Show simple item record

dc.contributor.authorProtas, Bartosz
dc.contributor.authorElcrat, Alan R.
dc.identifier.citationBartosz Protas and Alan Elcrat (2016). Linear stability of Hill’s vortex to axisymmetric perturbations. Journal of Fluid Mechanics, 799, pp 579-602en_US
dc.descriptionClick on the DOI link to access the article (may not be free).en_US
dc.description.abstractWe consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape differentiation to the contour dynamics formulation of the problem in a three-dimensional axisymmetric geometry. This approach allows us to systematically account for the effect of boundary deformations on the linearized evolution of the vortex under the constraint of constant circulation. The resulting singular integro-differential operator defined on the vortex boundary is discretized with a highly accurate spectral approach. This operator has two unstable and two stable eigenvalues complemented by a continuous spectrum of neutrally stable eigenvalues. By considering a family of suitably regularized (smoothed) eigenvalue problems solved with a range of numerical resolutions, we demonstrate that the corresponding eigenfunctions are in fact singular objects in the form of infinitely sharp peaks localized at the front and rear stagnation points. These findings thus refine the results of the classical analysis by Moffatt & Moore.en_US
dc.description.sponsorshipNSERC (Canada) Discovery grant.en_US
dc.publisherCambridge University Pressen_US
dc.relation.ispartofseriesJournal of Fluid Mechanics;v.799
dc.subjectComputational methodsen_US
dc.subjectMathematical foundationsen_US
dc.subjectVortex instabilityen_US
dc.titleLinear stability of Hill's vortex to axisymmetric perturbationsen_US
dc.rights.holder© 2016 Cambridge University Pressen_US

Files in this item


There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record