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Dynamics near the subcritical transition of the 3D Couette flow I : below threshold case /
"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,...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
[2020]
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| Colección: | Memoirs of the American Mathematical Society.
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| Temas: |
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX}
> Hydrodynamic stability
> Parallel shear flows.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX}
> Hydrodynamic stability
> Nonlinear effects.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX}
> Turbulence [See also 37-XX, 60Gxx, 60Jxx]
> Transition to turbulence.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX}
> Turbulence [See also 37-XX, 60Gxx, 60Jxx]
> Shear flows.
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| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
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| 008 | 200911t20202020riu ob 000 0 eng d | ||
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| 019 | |a 1197560936 |a 1356786186 |a 1373442665 |a 1380577324 |a 1390928121 |a 1397422586 | ||
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| 020 | |a 9781470462512 |q (electronic bk.) | ||
| 020 | |z 9781470442170 |q (paperback) | ||
| 020 | |z 1470442175 | ||
| 029 | 1 | |a AU@ |b 000069468542 | |
| 029 | 1 | |a AU@ |b 000069393762 | |
| 035 | |a (OCoLC)1194966413 |z (OCoLC)1197560936 |z (OCoLC)1356786186 |z (OCoLC)1373442665 |z (OCoLC)1380577324 |z (OCoLC)1390928121 |z (OCoLC)1397422586 | ||
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| 082 | 0 | 4 | |a 620.1/064 |2 23 |
| 084 | |a 35B35 |a 76E05 |a 76E30 |a 76F06 |a 76F10 |a 35B40 |a 76F25 |2 msc | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Bedrossian, Jacob, |d 1984- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjKWRFGgh6Tj7VgWJqrVT3 | |
| 245 | 1 | 0 | |a Dynamics near the subcritical transition of the 3D Couette flow I : |b below threshold case / |c Jacob Bedrossian, Pierre Germain, Nader Masmoudi. |
| 264 | 1 | |a Providence, RI : |b American Mathematical Society, |c [2020] | |
| 264 | 4 | |c ©2020 | |
| 300 | |a 1 online resource (v, 170 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society ; |v v. 266 | |
| 500 | |a "Forthcoming, volume 266, number 1294." | ||
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a 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. | |
| 520 | |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"-- |c Provided by publisher | ||
| 588 | 0 | |a Description based on print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Viscous flow |x Mathematical models. | |
| 650 | 0 | |a Stability. | |
| 650 | 0 | |a Shear flow. | |
| 650 | 0 | |a Inviscid flow. | |
| 650 | 0 | |a Mixing. | |
| 650 | 0 | |a Damping (Mechanics) | |
| 650 | 0 | |a Three-dimensional modeling. | |
| 650 | 6 | |a Écoulement visqueux |x Modèles mathématiques. | |
| 650 | 6 | |a Stabilité. | |
| 650 | 6 | |a Écoulement cisaillé. | |
| 650 | 6 | |a Écoulement non visqueux. | |
| 650 | 6 | |a Mélange. | |
| 650 | 6 | |a Amortissement (Mécanique) | |
| 650 | 6 | |a Modélisation tridimensionnelle. | |
| 650 | 7 | |a stability. |2 aat | |
| 650 | 7 | |a Estabilidad |2 embne | |
| 650 | 0 | 7 | |a Variedades en dimensión tres |2 embucm |
| 650 | 7 | |a Damping (Mechanics) |2 fast | |
| 650 | 7 | |a Inviscid flow |2 fast | |
| 650 | 7 | |a Mixing |2 fast | |
| 650 | 7 | |a Shear flow |2 fast | |
| 650 | 7 | |a Stability |2 fast | |
| 650 | 7 | |a Three-dimensional modeling |2 fast | |
| 650 | 7 | |a Viscous flow |x Mathematical models |2 fast | |
| 650 | 7 | |a Partial differential equations |x Qualitative properties of solutions |x Stability. |2 msc | |
| 650 | 7 | |a Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} |x Hydrodynamic stability |x Parallel shear flows. |2 msc | |
| 650 | 7 | |a Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} |x Hydrodynamic stability |x Nonlinear effects. |2 msc | |
| 650 | 7 | |a Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} |x Turbulence [See also 37-XX, 60Gxx, 60Jxx] |x Transition to turbulence. |2 msc | |
| 650 | 7 | |a Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} |x Turbulence [See also 37-XX, 60Gxx, 60Jxx] |x Shear flows. |2 msc | |
| 650 | 7 | |a Partial differential equations |x Qualitative properties of solutions |x Asymptotic behavior of solutions. |2 msc | |
| 650 | 7 | |a Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} |x Turbulence [See also 37-XX, 60Gxx, 60Jxx] |x Turbulent transport, mixing. |2 msc | |
| 700 | 1 | |a Germain, Pierre, |d 1979- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjHdV6WChFB9H4kxjJQxMq | |
| 700 | 1 | |a Masmoudi, Nader, |d 1974- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJppDqxfTBX8XQYbMQwDMP | |
| 776 | 0 | 8 | |i Print version: |a Bedrossian, Jacob, 1984- |t Dynamics near the subcritical transition of the 3D Couette flow I |z 9781470442170 |w (DLC) 2020032339 |w (OCoLC)1160025224 |
| 830 | 0 | |a Memoirs of the American Mathematical Society. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6346623 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH38606893 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6346623 | ||
| 938 | |a EBSCOhost |b EBSC |n 2618170 | ||
| 938 | |a YBP Library Services |b YANK |n 301522944 | ||
| 994 | |a 92 |b IZTAP | ||