Vortex ring models

Ionut Danaila, F. Kaplanski, Sergei Sazhin

Research output: Book/ReportBook - authoredpeer-review


The book offers a guide to understanding models of vortex rings, starting from classical ones (circular vortex filament, Hill and Norbury-Fraenkel inviscid models) to very recent models incorporating viscous effects and realistic shapes of the vortex core. Unconfined and confined viscous vortex rings are described by closed formulae for vorticity, stream function, translational velocity, energy, impulse and circulation. Models are applied to predict the formation number of optimal vortex rings and to describe two-phase vortex ring-like structures generated in internal combustion engines. The text provides a detailed presentation of analytical developments of models, backed-up by illustrations and systematic comparisons with results of direct numerical simulations. The book may be used by graduate students in applied mathematics, engineering and physical sciences. It could be a useful reference for researchers and practising engineers interested in modelling flows with vortex rings.
Original languageEnglish
Number of pages180
ISBN (Electronic)9783030681500
ISBN (Print)9783030681494
Publication statusPublished - 11 Apr 2021

Publication series

NameMathematical Engineering
ISSN (Print)2192-4732


  • Vortex rings
  • mathematical models


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