Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case

The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\epsilon \leq c_0\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is glob...

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Bibliographische Detailangaben
Hauptverfasser: Bedrossian, Jacob, Germain, Pierre, Masmoudi, Nader
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2020
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
Damping (Mechanics)
Inviscid flow
Mixing
Shear flow
Stability
Three-dimensional modeling
Viscous flow
Viscous flow > Mathematical models
ISBN:1470442175, 9781470442170
ISSN:0065-9266, 1947-6221
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\epsilon \leq c_0\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \rightarrow \infty $. For times $t \gtrsim \mathbf {Re}^1/3$, 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.
Bibliographie:Includes bibliographical reference (p. 155-158)
July 2020, volume 266, number 1294 (fourth of 6 numbers)
ISBN:1470442175
9781470442170
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1294