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In this paper, we analyze and develop modifications to two well-known analytical tornado-like models. First, the vortex sink with axial flow (VSAF) model is compared with results obtained from the vortex generator. It is shown that in a cylindrical coordinate system a secondary circulation at the tornado corner region can be responsible for structural discrepancies and vorticity distribution. A tangential velocity field is implemented in the VSAF model to predict an experimental distribution. A novel model is proposed to capture the secondary circulation. A modified model of the VSAF is introduced with piecewise-constant coefficients that enables to predict a shape of a tornado vortex. Further scaling analysis confirms dimensional similarity of tornadoes. The VSAF model is also modified using a Boussinesq-like approximation to take into account the effect of a buoyancy force within a tornado. Finally, the two-fluid model by Yih is used to show the influence of the atmospheric stratification on the radius of tornado.