= Rankine vortex
{c}
{title2=$u_\theta=\Omega r\ (r\leq a),\quad u_\theta=\Omega a^2/r\ (r>a)$}
A <Rankine vortex> models a finite rotating core joined continuously to an irrotational exterior. In cylindrical <polar coordinates>, its radial and vertical velocities vanish and its azimuthal <velocity> has the displayed form, where $a$ is the core radius and $\Omega$ is a signed angular velocity. The axial <vorticity> is $r^{-1}\partial_r(ru_\theta)$, equal to $2\Omega$ inside and zero outside. The velocity is continuous at $r=a$, although its first radial derivative has different one-sided values. The circulation outside the core is $2\pi\Omega a^2$.
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