(2) A horizontal slice through a tornado is modeled by two distinct regions. The inner or core region \((0 < r < R)\) is modeled by solid body rotation—a rotational but inviscid region of flow as discussed earlier. The outer region \((r > R)\) is modeled as an irrotational region of flow. The flow is two-dimensional in the \(r\theta\)-plane, and the components of the velocity field \( \vec{V} = (u_r, u_\theta) \) are given by velocity components: \[ u_r = 0, \quad u_\theta = \begin{cases} \omega r & 0 < r < R \\ \frac{\omega R^2}{r} & r > R \end{cases} \] where \(\omega\) is the magnitude of the angular velocity in the inner region.