Problem $3.(20$ points$)$ In addition to the customary horizontal velocity components of

the air in the atmosphere $($the "wind"$),$ there often are vertical air currents thermals$)$ caused

by buoyant effects due to uneven heating of the air, as indicated in Fig. $3.$ Assume that the

velocity field in a certain region is approximated by $u=U_0,v=0,y>hu=U_0,v=V_0(1-\frac{y}{h}),,$ and

$u=U_0,v=0,y>h.$ Derive the streamline function.

Figure $1$: Problem $3$