what do you mean with "the first one" and "the last one"?
1. = (\nabla \cdot \bold{v})\bold{v}
2. = (\bold{v} \cdot \nabla)\bold{v}
?
i can see my mistake, that i wrote a \cdot between (\nabla \cdot \bold{v}) and \bold{v}, which is no dot- but a scalar multiplication... But what i meant...
OK, then i still didn't get it...
in http://en.wikipedia.org/wiki/Advection
they say, that \bold{v}\cdot\nabla is a scalar.
And if i use
(\bold{v} \cdot \nabla) = \left( \frac{v_x \partial }{\partial x} + \frac{v_y \partial }{\partial y} + \frac{v_z \partial }{\partial z}...
Hello and Thanks for your answer!
... but i think i still don't know what to do...
in the linked PDF i saw that there are many definitions, but i didn't find a definition for v \cdot\nabla
encouraged by your post i searched for "abuse of nabla", and i found that it's not right to always treat...
Hello!
The incompressible Navier Stokes equation consists of the two equations
and
Why can't i insert the 2nd one into the first one so that the advection term drops out?!
\nabla\cdotv = v\cdot\nabla = 0
=>
(v\cdot\nabla)\cdotv = 0