A viscous model for atmospheric vortices with a central depression of pressure

Abstract

In this paper, we present an analytical model for atmospheric vortices that includes three velocity components—radial, azimuthal, and axial together with a pressure distribution. The model modifies a stream function with a central low-pressure core and applies a correction to the azimuthal velocity to capture the Reynolds number-dependent shear-layer behavior near the ground. The proposed model effectively confines rotational motion to a compact region around the core, with the azimuthal velocity decaying super-exponentially with radial distance, in contrast to classical vortex models such as those by Burgers, Vatistas, and Rankine, where the azimuthal velocity decays only algebraically and remains non-negligible at large radii. A range of vortex intensities can be represented using parametric control via a shape factor and Reynolds number. Comparative analysis shows that the present model produces sharper, more localized velocity peaks and pronounced vertical pressure variations, consistent with field observations. This model provides a more physically realistic description of atmospheric vortices.