Equations of motion for weakly compressible point vortices.
Philos Trans A Math Phys Eng Sci
; 380(2226): 20210052, 2022 Jun 27.
Article
in En
| MEDLINE
| ID: mdl-35527628
ABSTRACT
Equations of motion for compressible point vortices in the plane are obtained in the limit of small Mach number, M, using a Rayleigh-Jansen expansion and the method of Matched Asymptotic Expansions. The solution in the region between vortices is matched to solutions around each vortex core. The motion of the vortices is modified over long time scales [Formula see text] and [Formula see text]. Examples are given for co-rotating and co-propagating vortex pairs. The former show a correction to the rotation rate and, in general, to the centre and radius of rotation, while the latter recover the known result that the steady propagation velocity is unchanged. For unsteady configurations, the vortex solution matches to a far field in which acoustic waves are radiated. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.
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Collection:
01-internacional
Database:
MEDLINE
Language:
En
Journal:
Philos Trans A Math Phys Eng Sci
Journal subject:
BIOFISICA
/
ENGENHARIA BIOMEDICA
Year:
2022
Document type:
Article
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