Abstract:
We study the behavior of small disturbances to the periodic, plane 3D Couette flow at high Reynolds number. This problem is classical in applied fluid mechanics as the simplest example of subcritical instability: when the system appears nonlinearly unstable despite being linearly stable. In fact, the system is stable but the basin of asymptotic stability is shrinking as Reynolds number increases. In our work, we study how this stability threshold scales in inverse Reynolds number. For very smooth disturbances, we determine this scaling to be ~Re^{-1} whereas for relatively rough data we estimate that the scaling is <= Re^{-3/2}. Both of these results are consistent with numerical experiments performed by the physics community. Moreover, we obtain a reasonably precise picture of the global dynamics near the threshold, especially for smooth disturbances. |