight into NIW–mean-flow interaction processes. A simulation of a one-dimensional barotropic jet demonstrates how NIWs forced by wind slow down the jet as they propagate into the ocean interior. A simulation assuming plane travelling NIWs in the vertical shows how a vortex dipole is deflected by NIWs, illustrating the irreversible nature of the interactions. In both simulations energy is transferred from the mean flow to the NIWs.