This short note is to announce our recent results [2,3] which provide a complete mathematical proof of the viscous destabilization phenomenon, pointed out by Heisenberg (1924), C.C. Lin and Tollmien (1940s), among other prominent physicists. Precisely, we construct growing modes of the linearized Navier-Stokes equations about general stationary shear flows in a bounded channel (channel flows) or on a half-space (boundary layers), for sufficiently large Reynolds number . Such an instability is linked to the emergence of Tollmien-Schlichting waves in describing the early stage of the transition from laminar to turbulent flows.
@article{SLSEDP_2014-2015____A22_0,
author = {Grenier, Emmanuel and Guo, Yan and Nguyen, Toan T.},
title = {On the spectral instability of parallel shear flows},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:22},
pages = {1--14},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2014-2015},
doi = {10.5802/slsedp.82},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.82/}
}
TY - JOUR AU - Grenier, Emmanuel AU - Guo, Yan AU - Nguyen, Toan T. TI - On the spectral instability of parallel shear flows JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:22 PY - 2014-2015 SP - 1 EP - 14 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.82/ DO - 10.5802/slsedp.82 LA - en ID - SLSEDP_2014-2015____A22_0 ER -
%0 Journal Article %A Grenier, Emmanuel %A Guo, Yan %A Nguyen, Toan T. %T On the spectral instability of parallel shear flows %J Séminaire Laurent Schwartz — EDP et applications %Z talk:22 %D 2014-2015 %P 1-14 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.82/ %R 10.5802/slsedp.82 %G en %F SLSEDP_2014-2015____A22_0
Grenier, Emmanuel; Guo, Yan; Nguyen, Toan T. On the spectral instability of parallel shear flows. Séminaire Laurent Schwartz — EDP et applications (2014-2015), Exposé no. 22, 14 p. doi : 10.5802/slsedp.82. http://www.numdam.org/articles/10.5802/slsedp.82/
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