Lagrangian filtering for wave–mean flow decomposition

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

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