1. ## Fluid Dynamics

Hello, guys. I hope that you can help me with this problem. Here it is below. Thanks for the help.

Show that the voricity (w) for the isentropic flow satisfies

Dw/Dt = u(w . del)u.

vorticity =
u is a vector , and del operator is the upside down triangle. the dot represents the dot product between the two.

I know that
Dw/Dt = dw/dt + (u . del)w partial of w with respect to t, dw/dt but how do i get the rest?

2. Originally Posted by Dream
Hello, guys. I hope that you can help me with this problem. Here it is below. Thanks for the help.

Show that the voricity (w) for the isentropic flow satisfies

Dw/Dt = u(w . del)u.

vorticity =
u is a vector , and del operator is the upside down triangle. the dot represents the dot product between the two.

I know that
Dw/Dt = dw/dt + (u . del)w partial of w with respect to t, dw/dt but how do i get the rest?
What equations are you starting with? Are they

$\displaystyle (\rho u)_x + (\rho v)_y = 0$
$\displaystyle u u_x + v u_y = -\frac{p_x}{\rho}$
$\displaystyle u v_x + v v_y = - \frac{p_y}{\rho}$

and $\displaystyle p = k \rho^\gamma$ for isentropic flows?