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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 It\u00f4, Stratonovich, or a limit of Wong\u2013Zakai type. We examine this comparison in the wider context of discretizing stochastic differential equations with and without the L\u00e9vy 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 L\u00e9vy 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\u2013Zakai anomaly are physically motivated as arising due to correlations from a fast and mean scale fluid decomposition.<\/jats:p>","DOI":"10.1137\/24m1637271","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T04:01:11Z","timestamp":1741838471000},"page":"836-893","source":"Crossref","is-referenced-by-count":0,"title":["L\u00e9vy Areas, Wong\u2013Zakai Anomalies in Diffusive Limits of Deterministic Lagrangian Multitime Dynamics"],"prefix":"10.1137","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-9338-1620","authenticated-orcid":true,"given":"Theo","family":"Diamantakis","sequence":"first","affiliation":[{"name":"Department of Mathematics, Imperial College London, London, SW7 2AZ, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Woodfield","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Imperial College London, London, SW7 2AZ, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112078002773"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2425103"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.5802\/aif.233"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1998)055<0477:TBEOAO>2.0.CO;2"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1175\/JPO-D-19-0164.1"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/0134036"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.3934\/fods.2023011"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1214\/21-AIHP1203","volume":"58","author":"Chevyrev I.","year":"2022","journal-title":"Ann. 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