arXiv subjects

Lois E. Baker

Publications and source records attributed to Lois E. Baker.

3 recordsLinked to original sources

arXiv2026

Volume-preserving Lagrangian averaging using polar factorization

The generalised Lagrangian mean (GLM) theory of Andrews & McIntyre provides a powerful framework to study the interactions between waves and flows. A drawback of this theory is that the Lagrangian mean velocity is divergent even for incompressible fluids because the mean flow map, which sends the Lagrangian labels of fluid parcels to their mean positions, does not preserve volume. This results, for instance, in vortices shrinking under Lagrangian averaging. We overcome this drawback by revising the definition of the mean flow map, choosing it as the volume-preserving map closest to the "bare" GLM mean map. A standard result of optimal-transport theory then shows that the new mean map is the volume-preserving factor in the polar factorization of the GLM mean map. We develop and implement a numerical method for the computation of the corresponding Lagrangian mean fields from simulation data. The implementation builds on recently developed algorithms for the on-the-fly computation of Lagrangian means using the exponential and Butterworth filters. We demonstrate the value of volume-preserving Lagrangian averaging in simulations of the two-dimensional incompressible and shallow-water models. We compare the Lagrangian-mean fields obtained with and without the volume-preservation constraint.

physics.flu-dyn↗

arXiv2025

Lagrangian filtering for wave-mean flow decomposition

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 Poincaré waves.

physics.flu-dyn↗

arXiv2024

Efficient Lagrangian averaging with exponential filters

Lagrangian averaging is a valuable tool for the analysis and modelling of multiscale processes in fluid dynamics. The numerical computation of Lagrangian (time) averages from simulation data is challenging, however. It can be carried out by tracking a large number of particles or, following a recent approach, by solving a dedicated set of partial differential equations (PDEs). Both approaches are computationally demanding because they require an entirely new computation for each time at which the Lagrangian mean fields are desired. We overcome this drawback by developing a PDE-based method that delivers Lagrangian mean fields for all times through the single solution of evolutionary PDEs. This allows for an on-the-fly implementation, in which Lagrangian averages are computed along with the dynamical variables. This is made possible by the use of a special class of temporal filters whose kernels are sums of exponential functions. We focus on two specific kernels involving one and two exponential functions. We implement these in the rotating shallow-water model and demonstrate their effectiveness at filtering out large-amplitude Poincaré waves while retaining the salient features of an underlying slowly evolving turbulent flow.

physics.flu-dyn↗