| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910794335603321 |
|
|
Autore |
Bedrossian Jacob <1984-> |
|
|
Titolo |
Dynamics near the subcritical transition of the 3D Couette flow I : below threshold case / / Jacob Bedrossian, Pierre Germain, Nader Masmoudi |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Providence, RI : , : American Mathematical Society, , [2020] |
|
©2020 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (v, 158 pages) |
|
|
|
|
|
|
Collana |
|
Memoirs of the American Mathematical Society ; ; Number 1294 |
|
|
|
|
|
|
Classificazione |
|
35B3576E0576E3076F0676F1035B4076F25 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Inviscid flow |
Mixing |
Shear flow |
Stability |
Three-dimensional modeling |
Damping (Mechanics) |
Viscous flow - Mathematical models |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
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"-- |
|
|
|
|
|
| |