LEADER 03924nam 2200637 450 001 9910807220503321 005 20201203183643.0 010 $a1-4704-6251-6 035 $a(CKB)4100000011437133 035 $a(MiAaPQ)EBC6346623 035 $a(RPAM)21655465 035 $a(PPN)250799588 035 $a(EXLCZ)994100000011437133 100 $a20201203d2020 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDynamics near the subcritical transition of the 3D Couette flow I $ebelow threshold case /$fJacob Bedrossian, Pierre Germain, Nader Masmoudi 210 1$aProvidence, RI :$cAmerican Mathematical Society,$d[2020] 210 4$dİ2020 215 $a1 online resource (v, 158 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vNumber 1294 300 $a"July 2020, volume 266, number 1294 (fourth of 6 numbers)." 311 $a1-4704-4217-5 320 $aIncludes bibliographical references and index. 327 $aOutline 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. 330 $a"We study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. We prove that for sufficiently regular initial data of size [epsilon] [less than or equal to] c0Re-1 for some universal c0 > 0, the solution is global, remains within O(c0) of the Couette flow in L2, and returns to the Couette flow as t [right arrow] [infinity]. For times t >/-Re1/3, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of "2.5 dimensional" streamwise-independent solutions referred to as streaks. Our analysis contains perturbations that experience a transient growth of kinetic energy from O(Re-1) to O(c0) due to the algebraic linear instability known as the lift-up effect. Furthermore, solutions can exhibit a direct cascade of energy to small scales. The behavior is very different from the 2D Couette flow, in which stability is independent of Re, enstrophy experiences a direct cascade, and inviscid damping is dominant (resulting in a kind of inverse energy cascade). In 3D, inviscid damping will play a role on one component of the velocity, but the primary stability mechanism is the mixing-enhanced dissipation. Central to the proof is a detailed analysis of the interplay between the stabilizing effects of the mixing and enhanced dissipation and the destabilizing effects of the lift-up effect, vortex stretching, and weakly nonlinear instabilities connected to the non-normal nature of the linearization"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vNumber 1294. 606 $aInviscid flow 606 $aMixing 606 $aShear flow 606 $aStability 606 $aThree-dimensional modeling 606 $aDamping (Mechanics) 606 $aViscous flow$xMathematical models 615 0$aInviscid flow. 615 0$aMixing. 615 0$aShear flow. 615 0$aStability. 615 0$aThree-dimensional modeling. 615 0$aDamping (Mechanics) 615 0$aViscous flow$xMathematical models. 676 $a532.58 686 $a35B35$a76E05$a76E30$a76F06$a76F10$a35B40$a76F25$2msc 700 $aBedrossian$b Jacob$f1984-$01432124 702 $aGermain$b Pierre$f1979- 702 $aMasmoudi$b Nader$f1974- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910807220503321 996 $aDynamics near the subcritical transition of the 3D Couette flow I$94071607 997 $aUNINA