Dynamics near the subcritical transition of the 3D Couette flow I : below threshold case / / Jacob Bedrossian, Pierre Germain, Nader Masmoudi

• Autore: Bedrossian Jacob <1984->
• Pubblicazione: Providence, RI : , : American Mathematical Society, , [2020]; ©2020
• Descrizione fisica: 1 online resource (v, 158 pages)
• Disciplina: 532.58
• Soggetto topico: Inviscid flow; Mixing; Shear flow; Stability; Three-dimensional modeling; Damping (Mechanics); Viscous flow - Mathematical models
• Classificazione: 35B3576E0576E3076F0676F1035B4076F25
• Persona (resp. second.): GermainPierre <1979->; MasmoudiNader <1974->
• Note generali: "July 2020, volume 266, number 1294 (fourth of 6 numbers)."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: "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"--
• Titolo autorizzato: Dynamics near the subcritical transition of the 3D Couette flow I
• ISBN: 1-4704-6251-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910807220503321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Number 1294.