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" ...
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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.
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New. Memoirs of the American Mathematical Society . Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
