[Kastenfrosch]

When Vorticity confinement force is described, it's always written as follows:

with:



( Source:
http://http.developer.nvidia.com/GPUGems/gpugems_ch38.html#ch38equ20 )

In the 2D case: how can i compute the cross product (ψ x w) ?
Isn't ψ a vector (the gradient of a scalar field) and w a scalar (the vorticity in the 2D case is a scalar)?
And isn't the cross product of a vector and a scalar undefined?


When searchin in google for
"Cross product of a scalar"
the only site, that doesn't say ".. and a vector is not defined" is the following:

http://eprints.nottingham.ac.uk/912/1/paper-submitted.pdf

which says

"(...) the cross product of a scalar and
a vector is

a × b = (−a*b_2, a*b_1)."

I think that's also the way that nvidea implemented vorticity confinement in its example code.

Can anybody explain this to me? is it really a cross product of a scalar and a vector? And why do 99% of the sites say this is impossible?