eprintid: 10128322
rev_number: 19
eprint_status: archive
userid: 608
dir: disk0/10/12/83/22
datestamp: 2021-05-21 09:32:33
lastmod: 2021-11-21 07:10:20
status_changed: 2021-05-21 09:32:33
type: article
metadata_visibility: show
creators_name: Crowe, M
creators_name: Kemp, C
creators_name: Johnson, E
title: The decay of Hill's vortex in a rotating flow
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
abstract: Hill's vortex is a classical solution of the incompressible Euler equations which consists of an axisymmetric spherical region of constant vorticity matched to an irrotational external flow. This solution has been shown to be a member of a one-parameter family of steady vortex rings and as such is commonly used as a simple analytic model for a vortex ring. Here, we model the decay of a Hill's vortex in a weakly rotating flow due to the radiation of inertial waves. We derive analytic results for the modification of the vortex structure by rotational effects and the generated wave field using an asymptotic approach where the rotation rate, or inverse Rossby number, is taken to be small. Using this model, we predict the decay of the vortex speed and radius by combining the flux of vortex energy to the wave field with the conservation of peak vorticity. We test our results against numerical simulations of the full axisymmetric Navier–Stokes equations.
date: 2021-07-25
date_type: published
publisher: Cambridge University Press
official_url: https://doi.org/10.1017/jfm.2021.386
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1865737
doi: 10.1017/jfm.2021.386
lyricists_name: Crowe, Matthew
lyricists_name: Johnson, Edward
lyricists_id: MNCRO25
lyricists_id: ERJOH80
actors_name: Crowe, Matthew
actors_id: MNCRO25
actors_role: owner
full_text_status: public
publication: Journal of Fluid Mechanics
volume: 919
article_number: A6
citation:        Crowe, M;    Kemp, C;    Johnson, E;      (2021)    The decay of Hill's vortex in a rotating flow.                   Journal of Fluid Mechanics , 919     , Article A6.  10.1017/jfm.2021.386 <https://doi.org/10.1017/jfm.2021.386>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10128322/1/main_accepted.pdf