Dynamics near the subcritical transition of the 3D Couette flow I below threshold case / Jacob Bedrossian, Pierre Germain, Nader Masmoudi.
| Author/creator | Bedrossian, Jacob, 1984- |
| Other author | Germain, Pierre, 1979- |
| Other author | Masmoudi, Nader, 1974- |
| Format | Electronic |
| Publication Info | Providence, RI : American Mathematical Society, [2020] |
| Description | v, 158 pages ; 26 cm |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Supplemental Content | Full text available from eBooks on EBSCOhost |
| Subjects |
| Series | Memoirs of the American Mathematical Soceity ; volume 1294 |
| Contents | 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. |
| Abstract | "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. |
| General note | "Forthcoming, volume 266, number 1294." |
| Bibliography note | Includes bibliographical references. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2020032339 |
| ISBN | 9781470442170 (paperback) |
| ISBN | (pdf) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | ✔ Available |