A unified model and analytical solution for wind fields associated with tornado vortices

The violent winds in tornadoes cause damage to infrastructure and loss of life. Although the wind fields of various types of tornado vortices (e.g., single-cell vortex, double-cell vortex and their combination) are essentially governed by the Navier-Stokes equations, existing efforts in the development of analytical tornado wind model mainly focus on a certain vortex type. To develop a unified model with an analytical solution for wind fields associated with various tornado vortices, the scale analysis is first utilized here to simplify the Navier-Stokes equations. The simplified governing equations (unified tornado model) are then solved using separation of variables method. The undetermined coefficients in the analytical solution for tornado wind and pressure fields are identified by theoretical boundary conditions and field-measurement data. The analytical solutions of the unified model are validated using three different vortex types of natural tornadoes [i.e., Happy tornado (volume 1) with a single-cell vortex, Happy tornado (volume 2) with vortex breakdown, and Spencer tornado with a double-cell vortex]. The obtained three-dimensional vortex flow fields are based on seven engineering parameters (e.g., swirl ratio, Reynolds number, core aspect ratio, and maximum tangential velocity), showing great promise in rapid wind and pressure field estimation for a detected tornado.