Vanon, R. and Ohkitani, K. (2018) Applications of a Cole-Hopf transform to the 3D Navier-Stokes equations. Journal of Turbulence, 19 (4). pp. 322-333. ISSN 1468-5248
Abstract
The Navier-Stokes equations written in the vector potential can be recast as the nonlinear Schr¨odinger equations at imaginary times, i.e. the heat equations with a potential term, using the Cole-Hopf transform introduced in Ohkitani(2017). On this basis, we study two kinds of Navier-Stokes flows by means of direct numerical simulations. In an experiment on vortex reconnection, it is found that the potential term takes large negative values in regions where intensive reconnection is taking place, whereas the signature of the nonlinear term is more broadly spread. For decaying turbulence starting from a random initial condition, such a correspondence is also observed in the early stage when the flow is dominated by vorticity layers. At later times, when the flow features several tubular vortices, this correspondence becomes weaker. Finally, a similar set of transformations is presented for the magnetohydrodynamic equations, which reduces them to a set of heat equations with suitable potential terms, thereby obtaining new criteria for the regularity of their solutions.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2018 Informa UK Limited, trading as Taylor & Francis Group. This is an author-produced version of a paper subsequently published in Journal of Turbulence. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Navier-Stokes equations; Cole-Hopf transform; Feynman-Kac formula; Duhamel principle |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/N022548/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 19 Jan 2018 11:08 |
Last Modified: | 10 Nov 2020 16:39 |
Status: | Published |
Publisher: | Taylor & Francis |
Refereed: | Yes |
Identification Number: | 10.1080/14685248.2018.1431395 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:126397 |