Abstract <p>Modeling of atmospheric phenomena based on systems of ordinary differential equations and partial differential equations with their subsequent numerical study has been carried out. As a result of discretization of these equations, we arrive at systems with millions and even billions of unknowns. Owing to the nonlinearity of the complete Navier–Stokes system of equations, construction of its solutions is very labor-intensive. As a consequence, a linearization procedure on the exact solution (homogeneous rest) has been applied. For a linearized system, the emergence and development of ascending swirling flows of different intensities has been numerically simulated using blowing up the pipe with allowance for the action of gravity and Coriolis forces. Numerical calculation of the velocity characteristics of a three-dimensional unsteady flow of viscous heat-conducting gas in an ascending swirling flow initiated by vertical blowing has shown that the gas swirl occurs in the positive direction and is caused by the presence of terms describing the Coriolis acceleration in the linearized complete system of Navier–Stokes equations. Thus, the scheme of the emergence of an ascending swirling flow has been numerically confirmed once again. A conclusion about the possibility of applying this approach to the study of ascending swirling flows of the tornado and tropical cyclone types has also been made.</p>