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.
- ISBN:
- 9781470442170
- 9781470442170
-
Category:
- Engineering: general
- Format:
- Paperback
- Publication Date:
-
30-10-2020
- Language:
- English
- Publisher:
- American Mathematical Society
- Country of origin:
- United States
- Dimensions (mm):
- 254x178mm
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