Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
The Nvortex problem on a rotating sphere: IV. Ring configurations coupled to a background field
Title:  The Nvortex problem on a rotating sphere: IV. Ring configurations coupled to a background field 
Authors:  NEWTON, Paul K. Browse this author  SAKAJO, Takashi Browse this author 
Keywords:  Nvortex problem  rotating sphere  Background vorticity gradients  Embedded dynamical system 
Issue Date:  1Aug2006 
Publisher:  Department of Mathematics, Hokkaido University 
Journal Title:  Hokkaido University Preprint Series in Mathematics 
Volume:  797 
Start Page:  1 
End Page:  19 
Abstract:  We study the evolution of Npoint vortices in ring formation embedded in a background flowfield that initially corresponds to solidbody rotation on a sphere. The evolution of the point vortices are tracked numerically as an embedded dynamical system along with the M contours which separate strips of constant vorticity. The full system is a discretization of the Euler equations for incompressible flow on a rotating spherical shell, hence a ‘barotropic’ model of the onelayer atmosphere. We describe how the coupling creates a mechanism by which energy is exchanged between the ring and the background, which ultimately serves to breakup the structure. When the centerofvorticity vector associated with the ring is initially misaligned with the axis of rotation of the background field, it sets up the propagation of RossbyHaurwitz waves around the sphere which move retrograde to the solidbody rotation. These waves pass energy to the ring (in the case when the solidbody field and the ring initially corotate), or extract energy from the ring (when the solidbody field and the ring initially counterrotate), hence the Hamiltonian and the centerofvorticity vector associated with the Npoint vortices are no longer conserved as they are for the oneway coupled model described in Newton & Shokraneh (2006a). In the first case, energy is transferred to the ring, the length of the centerofvorticity vector increases, while its tip spirals in a clockwise manner towards the North Pole. The ring stays relatively intact for short times but ultimately breaksup on a longer timescale. In the later case, energy is extracted from the ring, the length of the centerofvorticity vector decreases while its tip spirals towards the North Pole and the ring loses its coherence more quickly than in the corotating case. The special case where the ring is initially oriented so that its centerofvorticity vector is perpendicular to the axis of rotation is also examined as it shows how the coupling to the background field breaks this symmetry. In this case, both the length of the centerofvorticity vector and the Hamiltonian energy of the ring achieve a local maximum at roughly the same time. 
Type:  bulletin (article) 
URI:  http://hdl.handle.net/2115/69605 
Appears in Collections:  理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用
