  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.
