Serrin's Vortex Model Revisited
James E Coleman
David R Smith
Oceanography Department
US Naval Academy
and
Reza Malek-Madani
Mathematics Department
US Naval Academy
Corresponding Author: David R. Smith, Oceanography Department, United
States Naval Academy,
572 Holloway Road, Annapolis, MD 21402
Phone (for D.R.Smith): 410-293-6553
Fax: 410-293-2137
E-mail: drsmith@nadn.navy.mil
Serrin's vortex (1972), a particular solution to the Navier-Stokes
equation for rotating flows, is revisited utilizing Mathematica software
to model tornadic flow. The solution assumes an inverse relationship
between particle velocity and radial distance from the vortex line, a no
slip condition at the surface, and a balance between buoyancy and gravity.
Varying parameter values, indicative of the average level of turbulence of
the flow, results in unique solutions resembling one and two-celled
tornadic flows. Analysis and animations of the solutions correlate well
with documented laboratory measurements of velocity fields and with
flow visualizations of laboratory vortices. The simplicity of the solution
allows for in-depth analysis including vorticity contours, pressure
distributions and component changes in velocity, vorticity, and pressure
affecting a single particle transitioning the flow. This paper will
describe the model used and present examples of vortical flows and how
they relate to naturally occurring tornadoes.