用于波-平均流分解的拉格朗日滤波
Lagrangian filtering for wave-mean flow decomposition
AI总结：
针对波分辨数值模拟中波与平均流难以分离的问题，本研究改编KV23方法，利用任意卷积滤波器开发了一种灵活、即时、基于PDE的拉格朗日滤波方法，成功从非线性模拟中干净地恢复了波场。
摘要：
地球物理流动通常由具有大范围重叠时间尺度的波动和平均运动组成，这使得在波分辨数值模拟中分离这两类运动极具挑战性。拉格朗日滤波——即在流动参考系中应用时间滤波器——是克服这一挑战的有效方法，它允许基于拉格朗日参考系中的频率分离，将波动与平均流干净地分离开来。以往的拉格朗日滤波实现采用了粒子追踪方法，这会带来巨大的内存需求或粒子聚集方面的困难。Kafiabad和Vanneste（2023，KV23）最近提出了一种无需粒子追踪即可寻找拉格朗日平均量的新方法，该方法通过求解一组偏微分方程与流动的控制方程来实现。在本研究中，我们改编了KV23的方法，利用任意卷积滤波器开发了一种灵活的、即时（on-the-fly）的、基于PDE的拉格朗日滤波方法。我们展示了多种不同的波-平均分解，证明了我们的拉格朗日方法能够从地转湍流与Poincaré波相互作用的非线性模拟中恢复出干净的波场。
英文摘要：
Geophysical flows are typically composed of wave and mean motions with a wide range of overlapping temporal scales, making separation between the two types of motion in wave-resolving numerical simulations challenging. Lagrangian filtering - whereby a temporal filter is applied in the frame of the flow - is an effective way to overcome this challenge, allowing clean separation of waves from mean flow based on frequency separation in a Lagrangian frame. Previous implementations of Lagrangian filtering have used particle tracking approaches, which are subject to large memory requirements or difficulties with particle clustering. Kafiabad and Vanneste (2023, KV23) recently proposed a novel method for finding Lagrangian means without particle tracking by solving a set of partial differential equations alongside the governing equations of the flow. In this work, we adapt the approach of KV23 to develop a flexible, on-the-fly, PDE-based method for Lagrangian filtering using arbitrary convolutional filters. We present several different wave-mean decompositions, demonstrating that our Lagrangian methods are capable of recovering a clean wave-field from a nonlinear simulation of geostrophic turbulence interacting with Poincaré waves.
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