  We consider a modification of the fluid flow model for a tornado-like
swirling vortex developed by J. Serrin, where velocity decreases as the
reciprocal of the distance from the vortex axis. Recent studies, based on radar
data of selected severe weather events, indicate that the angular momentum in a
tornado may not be constant with the radius, and thus suggest a different
scaling of the velocity/radial distance dependence.
  Motivated by this suggestion, we consider Serrin's approach with the
assumption that the velocity decreases as the reciprocal of the distance from
the vortex axis to the power $b$ with a general $b>0$. This leads to a
boundary-value problem for a system of nonlinear differential equations. We
analyze this problem for particular cases, both with nonzero and zero
viscosity, discuss the question of existence of solutions, and use numerical
techniques to describe those solutions that we cannot obtain analytically.
