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Dynamics of Planar Vortex Clusters with Binaries by Lu Ting; Omar Knio; Denis Blackmore is a Engineering article available to read on EtoBox.

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## Abstract We study an __N__ ‐vortex problem having __J__ of them forming a cluster, which means the distances between the vortices in the cluster is much smaller by __O__ (__ε__) than the distances, __O__ (l), to the __N__ – __J__ vortices outside of the cluster. With the strengths of __N__ vortices being of the same order, the velocity and time scales for the motion of the __J__ vortices relative to those of the __N__ – __J__ vortices are __O__ (__ε__^–1^) and __O__ (__ε__^2^) respectively. We show that this two‐time and two‐length scale problem can be converted to a standard two‐time scale problem and then the leading order solution of the __N__ ‐vortex problem can be uncoupled to two problems, one for the motion of __J__ vortices in the cluster relative to the center of the cluster and one for the motion of the __N__ – __J__ vortex plus the center of the cluster. For __N__ = 3 and __J__ = 2, the 3‐vortex problem is uncoupled to two binary vortices problems in the length scales l and l__ε__ respectively. When perturbed in the scale l, say by a fourth vortex even of finite strength, the binary problem becomes a 3‐vortex problem, admitting periodic solutions. Since 3‐vortex probl

Who reads Dynamics of Planar Vortex Clusters with Binaries?

Author

Lu Ting; Omar Knio; Denis Blackmore

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); Wiley (ISSN 1617-7061)

Published

2007

Field

Engineering (Physical Sciences)