Calculating Vorticity of 2-D Flow Motion

[squenshl]

Homework Statement

Consider 2-D flow motion (u,v) = (y,-x). Calculate the vorticity field of the flow.

Homework Equations

$$\omega$$ = v_x - u_y

The Attempt at a Solution

I calculated $$\omega$$ = -2, so using the vorticity equation I get zero. So I guess what I am asking is what exactly am I calculating.

 

[hunt_mat]

Vorticity is defined as $$\mathbf{\omega}=\nabla\times\mathbf{u}$$, as far as I can remember the vorticity equation describes the change in vorticity.

 

[cristo]

I calculated $$\omega$$ = -2, so using the vorticity equation I get zero.

What do you mean by this?

Vorticity is a vector field, defined as the curl of the fluid velocity. For a 2D flow this reduces to
$$\vec{\omega}=\vec{k}\Big(\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y}\Big)$$

What do you get when you use this definition?

 

[squenshl]

The answer is $$\omega = 2$$