A novel three-dimensional analytical tornado model constructed based on force balance analysis

Abstract

The analytical model for tornado vortices is crucial in both the wind field characterization and the tornado-resistant design of civil structures. The objective of this study is to derive a novel three-dimensional analytical tornado model from the vortex governing equations simplified based on the force balance analysis in tornado-like vortices (TLVs). First, TLVs with different swirl ratios are generated in a numerical simulator utilizing the large-eddy simulation. Then, the forces in the axisymmetric vortex governing equations are calculated for time-averaged TLVs. The governing equations in the single-cell TLV are simplified by ignoring some significantly small terms. Finally, a novel three-dimensional analytical tornado model, which contains the radial, tangential, and vertical velocity as well as the pressure, has been proposed and validated. The result shows that the force balance in the single-cell TLV is simpler than that in TLVs with larger swirl ratios. In the single-cell TLV, the viscous forces in the radial and vertical directions can be neglected, while the tangential viscous force remains to play an important role in the force balance. The proposed model mitigates the limitations of existing models in describing single-cell tornado vortices, such as only two-dimensional velocity being given, the neglection of the vertical shear effects near the ground, and the infinite velocity at high altitudes. It shows good agreement with the numerical and experimental TLVs as well as the real tornado.