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

Jacob Bedrossian, Pierre Germain, Nader Masmoudi

Paperback (30 Nov 2022)

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Publisher's Synopsis

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.

Book information

ISBN:	9781470472252
Publisher:	American Mathematical Society
Imprint:	American Mathematical Society
Pub date:	30 Nov 2022
DEWEY:	620.1064
DEWEY edition:	23/eng/20221129
Language:	English
Number of pages:	133
Weight:	363g
Height:	254mm
Width:	178mm