User:Lothar.brendel: Difference between revisions
Jump to navigation
Jump to search
(PNG-Test) Tag: Reverted |
(→Scratch Pad: -Img-Test) Tag: Manual revert |
||
| Line 9: | Line 9: | ||
* 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: \(\vec\nabla\omega=\vec e_\rho\partial_\rho\omega+\displaystyle\frac{\vec e_\phi}{\rho}\partial_\phi\omega\) | ||
Revision as of 06:28, 10 June 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: \(\vec\nabla\omega=\vec e_\rho\partial_\rho\omega+\displaystyle\frac{\vec e_\phi}{\rho}\partial_\phi\omega\)