TY - JOUR
T1 - Localized instabilities of vortex rings with swirl
AU - Lifschitz, Alexander
AU - Hameiri, Eliezer
PY - 1993/11
Y1 - 1993/11
N2 - Axisymmetric vortex rings with swirl in an inviscid incompressible fluid are considered and it is demonstrated how the geometrical optics method can be used for investigating their stability. The evolution of rapidly oscillating initial data is studied and it is shown that the corresponding rings are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. It is shown that unbounded solutions grow either exponentially or algebraically. By means of the analysis of the corresponding transport equations effective stability conditions for general vortex rings with swirl are obtained. © 1993 John Wiley & Sons, Inc.
AB - Axisymmetric vortex rings with swirl in an inviscid incompressible fluid are considered and it is demonstrated how the geometrical optics method can be used for investigating their stability. The evolution of rapidly oscillating initial data is studied and it is shown that the corresponding rings are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. It is shown that unbounded solutions grow either exponentially or algebraically. By means of the analysis of the corresponding transport equations effective stability conditions for general vortex rings with swirl are obtained. © 1993 John Wiley & Sons, Inc.
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U2 - 10.1002/cpa.3160461005
DO - 10.1002/cpa.3160461005
M3 - Article
AN - SCOPUS:0000547962
SN - 0010-3640
VL - 46
SP - 1379
EP - 1408
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 10
ER -