Lagrangian filtering for wave-mean flow decomposition

TL;DR

This paper introduces a PDE-based Lagrangian filtering method for wave-mean flow decomposition that avoids particle tracking, enabling effective separation of waves from mean flow in complex geophysical simulations.

Contribution

It adapts a recent PDE approach to develop a flexible, on-the-fly Lagrangian filtering technique using arbitrary convolutional filters.

Findings

Successfully separates wave and mean flow in nonlinear geostrophic turbulence simulations.

Demonstrates the method's ability to recover clean wave-fields from complex flows.

Provides a versatile framework for wave-mean decomposition without particle tracking.

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 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 Poincar\'e waves.