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

Details Multi-frequency Craik-Criminale solutions of the Navier-Stokes equations Multi-frequency Craik-Criminale solutions of the Navier-Stokes equations

2003-04-24

arxiv.org/abs/nlin/0304049v2

Journal of Fluid Mechanics (2004), 506:207-215

Nonlinear Sciences

Chaotic Dynamics

9 pages, 2 figures, submitted to J. Fluid Mech

Scientific paper

10.1017/S0022112004008511

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.

Affiliated with

Also associated with

No associations

Rating

Multi-frequency Craik-Criminale solutions of the Navier-Stokes equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Multi-frequency Craik-Criminale solutions of the Navier-Stokes equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multi-frequency Craik-Criminale solutions of the Navier-Stokes equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-699175