Internal Dynamics of Tornado-Like Vortices

Abstract

A simple model of flow through a tornado vortex simulator is described. This model assumes a very simple distribution in the vertical of the radial and tangential components of the wind, consistent with the flow found in the simulator. With these assumptions, and with careful attention to the distribution of pressure in the lower and upper portions of the chamber, the axisymmetric equations can be reduced to one-dimensional equations. The model illustrates that all interesting dynamics of the vortex, such as the development of the downdraft and the expansion of the core, are a result of the pressure distribution in the upper part of the chamber. In this model, this pressure distribution is caused by a slow radial spreading with height of the vorticity of the vortex, due to diffusion processes. The model is shown to provide a realistic distribution of observed velocity fields in the simulator, including the downdraft at the center. The dependence of the vertical velocity distribution on swirl ratio is shown and the details explained. An equation that predicts the core radius as a function of swirl ratio is given; it appears superior to previous similar equations. Finally, predictions of the minimum pressure as a function of swirl ratio given by the model are presented. It is suggested that the observed minimum pressure curve shows two regimes, turbulent at high swirl ratio and nonturbulent at low swirl ratio. It is shown why the pressure in a turbulent vortex is much higher than in a nonturbulent vortex at the same swirl ratio and volume flow rate, and why this explains the observed curve.