Dynamics Near the Subcritical Transition of the 3D Couette Flow I (eBook)

Below Threshold Case

Jacob P Bedrossian (Autor)

eBook Download: PDF

154 Seiten
American Mathematical Society (Verlag)
978-1-4704-6251-2 (ISBN)

Infos

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 "e;2.5 dimensional"e; streamwise-independent solutions referred to as streaks.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• ISBN-10: 1-4704-6251-6 / 1470462516
• ISBN-13: 978-1-4704-6251-2 / 9781470462512