User:Lothar.brendel: Difference between revisions
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* vorticity: \(\omega=(\vec\nabla\times\vec v)\cdot\vec e_z=\partial_\rho v_\phi+\displaystyle\frac{v_\phi-\partial_\phi v_\rho}{\rho }\) | * vorticity: \(\omega=(\vec\nabla\times\vec v)\cdot\vec e_z=\partial_\rho v_\phi+\displaystyle\frac{v_\phi-\partial_\phi v_\rho}{\rho }\) | ||
* its gradient: \(\vec\nabla\omega=\vec e_\rho\partial_\rho\omega+\displaystyle\frac{\vec e_\phi}{\rho}\partial_\phi\omega\) | * its gradient: \(\vec\nabla\omega=\vec e_\rho\partial_\rho\omega+\displaystyle\frac{\vec e_\phi}{\rho}\partial_\phi\omega\) | ||
[[File:Test-LB-Steep.png|thumb|1D-Hydro-Test]] | |||
Revision as of 09:48, 22 May 2024
Lothar Brendel
"Admin" of this Wiki
Scratch Pad
2D flow in polar coordinates \((\rho,\phi)\)
- vorticity: \(\omega=(\vec\nabla\times\vec v)\cdot\vec e_z=\partial_\rho v_\phi+\displaystyle\frac{v_\phi-\partial_\phi v_\rho}{\rho }\)
- its gradient: \(\vec\nabla\omega=\vec e_\rho\partial_\rho\omega+\displaystyle\frac{\vec e_\phi}{\rho}\partial_\phi\omega\)
