Lévy areas, Wong–Zakai anomalies in diffusive limits of deterministic Lagrangian multitime dynamics
File(s)
Accepted version
OA Location
Author(s)
Diamantakis, Theo
Woodfield, James
Type
Journal Article
Abstract
Stochastic modeling necessitates an interpretation of noise. In this paper, we describe the loss of deterministically stable behavior in a fundamental fluid mechanics problem, conditional to whether noise is introduced in the sense of Itô, Stratonovich, or a limit of Wong–Zakai type. We examine this comparison in the wider context of discretizing stochastic differential equations with and without the Lévy area. We study stochastic advection by Lie transport and its derivation from homogenization theory, which introduces drift corrections of the same class naturally. From a numerical viewpoint, we demonstrate that performing higher order discretizations with the use of a Lévy area can also lead to the loss of conserved area and angle quantities. Such behavior is not physically expected in the Stratonovich model. From the viewpoint of homogenization, the qualitative properties of the Wong–Zakai anomaly are physically motivated as arising due to correlations from a fast and mean scale fluid decomposition.
Date Issued
2025-03-31
Date Acceptance
2024-10-23
Citation
SIAM Journal on Applied Dynamical Systems, 2025, 24 (1), pp.836-893
ISSN
1536-0040
Publisher
Society for Industrial and Applied Mathematics
Start Page
836
End Page
893
Journal / Book Title
SIAM Journal on Applied Dynamical Systems
Volume
24
Issue
1
License URL
Copyright © 2025 Society for Industrial and Applied Mathematics. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
Publication Status
Published
Date Publish Online
2025-03-13