Simulated Doppler Velocity Signatures of Evolving Tornado-Like Vortices

Abstract

Exact solutions of the Navier?Stokes or Euler equations of motion and the continuity equation in cylindrical coordinates for 3D, axisymmetric, inviscid, or laminar flows are utilized to represent evolving vortices that roughly model tornado cyclones or misocyclones contracting to tornadoes. These solutions are unsteady versions of the diffusive Burgers?Rott vortex and the inviscid Rankine-combined vortex. They satisfy the free-slip condition at the ground. Different vortices are obtained by choosing different values of the constant eddy viscosity and uniform horizontal convergence while holding the circulation at infinity constant. A simulated Weather Surveillance Radar-1988 Doppler (WSR-88D) is employed to generate time-varying Doppler velocity signatures in uniform reflectivity of these analytical vortices at ranges of 25 and 50 km from the radar. Mean Doppler velocities are determined by computing 3D integrals over effective resolution volumes. Magnitudes of Doppler vortex signatures at different times in the evolution of the stationary vortices are computed for effective beamwidths of 1.02° and 1.39°, which correspond to azimuthal sampling intervals of 0.5° and 1.0°, respectively. Four tornado predictors?rotational velocity, shear, excess rotational kinetic energy, and circulation?are examined. Results of the simulations show that for smaller effective beamwidths, Doppler vortex signatures are stronger and exceed fixed threshold values of rotational velocity and shear earlier. With finer azimuthal resolution, tornado cyclone, misocyclone, or tornado signatures switch to tornadic vortex signatures later. Circulations of the vortex signatures give good estimates of the circulations of the simulated tornadoes and tornado cyclones with relative insensitivity to range, effective beamwidth, and stage of evolution. High circulation and convergence values of a rotation signature reveal the potential for a tornado earlier than all the other predictors, which increase significantly during tornadogenesis.