Dynamics Near the Subcritical Transition of the 3D Couette Flow II: Above Threshold Case (Paperback)

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.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Memoirs of the American Mathematical Society
Release date:	December 2022
Authors:	Jacob Bedrossian • Pierre Germain • Nader Masmoudi
Dimensions:	254 x 178mm (L x W)
Format:	Paperback
Pages:	133
ISBN-13:	978-1-4704-7225-2
Categories:	Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Applied mathematics > General Promotions
LSN:	1-4704-7225-2
Barcode:	9781470472252

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