R(t) = the propagation function of the vortex, where R=sqrt(4vt + R0^2)

R0 = initial radius.

w0 = initial angular velocity.

Rf = the radius of the boundary confining the fluid.

The Lamb-Oseen vortex without no-slip has a critical radii of q(t) = R(t)sqrt(2pi/5), which is the location of the absolute maximum on the r-axis. As "t" approaches infinity, q(t) also approaches infinity (with exponential decay).

With the no-slip condition, where the tangential velocity at r=0 and r=Rf is zero, q(t) seems to approach Rf/2. Taking the partial derivative w.r.t "r" of this vector function in polar coordinates, uθ(r,t), and setting it equal to zero yields an algebraic expression with no solutions. Graphically, duθ/dr =0 has real r-intercepts for all "t" that defines q(t).