基于拉格朗日分析法的中尺度涡精细三维结构研究及其误差估计

在前人的工作中，拉格朗日分析法被用来演示大尺度环流，同时拉格朗日拟序结构可以较好的演示中尺度涡两维结构的发展过程。然而，很少研究关注怎么利用拉格朗日分析法针对中尺度涡三维结构进行演示。与以往利用欧拉方法研究中尺度涡三维结构的工作不同，我们利用拉格朗日分析法，从另一个视角来研究涡旋结构。我们在海山上方模拟出一个理想的气旋涡，涡旋内的下沉流和涡旋旁的上升流形成一个闭合的环流。这种结构很难从欧拉角度来演示。然而，粒子的运动轨迹很好地展示了整个循环:流体在涡旋中旋转下沉，汇聚到底层的上升流区，并通过上升流返回到海表面。我们也将拉格朗日分析法应用于真实的模拟结果中。作为中国南海的一个重要现象，靠近越南中部的海域中的偶极子（反气旋涡/气旋涡），关于其结构的研究已经比较成熟了，但这些研究主要关注的是海面过程。通过拉格朗日分析，我们很好的演示了偶极子的三维结构:流体在反气旋涡(气旋涡)内部旋转上升(下沉)。更重要的是，粒子的轨迹表明，这两个涡旋之间不存在水团交换，因为强边界急流将它们彼此分开。以上结论均得到了计算误差估计的可信度支持。尽管在强辐散流和强垂直扩散流中，计算误差逐渐增大，但是在一定的时间步长和积分周期内，计算误差始终保持在一个较小的值。

Demonstration of the refined three-dimensional structure of mesoscale eddies and computational error estimates via Lagrangian analysis

In previous studies, Lagrangian analyses were used to assess large-scale ocean circulation, and the Lagrangian coherent structure could also reveal the evolution of the two-dimensional structure of the mesoscale eddies. However, few studies have demonstrated the three-dimensional structure of the mesoscale eddies via Lagrangian analysis. Compared with previous studies, which investigated the eddy structure via a Eulerian view, we used a Lagrangian view to provide a different perspective to study the eddy structure. An idealized cyclonic mesoscale eddy is built up over a seamount, and it presents downwelling inside the eddy and upwelling alongside the eddy formed within a closed circulation system. This structure is difficult to display via a Eulerian analysis. However, the trajectories of particles can well demonstrate the full cycle: the fluid sank and rotated inside the eddies, converged to the upwelling zone of the bottom layer and returned to the surface through upwelling. We also applied a Lagrangian analysis to a realistic simulation. As a significant phenomenon in the South China Sea, the dipole structure of the anticyclonic eddy (AE)/cyclonic eddy (CE) pair off of central Vietnam has been well studied but mainly at the sea surface. With a Lagrangian analysis, we illustrate the three-dimensional structure of the eddy pair: the fluid sank (rose) and rotated inside the AE (CE). More importantly, the trajectories of the particles suggested that there was no fluid exchange between the two eddies since the strong boundary jet separates them from each other. All the conclusions above have been verified and are supported by the computational error estimate. With a selected time step and integral period, the computational errors always present small values, although they increase with strong divergent and vertical diffusive flow.