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Nonlinear Sciences > Chaotic Dynamics

arXiv:nlin/0304049 (nlin)
[Submitted on 24 Apr 2003 (v1), last revised 18 Sep 2003 (this version, v2)]

Title:Multi-frequency Craik-Criminale solutions of the Navier-Stokes equations

Authors:Bruce R. Fabijonas, Darryl D. Holm
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Abstract: An exact Craik-Criminale (CC) solution to the incompressible Navier-Stokes (NS) equations describes the instability of an elliptical columnar flow interacting with a single Kelvin wave. These CC solutions are extended to allow multi-harmonic Kelvin waves to interact with any exact ``base'' solution of the NS equations. The interaction is evaluated along an arbitrarily chosen flowline of the base solution, so exact nonlinear instability in this context is locally convective, rather than absolute. Furthermore, an iterative method called ``WKB-bootstrapping'' is introduced which successively adds Kelvin waves with incommensurate phases to the extended CC solutions. This is illustrated by constructing an extended CC solution consisting of several Kelvin waves with incommensurate phases interacting with an elliptical columnar flow.
Comments: 9 pages, 2 figures, submitted to J. Fluid Mech
Subjects: Chaotic Dynamics (nlin.CD); Fluid Dynamics (physics.flu-dyn)
Cite as: arXiv:nlin/0304049 [nlin.CD]
  (or arXiv:nlin/0304049v2 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.nlin/0304049
Journal reference: Journal of Fluid Mechanics (2004), 506:207-215
Related DOI: https://doi.org/10.1017/S0022112004008511

Submission history

From: Bruce Fabijonas [view email]
[v1] Thu, 24 Apr 2003 20:44:39 UTC (312 KB)
[v2] Thu, 18 Sep 2003 23:20:11 UTC (342 KB)
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