A new mathematical model for describing the origin and development of a tornado has been developed by specialists from the Department of Mathematical Physics of the Faculty of Computational Mathematics and Cybernetics (VMK) of Moscow State University, the university’s press service reported on August 29.
The model is based on the equations of continuity and motion of a non-homogeneous fluid. Their research showed that the key factor in the formation of a tornado is the high speed of rotation of the air, the vortex, which creates a significant pressure difference between the external and internal cavity of the vortex.
The results of the study were presented in the report “Mathematical model of a tornado and Navier-Stokes equations”, presented at the All-Russian conference “Lomonosov Readings-2024”.
The model shows that a tornado originates when a vortex moves downward from the upper layers of the atmosphere at a high rotational speed and, as it develops, it continues to increase this speed, until it finally reaches the Earth’s surface. After this, the development of the tornado becomes almost stationary, except for a thin boundary layer that ensures compliance with the boundary conditions at the Earth’s surface.
The external shape of a tornado is determined non-linearly by the rotation rate and the excitation source in the upper atmosphere. It is therefore impossible to specify a single geometric shape for all vortices. Inside a tornado cavity, the pressure is 10% to 20% lower than the normal pressure at the same altitude. This pressure difference causes a vertical upward flow of a mixture of gas, dust and water from land to sea.
Air viscosity plays an important role in the mathematical model of the phenomenon. However, under normal atmospheric conditions, the disappearance of a tornado is due to the cessation of external forces in the upper layers of the atmosphere and not to viscous friction.
Andrey Baev, Professor of the Department of Mathematical Physics at the Faculty of Computational Mathematics and Cybernetics of Moscow State University, noted:
“This work represents an important step forward in understanding the mechanism of tornado initiation and development. We are confident that our results will help in the development of more accurate models to predict this phenomenon.”.
Source: Rossa Primavera
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