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arXiv · 2410.13127

Energy dissipation near the outflow boundary in the vanishing viscosity limit

Jincheng Yang·Vincent R. Martinez·Anna L. Mazzucato·Alexis F. Vasseur
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Abstract

We consider the incompressible Navier-Stokes and Euler equations in a bounded domain with non-characteristic boundary condition, and study the energy dissipation near the outflow boundary in the zero-viscosity limit. We show that in a general setting, the energy dissipation rate is proportional to $\bar U \bar V ^2$, where $\bar U$ is the strength of the suction and $\bar V$ is the tangential component of the difference between the Euler and the Navier-Stokes solutions on the outflow boundary. Moreover, we show that the enstrophy within a layer of order $\nu / \bar U$ is comparable with the total enstrophy. The rate of enstrophy production near the boundary is inversely proportional to $\nu$.

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Jincheng Yang, Vincent R. Martinez, Anna L. Mazzucato, Alexis F. Vasseur. 2024-10-17. Energy dissipation near the outflow boundary in the vanishing viscosity limit. https://arxiv.org/abs/2410.13127

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