Altmetric

Multipole Vortex Blobs (MVB): Symplectic Geometry and Dynamics

File Description SizeFormat 
Holm-Jacobs2017_Article_MultipoleVortexBlobsMVBSymplec.pdfPublished version1.99 MBAdobe PDFView/Open
Title: Multipole Vortex Blobs (MVB): Symplectic Geometry and Dynamics
Authors: Holm, DD
Jacobs, HO
Item Type: Journal Article
Abstract: Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article, we observe that the dynamics need not be trivial if one is willing to consider distributional derivatives of Dirac delta functionals as valid vorticity distributions. More specifically, a new singular vortex theory is presented for regularized Euler fluid equations of ideal incompressible flow in the plane. We determine the conditions under which such regularized Euler fluid equations may admit vorticity singularities which are stronger than delta functions, e.g., derivatives of delta functions. We also describe the symplectic geometry associated with these augmented vortex structures, and we characterize the dynamics as Hamiltonian. Applications to the design of numerical methods similar to vortex blob methods are also discussed. Such findings illuminate the rich dynamics which occur below the regularization length scale and enlighten our perspective on the potential for regularized fluid models to capture multiscale phenomena.
Issue Date: 1-Jun-2017
Date of Acceptance: 18-Dec-2016
URI: http://hdl.handle.net/10044/1/63163
DOI: https://dx.doi.org/10.1007/s00332-017-9367-4
ISSN: 0938-8974
Publisher: Springer Verlag
Start Page: 973
End Page: 1006
Journal / Book Title: Journal of Nonlinear Science
Volume: 27
Issue: 3
Copyright Statement: © 2017 The Author(s). Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: 267382
Keywords: Science & Technology
Physical Sciences
Technology
Mathematics, Applied
Mechanics
Physics, Mathematical
Mathematics
Physics
Vortex blob methods
Singular momentum maps
Regularized Euler fluid equations
Hamiltonian dynamics
SINGULARITIES
CONVERGENCE
EQUATIONS
VORTICES
MOTION
SIMULATIONS
DIMENSIONS
MERGER
FLUIDS
FLOW
physics.flu-dyn
math.DS
math.SG
0102 Applied Mathematics
Fluids & Plasmas
Publication Status: Published
Online Publication Date: 2017-03-16
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commonsx