Problem $2.(10$ points$)$ In a rotating frame, the momentum and mass equations for an incompressible,

inviscid flow are

$\frac{Du}{Dt}+(2hat(z))u=-\frac{1}{}$gradp$+f,$ and $,$grad$*u=0$

where the vector $(2hat(z)$ tells us that the fluid is rotating at an angular velocity $$ about the vertical $(z)$ axis.

Derive the governing equation for the vertical component of the vorticity, $=$del$\frac{v}{d}$elx$-$del$\frac{u}{d}$ely, assuming

body forces are conservative. How does this equation simplify if the flow is $2$D in the horizontal $xy-$plane

$($i$.$e$.$ if $w=0$ and $de\frac{l}{d}$elz$=0)?$