The magnitude of the Doppler velocity signature of a tornado depends on the physical width of the radar beam relative to the size of the tornado. The tornadic vortex signature (TVS) having a large value of azimuthal shear between two adjacent sampling volumes in a Doppler radial velocity field occurs when the tornado's core diameter is equal to or smaller than the radar's half-power beamwidth. The signature is exemplified by extreme Doppler velocity values of opposite sign. On one side of the vortex there is maximum flow toward the radar and on the other side there is maximum flow away from the radar. A simulated WSR-88D (Weather Surveillance Radar-1988 Doppler) was used to produce simulated time-varying TVSs from a time-dependent version of the Burgers-Rott vortex centered at various ranges from the radar. This one-celled vortex was an exact solution to the Navier-Stokes equations of motion and continuity in two-dimensional cylindrical coordinates (r,z) for axisymmetric, viscous flow. Three important parameters included in the solution were eddy diffusion, horizontal convergence, and angular momentum at infinity which were independent of height. Furthermore, the meridional flow was in its steady state. With the angular momentum being constant, four experiments were selected including two different values of horizontal convergence and two different values of eddy diffusion. In the simulation, the tornado's peak tangential velocity increased while at the same time its core diameter decreased its magnitude. Results showed that Doppler velocity differences increased with time as the tornado began to intensify. Doppler velocity differences became steady state 2-8 minutes before the tornado's peak tangential velocity and core diameter became steady state. Detailed results will be presented at the Conference.