A line vortex in a two-fluid system

This paper considers the classical problem of a line vortex in planar flow of a fluid. However, an interface is present at some finite radius from the line vortex, and beyond that is a second fluid of different density. The interface is therefore subject to shearing-type instabilities and may overtu...

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Bibliographic Details
Published in:Journal of engineering mathematics Vol. 84; no. 1; pp. 181 - 199
Main Authors: Forbes, Lawrence K., Cosgrove, Jason M.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.02.2014
Subjects:
Applications of Mathematics
Computational fluid dynamics
Computational Mathematics and Numerical Analysis
Density
Filtering
Fluid flow
Fluids
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Spectral methods
Theoretical and Applied Mechanics
Vortices
Boussinesq approximation
Fluid interface
Interfacial roll-up
Line vortex
Spectral methods
Curvature singularity
ISSN:0022-0833, 1573-2703
Online Access:Get full text
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Summary:This paper considers the classical problem of a line vortex in planar flow of a fluid. However, an interface is present at some finite radius from the line vortex, and beyond that is a second fluid of different density. The interface is therefore subject to shearing-type instabilities and may overturn as time progresses. A linearized inviscid theory is developed and reveals unstable behaviours, dependent on the parameters in the system. The non-linear inviscid problem is solved by a spectral method, and high-frequency modes are regularized by a type of filtering. In addition, a Boussinesq viscous model is presented and allows the overturning interface to fold. Results are discussed and compared with the predictions of the inviscid theory.
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ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-012-9606-5