MHB What is the role of $$\hat{\jmath} \times r$$ in computing vorticity?

[shen07]

A fluid motion has velocity $$\underline{u}=\sin{(at)}\hat{\imath}+\hat{\jmath} \times r +\cos{(at)}\hat{k}$$

I need to know what is $$\hat{\jmath} \times r$$ to find Vorticity and other things.

 

[Sudharaka]

Hi guys, i am solving a problem but I am unable to figure out what is $$\hat{\jmath} \times r$$? Please help me

Hi shen07, :)

Obviously what is meant by $\hat{\jmath} \times r$ depends on the context. Can you post the full question please?

 

[shen07]

Hi shen07, :)

Obviously what is meant by $\hat{\jmath} \times r$ depends on the context. Can you post the full question please?

I just edited it

 

[MarkFL]

I just edited it

I edited the thread title. Please do not use $\LaTeX$ in thread titles. I have also moved this thread.

 

[Evgeny.Makarov]

A fluid motion has velocity $$\underline{u}=\sin{(at)}\hat{\imath}+\hat{\jmath} \times r +\cos{(at)}\hat{k}$$

I need to know what is $$\hat{\jmath} \times r$$ to find Vorticity and other things.

$\hat{\jmath} \times r$ is the cross product of $\hat{\jmath}$ and $r$, but you already know this. Are you asking how to compute it? Then see here. Are you asking what $\hat{\jmath}$ and $r$ are? It looks like $\hat{\imath}$, $\hat{\jmath}$ and $\hat{k}$ are unit coordinate vectors. I don't know what $r$ is. Or are you asking what the physical meaning of the term $\hat{\jmath} \times r$ is?

 

[I like Serena]

$r$ would be the positional vector of the volume element for which we're calculating the velocity.