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

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 $\theta$ 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 $q = \bom\cdot\nabla(\lnρ)$.

UTAM Symposium on Understanding Common Aspects of Extreme Events in Fluids

References in corpus (2)

• On admissibility criteria for weak solutions of the Euler equations
• Quasi-conservation laws for compressible 3D Navier-Stokes flow