Consider a vortex whose vorticity is zeta = (a*gamma/2*pi*v)exp(-ara^2/2v). What is the tangential velocity for such a flow?
Work:
vorticity = del X V
tangential velocity = V@ = c1r/2 + c2/r
V@ = r*(vorticity)/2
V@ = wr, r < or = rc
vorticity = V@/r + dV@/dr
V@ = r*vorticity/2
V@ = ra(gamma)exp(-ar^2/2v)/(4*pi*v)
V@ = r(vorticity)/2 = ra(gamma)exp(-ar^2/2v)/(4*pi*v)