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Lagrangian filtering for wave–mean flow decomposition

Baker, Lois E.; Kafiabad, Hossein A.; Maitland-Davies, Cai; Vanneste, Jacques

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Authors

Lois E. Baker

Jacques Vanneste



Abstract

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 & Vanneste (2023, Computing Lagrangian means, J. Fluid Mech., vol. 960, A36) 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 Kafiabad & Vanneste to develop a flexible, on-the-fly, partial differential equation-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.

Citation

Baker, L. E., Kafiabad, H. A., Maitland-Davies, C., & Vanneste, J. (2025). Lagrangian filtering for wave–mean flow decomposition. Journal of Fluid Mechanics, 1009, Article A40. https://doi.org/10.1017/jfm.2025.42

Journal Article Type Article
Acceptance Date Dec 24, 2024
Online Publication Date Apr 23, 2025
Publication Date Apr 25, 2025
Deposit Date Apr 30, 2025
Publicly Available Date May 14, 2025
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 1009
Article Number A40
DOI https://doi.org/10.1017/jfm.2025.42
Public URL https://durham-repository.worktribe.com/output/3806425

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