Dynamics Near the Subcritical Transition of the 3D Couette Flow II: Above Threshold Case (Memoirs of the American Mathematical Society)

Bedrossian, Jacob/ Germain, Pierre/ Masmoudi, Nader

American Mathematical Society（2022/11発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 133 p.
• 言語 ENG
• 商品コード 9781470472252
• DDC分類 620.1064

Full Description

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.