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 NavierStokes equations at high Reynolds number Re. We prove that for sufficiently regular initial data of size [epsilon] [less than or equal to] c0Re1 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 mixingenhanced dissipation effect and the solution is rapidly attracted to the class of "2.5 dimensional" streamwiseindependent solutions referred to as streaks. Our analysis contains perturbations that experience a transient growth of kinetic energy from O(Re1) to O(c0) due to the algebraic linear instability known as the liftup 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 mixingenhanced 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 liftup effect, vortex stretching, and weakly nonlinear instabilities connected to the nonnormal nature of the linearization" Provided by publisher 

Print version record 
Subject 
Viscous flow  Mathematical models


Stability


Shear flow


Inviscid flow


Mixing


Damping (Mechanics)


Threedimensional modeling


Damping (Mechanics) fast (OCoLC)fst00887306


Inviscid flow. fast (OCoLC)fst01739298


Mixing. fast (OCoLC)fst01024112


Shear flow. fast (OCoLC)fst01115427


Stability. fast (OCoLC)fst01131203


Threedimensional 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 74XX}  Hydrodynamic stability  Parallel shear flows. msc


Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74XX}  Hydrodynamic stability  Nonlinear effects. msc


Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74XX}  Turbulence [See also 37XX, 60Gxx, 60Jxx]  Transition to turbulence. msc


Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74XX}  Turbulence [See also 37XX, 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 74XX}  Turbulence [See also 37XX, 60Gxx, 60Jxx]  Turbulent transport, mixing. msc

Alt Author 
Germain, Pierre, 1979 author


Masmoudi, Nader, 1974 author

