Motion of a Buoyant Vortex Patch

The motion of a two-dimensional buoyant vortex patch, i.e. a vortex patch with a uniform density different from the uniform density of the surrounding fluid, is analyzed in terms of evolution equations for the motion of its centroid, deformation of its boundary and the strength of a vortex sheet whi...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-05
Main Authors: Shashikanth, Banavara N, Rangachari Kidambi
Format: Article
Language:English
Subjects:
Buoyancy
Centroids
Deformation
Density
Evolution
Integral equations
Mathematical analysis
Vortex sheets
Vortices
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The motion of a two-dimensional buoyant vortex patch, i.e. a vortex patch with a uniform density different from the uniform density of the surrounding fluid, is analyzed in terms of evolution equations for the motion of its centroid, deformation of its boundary and the strength of a vortex sheet which is essential to enforce pressure continuity across the boundary. The equations for the centroid are derived by a linear momentum analysis and that for the sheet strength by applying Euler's equations on the boundary, while the boundary deformation is studied in the centroid-fixed frame. A complicated coupled set of equations is obtained which, to the best of our knowledge, has not been derived before. The evolution of the sheet strength is obtained as an integral equation. The equations are also examined in the limit of a patch of vanishing size or a buoyant point vortex.
ISSN:2331-8422
DOI:10.48550/arxiv.2002.01103