## 1 Introduction
### Strong Wind Models
To properly study a tornado, it is necessary to create an appropriate analytical model of the phenomenon. [PERSON], [PERSON], and [PERSON] started such activities [14; 15; 16; 17; 18]. Currently, many new experimental and analytical models are being developed, based on previously developed ones, describing tornadoes and their effects. The general concept of the tornado model is shown below. Modified models of vortices of the mentioned authors were used. The differences between them were collected and explained. Engineering structures are designed for many years, during which time the climate changes and the structure begins to be exposed to wind, which significantly exceeds the pressures specified in the standard [7]. In recent years, the frequency of tornadoes has been increasing, so their loads should be considered in the design in many cases. The purpose of the following research is to describe the nature of strong winds, thanks to which it will be possible to predict the impact of a tornado on buildings and structures. In general, the nature of tornadoes is similar over the years, so many researchers use existing data from the past. It is difficult to clearly define all tornado parameters (e.g., speed), which is why other methods are also used for research, such as assessing damage to objects after a tornado has passed. In order to analyze the vortex motion, we can use the model of an incompressible ideal fluid of uniform density. The Navier-Stokes equations [19] are used to describe viscous liquids:  
\[\frac{\partial u}{\partial t}+(u*\
abla)*u=g-\frac{\
abla p}{\rho}+\
u\Delta u \tag{1}\]  
where \(p\) is pressure of the fluid, \(g\) is Earth's gravity, \(u\) is the body's velocity, \(\rho\) is the density of the air, \(\
u\) is the kinematic viscosity coefficient, and \(t\) is time. Tornadoes occur all over the world; the observed phenomena occurring in Scandinavia were used to create [PERSON]'s original model. He noticed a large concentration of air flows along lines oriented in front of the tornado's path. Cold air masses trap warm air in the tornado section. The greatest intensity of a tornado is reached when the closed masses of warm air rise towards the upper parts of the tornado, and the potential energy is changed into the kinetic energy of the wind. Based on these observations, on the model proposed by [PERSON], and on meteorological records obtained from some observatories along the route of a tornado in one of the Japanese cities, in [20] the formula for the tangential velocity was presented:  
\[V=2V_{max}\frac{\left(\frac{r}{r_{max}}\right)}{1+\left(\frac{r}{r_{max}} \right)^{2}} \tag{2}\]  
In the analyses of [PERSON] [14; 15], the vortex model they created adopts single-cell characteristics. With this in mind, the following assumptions can be made employing the Navier-Stokes equations:  
\[V=V(r),\ \ W=W(z),\ \ U=U(r),\ \ p=p(r,z). \tag{3}\]where \(V\), \(W\), and \(U\) are the tangential, axial, and radial components of the velocity vector, and \(p\) is the pressure. In his investigations, [PERSON] [17] made some assumptions: the area of the cross-section is only in one dimension, the state of the body is fixed, and the flow is not viscous. This creates a modified vortex model where body forces are neglected in the analysis. Adopting the aforementioned [PERSON] model, two separate areas can be distinguished: external and internal. The first one is characterized by the fact that the tangential velocity decreases as the radius increases. There are no vortices; therefore the flow is called potential. In the second region, the tangential velocity increases linearly from zero to the maximum value at the edges of the region, which is defined by \(r<r_{max}\). The air in this area swirls as a solid.