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arXiv · 1311.0382

Stretching and folding processes in the 3D Euler and Navier-Stokes equations

J. D. Gibbon·D. D. Holm
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Abstract

Stretching and folding dynamics in the incompressible, stratified 3D Euler and Navier-Stokes equations are reviewed in the context of the vector $\bdB = \nabla q\times\nablaθ$ where $q=\bom\cdot\nablaθ$. The variable $θ$ is the temperature and $\bdB$ satisfies $\partial_{t}\bdB = \mbox{curl}\,(\bu\times\bdB)$. These ideas are then discussed in the context of the full compressible Navier-Stokes equations where $q$ takes the two forms $q = \bom\cdot\nablaρ$ and $q = \bom\cdot\nabla(\lnρ)$.

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J. D. Gibbon, D. D. Holm. 2013-11-02. Stretching and folding processes in the 3D Euler and Navier-Stokes equations. https://arxiv.org/abs/1311.0382

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