A viscous model of wind fields in single-cell tornado-like vortices

Abstract

Purpose

This study aims to generalize the Baker and Sterling’s model (2017) by additionally considering viscous flow and introducing a cylindrical central zone of low pressure. Unlike other models, in which the azimuthal velocity is deduced as a special solution using the variables-separable approach, the novelty in this is that it yields a more general form.

Design/methodology/approach

Flow is incompressible, steady, axisymmetric and viscous. Radial velocity is assumed similar to that of the Baker and Sterling model (2017) by incorporating a central low-pressure zone. The continuity and the Navier−Stokes equations are employed to obtain other velocity components and pressure. Unlike earlier models, azimuthal velocity is obtained from the radial and the axial momentum equations.

Findings

Azimuthal velocity does not asymptotically vanish in the radial direction, it rather sharply reduces to zero, which is practically observed in real vortices occurring in nature. Also, with an increase in water content in tornado fluid, the vortex becomes slightly thinner with comparatively slower rotation. Furthermore, the consideration of a central low-pressure zone shifts the maximum of the axial velocity somewhat away from the boundary of the low pressure. Also, as the low-pressure zone narrows, pressure from the outer zone to the boundary of the low-pressure central zone drops more rapidly, representing a stronger vortex.

Originality/value

To the best of the authors’ knowledge, no such analysis is available in the literature. The work is original and is not under consideration for publication elsewhere. Also, the analysis is balanced and fair.