06655nam 22008533 450 991096467810332120231110212605.097814704723131470472317(CKB)5680000000076881(MiAaPQ)EBC29731913(Au-PeEL)EBL29731913(OCoLC)1343248404(EXLCZ)99568000000007688120221021d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDynamics near the Subcritical Transition of the 3D Couette Flow II1st ed.Providence :American Mathematical Society,2022.©2022.1 online resource (148 pages)Memoirs of the American Mathematical Society ;v.2799781470472252 1470472252 Cover -- Title page -- Chapter 1. Introduction -- 1.1. Linear behavior and streaks -- 1.2. Statement of main results -- 1.3. Notations and conventions -- Acknowledgments -- Chapter 2. Outline of the proof -- 2.1. Summary and weakly nonlinear heuristics -- 2.2. Choice of the norms -- 2.3. Instantaneous regularization and continuation of solutions -- 2.4. ⁱ formulation, the coordinate transformation, and some key cancellations -- 2.5. The toy model and design of the norms -- 2.6. Design of the norms based on the toy model -- 2.7. Main energy estimates -- Chapter 3. Regularization and continuation -- Chapter 4. Multiplier and paraproduct tools -- 4.1. Basic inequalities regarding the multipliers -- 4.2. Paraproducts and related notations -- 4.3. Product lemmas and a few immediate consequences -- Chapter 5. High norm estimate on ² -- 5.1. Zero frequencies -- 5.2. Non-zero frequencies -- Chapter 6. High norm estimate on ³ -- 6.1. Zero frequencies -- 6.2. Non-zero frequencies -- Chapter 7. High norm estimate on ¹₀ -- 7.1. Transport nonlinearity -- 7.2. Nonlinear stretching -- 7.3. Forcing from non-zero frequencies -- 7.4. Dissipation error terms -- Chapter 8. High norm estimate on ¹_{≠} -- 8.1. Linear stretching term 1 -- 8.2. Lift-up effect term -- 8.3. Linear pressure term 1 -- 8.4. Nonlinear pressure -- 8.5. Nonlinear stretching -- 8.6. Transport nonlinearity -- 8.7. Dissipation error terms -- Chapter 9. Coordinate system controls -- 9.1. High norm estimate on -- 9.2. Low norm estimate on -- 9.3. Long time, high norm estimate on ⁱ -- 9.4. Shorter time, high norm estimate on ⁱ -- 9.5. Low norm estimate on -- Chapter 10. Enhanced dissipation estimates -- 10.1. Enhanced dissipation of ³ -- 10.2. Enhanced dissipation of ² -- 10.3. Enhanced dissipation of ¹ -- Chapter 11. Sobolev estimates -- 11.1. Improvement of (2.45c)and (2.45b).11.2. Improvement of (2.45a) -- Appendix A. Fourier analysis conventions, elementary inequalities, and Gevrey spaces -- Appendix B. Some details regarding the coordinate transform -- Appendix C. Definition and analysis of the norms -- C.1. Definition and analysis of -- C.2. The design and analysis of _{ } -- Appendix D. Elliptic estimates -- D.1. Lossy estimates -- D.2. Precision lemmas -- Bibliography -- Back Cover."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 , independent of Re, such that sufficiently regular disturbances of size for any exist at least until and in general evolve to be due to the lift-up effect. Further, after times , the streamwise dependence of the solution is rapidly diminished by a mixing-enhanced dissipation effect 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 . Hence, our work strongly suggests, for all (sufficiently regular) initial data, the genericity of the "lift-up effect 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"--Provided by publisher.Memoirs of the American Mathematical Society Dynamics Near the Subcritical Transition of the 3D Couette Flow IIViscous flowMathematical modelsStabilityShear flowInviscid flowMixingDamping (Mechanics)Three-dimensional modelingPartial differential equations -- Qualitative properties of solutions -- StabilitymscFluid mechanics -- Hydrodynamic stability -- Parallel shear flowsmscFluid mechanics -- Hydrodynamic stability -- Nonlinear effectsmscFluid mechanics -- Turbulence -- Transition to turbulencemscFluid mechanics -- Turbulence -- Shear flowsmscPartial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutionsmscFluid mechanics -- Turbulence -- Turbulent transport, mixingmscViscous flowMathematical models.Stability.Shear flow.Inviscid flow.Mixing.Damping (Mechanics)Three-dimensional modeling.Partial differential equations -- Qualitative properties of solutions -- Stability.Fluid mechanics -- Hydrodynamic stability -- Parallel shear flows.Fluid mechanics -- Hydrodynamic stability -- Nonlinear effects.Fluid mechanics -- Turbulence -- Transition to turbulence.Fluid mechanics -- Turbulence -- Shear flows.Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions.Fluid mechanics -- Turbulence -- Turbulent transport, mixing.620.1/064620.106435B3576E0576E3076F0676F1035B4076F25mscBedrossian Jacob1432124Germain Pierre709773Masmoudi Nader1801358MiAaPQMiAaPQMiAaPQBOOK9910964678103321Dynamics near the Subcritical Transition of the 3D Couette Flow II4346522UNINA