Lagrangian filtering for wave–mean flow decomposition

• Published in: Journal of fluid mechanics Vol. 1009
• Main Authors: Baker, Lois E., Kafiabad, Hossein A., Maitland-Davies, Cai, Vanneste, Jacques
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 23.04.2025
• Subjects: JFM Notebooks; JFM Papers; wave-turbulence interactions; waves in rotating fluids; internal waves
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2025.42

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.