03924nam 2200637 450 991079433560332120201203183643.01-4704-6251-6(CKB)4100000011437133(MiAaPQ)EBC6346623(RPAM)21655465(PPN)250799588(EXLCZ)99410000001143713320201203d2020 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDynamics near the subcritical transition of the 3D Couette flow I below threshold case /Jacob Bedrossian, Pierre Germain, Nader MasmoudiProvidence, RI :American Mathematical Society,[2020]©20201 online resource (v, 158 pages)Memoirs of the American Mathematical Society ;Number 1294"July 2020, volume 266, number 1294 (fourth of 6 numbers)."1-4704-4217-5 Includes bibliographical references and index.Outline of the proof -- Regularization and continuation -- High norm estimate on Q2 -- High norm estimate on Q3 -- High norm estimate on Q1/0 -- High norm estimate on Q1/[not equal] -- Coordinate system controls -- Enhanced dissipation estimates -- Sobolev estimates."We study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. We prove that for sufficiently regular initial data of size [epsilon] [less than or equal to] c0Re-1 for some universal c0 > 0, the solution is global, remains within O(c0) of the Couette flow in L2, and returns to the Couette flow as t [right arrow] [infinity]. For times t >/-Re1/3, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of "2.5 dimensional" streamwise-independent solutions referred to as streaks. Our analysis contains perturbations that experience a transient growth of kinetic energy from O(Re-1) to O(c0) due to the algebraic linear instability known as the lift-up effect. Furthermore, solutions can exhibit a direct cascade of energy to small scales. The behavior is very different from the 2D Couette flow, in which stability is independent of Re, enstrophy experiences a direct cascade, and inviscid damping is dominant (resulting in a kind of inverse energy cascade). In 3D, inviscid damping will play a role on one component of the velocity, but the primary stability mechanism is the mixing-enhanced dissipation. Central to the proof is a detailed analysis of the interplay between the stabilizing effects of the mixing and enhanced dissipation and the destabilizing effects of the lift-up effect, vortex stretching, and weakly nonlinear instabilities connected to the non-normal nature of the linearization"--Provided by publisher.Memoirs of the American Mathematical Society ;Number 1294.Inviscid flowMixingShear flowStabilityThree-dimensional modelingDamping (Mechanics)Viscous flowMathematical modelsInviscid flow.Mixing.Shear flow.Stability.Three-dimensional modeling.Damping (Mechanics)Viscous flowMathematical models.532.5835B3576E0576E3076F0676F1035B4076F25mscBedrossian Jacob1984-1432124Germain Pierre1979-Masmoudi Nader1974-MiAaPQMiAaPQMiAaPQBOOK9910794335603321Dynamics near the subcritical transition of the 3D Couette flow I3791057UNINA