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Dynamics Near the Subcritical Transition of the 3D Couette Flow II

Dynamics Near the Subcritical Transition of the 3D Couette Flow II : Above Threshold Case.

・ISBN 978-1-4704-7225-2 paper US$ 85.00

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お気に入り
著者・編者Bedrossian, Jacob / Germain, Pierre / Masmoudi, Nader,
シリーズMemoirs of the American Mathematical Society
出版社(American Mathematical Society, US)
出版年月2022
ページ数133 pp.
言語ENG
ニュース番号<M25-13773>

解説

This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re. In this work, we show that there is constant 0 0 exist at least until t = c0???1 and in general evolve to be O(c0) due to the lift-up e?ect. Further, after times t Re1/3, the streamwise dependence of the solution is rapidly diminished by a mixing-enhanced dissipation e?ect and the solution is attracted back to the class of "2.5 dimensional" streamwise-independent solutions (sometimes referred to as "streaks"). The largest of these streaks are expected to eventually undergo a secondary instability at t ? ???1. Hence, our work strongly suggests, for all (sufficiently regular) initial data, the genericity of the "lift-up e?ect streak growth streak breakdown" scenario for turbulent transition of the 3D Couette flow near the threshold of stability forwarded in the applied mathematics and physics literature.