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,...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bedrossian, Jacob, 1984- (Autor), Germain, Pierre, 1979- (Autor), Masmoudi, Nader, 1974- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, [2020]
Colección:Memoirs of the American Mathematical Society.
Temas:
Viscous flow > Mathematical models.
Stability.
Shear flow.
Inviscid flow.
Mixing.
Damping (Mechanics)
Three-dimensional modeling.
Écoulement visqueux > Modèles mathématiques.
Stabilité.
Écoulement cisaillé.
Écoulement non visqueux.
Mélange.
Amortissement (Mécanique)
Modélisation tridimensionnelle.
stability.
Estabilidad
Variedades en dimensión tres
Inviscid flow
Mixing
Shear flow
Stability
Three-dimensional modeling
Viscous flow > Mathematical models
Partial differential equations > Qualitative properties of solutions > Stability.
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.
Partial differential equations > Qualitative properties of solutions > Asymptotic behavior of solutions.
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} > Turbulence [See also 37-XX, 60Gxx, 60Jxx] > Turbulent transport, mixing.
Acceso en línea:Texto completo
Descripción
Sumario:"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"--
Notas:"Forthcoming, volume 266, number 1294."
Descripción Física:1 online resource (v, 170 pages)
Bibliografía:Includes bibliographical references.
ISBN:1470462516
9781470462512

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