Exact and Asymptotic Conditions on Traveling Wave Solutions of the Navier-Stokes Equations

Y. Charles Li; Divakar Viswanath

doi:10.1063/1.3244660

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arXiv · 0811.0383

Exact and Asymptotic Conditions on Traveling Wave Solutions of the Navier-Stokes Equations

Y. Charles Li·Divakar Viswanath

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Abstract

We derive necessary conditions that traveling wave solutions of the Navier-Stokes equations must satisfy in the pipe, Couette, and channel flow geometries. Some conditions are exact and must hold for any traveling wave solution irrespective of the Reynolds number ($Re$). Other conditions are asymptotic in the limit $Re\to\infty$. The exact conditions are likely to be useful tools in the study of transitional structures. For the pipe flow geometry, we give computations up to $Re=100000$ showing the connection of our asymptotic conditions to critical layers that accompany vortex structures at high $Re$.

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Y. Charles Li, Divakar Viswanath. 2009-07-06. Exact and Asymptotic Conditions on Traveling Wave Solutions of the Navier-Stokes Equations. https://doi.org/10.1063/1.3244660

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