The critical layer in pipe flow at high Reynolds number

Autor: Viswanath, D.
Rok vydání: 2008
Předmět:
Zdroj: Phil. Trans. R. Soc. A, 367 (2009), 561-576
Druh dokumentu: Working Paper
DOI: 10.1098/rsta.2008.0225
Popis: We report the computation of a family of traveling wave solutions of pipe flow up to $Re=75000$. As in all lower-branch solutions, streaks and rolls feature prominently in these solutions. For large $Re$, these solutions develop a critical layer away from the wall. Although the solutions are linearly unstable, the two unstable eigenvalues approach 0 as $Re\to\infty$ at rates given by $Re^{-0.41}$ and $Re^{-0.87}$ -- surprisingly, the solutions become more stable as the flow becomes less viscous. The formation of the critical layer and other aspects of the $Re\to\infty$ limit could be universal to lower-branch solutions of shear flows. We give implementation details of the GMRES-hookstep and Arnoldi iterations used for computing these solutions and their spectra, while pointing out the new aspects of our method.
Databáze: arXiv
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