A Resolution of the Sommerfeld Paradox

  title={A Resolution of the Sommerfeld Paradox},
  author={Y. Li and Zhiwu Lin},
  journal={SIAM J. Math. Anal.},
  • Y. Li, Zhiwu Lin
  • Published 2011
  • Mathematics, Computer Science, Physics
  • SIAM J. Math. Anal.
Sommerfeld paradox roughly says that mathematically Couette linear shear is linearly stable for all Reynolds number, but experimentally arbitrarily small perturbations can induce the transition from the linear shear to turbulence when the Reynolds number is large enough. The main idea of our resolution of this paradox is to show that there is a sequence of linearly unstable shears which approaches the linear shear in the kinetic energy norm but not in the enstrophy (vorticity) norm. These… Expand
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