Phys. Rev. Lett. 78, 1900 - 1903 (1997)Secondary Instabilities of Flows with Elliptic Streamlines |
Bruce Fabijonas1, Darryl D. Holm2, and Alexander Lifschitz1
1Department of Mathematics, Statistics, and Computer Science, The University of Illinois at Chicago, Chicago, Illinois 60607
2Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Received 8 November 1996
We examine the stability of flows which are the sum of a linear flow with elliptic streamlines and a transverse standing wave. Such flows are exact solutions of the 3D Euler equations for an inviscid incompressible fluid. We examine the stability of such flows under local 3D high frequency perturbations, which can be viewed as secondary perturbations of the elliptic flow itself. We find that these flows are unstable to such perturbations and compute growth rate in several cases.
©1997 The American Physical Society
URL: http://link.aps.org/abstract/PRL/v78/p1900
DOI: 10.1103/PhysRevLett.78.1900
PACS: 47.20.Lz, 03.40.Gc
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