A generalized analytical viscous model for steady-state atmospheric vortices

Abstract

This paper presents a generalised analytical viscous model for atmospheric vortices. All the velocity components are dependent on the radial and axial coordinates. The model begins with radial velocity derived by Onishchenko et al. (2021). The other components are derived from the governing equations. Rankine (1882) and Burgers (1948) models are used as the boundary condition for imposing cyclostrophic balance. All the velocity components of this model are bounded. The radial pressure is also deduced. Radial profiles of axial, azimuthal velocities and radial pressure are plotted. The azimuthal velocity derived with the Rankine model as the boundary condition shows a sharp turn at the core layer where it is maximum and increases with height, while the changes are smooth near the core and not necessarily maximum at the core for the Burgers boundary condition. The azimuthal component of velocity increases at lower altitudes but declines at higher ones. It shows a reverse trend in the inner and the outer regions close to the core radius. Further, radial velocity reduces in magnitude with height. In both cases, radial pressure is higher in the outer region but lessens gradually in the core to vanish at the axis. It also increases with height.