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Author Bedrossian, Jacob, 1984- author
Title Dynamics near the subcritical transition of the 3D Couette flow I : below threshold case / Jacob Bedrossian, Pierre Germain, Nader Masmoudi
Imprint Providence, RI : American Mathematical Society, [2020]
book jacket
LOCATION CALL # STATUS OPACMSG BARCODE
 Mathematics Library  TA357.5.V56 B43 2020    AVAILABLE    30340200568008
Descript text txt rdacontent
computer c rdamedia
Series Memoirs of the American Mathematical Society Ser. ; v.266
Memoirs of the American Mathematical Society Ser
Note "Forthcoming, volume 266, number 1294."
Includes bibliographical references
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
"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
Print version record
Subject Viscous flow -- Mathematical models
Stability
Shear flow
Inviscid flow
Mixing
Damping (Mechanics)
Three-dimensional modeling
Damping (Mechanics) fast (OCoLC)fst00887306
Inviscid flow. fast (OCoLC)fst01739298
Mixing. fast (OCoLC)fst01024112
Shear flow. fast (OCoLC)fst01115427
Stability. fast (OCoLC)fst01131203
Three-dimensional modeling. fast (OCoLC)fst01910261
Viscous flow -- Mathematical models. fast (OCoLC)fst01167827
Partial differential equations -- Qualitative properties of solutions -- Stability. msc
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} -- Hydrodynamic stability -- Parallel shear flows. msc
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} -- Hydrodynamic stability -- Nonlinear effects. msc
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} -- Turbulence [See also 37-XX, 60Gxx, 60Jxx] -- Transition to turbulence. msc
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} -- Turbulence [See also 37-XX, 60Gxx, 60Jxx] -- Shear flows. msc
Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions. msc
Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} -- Turbulence [See also 37-XX, 60Gxx, 60Jxx] -- Turbulent transport, mixing. msc
Alt Author Germain, Pierre, 1979- author
Masmoudi, Nader, 1974- author
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