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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

An Analytical Model of the Tornado-Like Stationary Atmospheric Vortices

Journal of Applied Nonlinear Dynamics 13(3) (2024) 461--473 | DOI:10.5890/JAND.2024.09.004

Jagdish Prasad Maurya

Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Itanagar, Arunachal Pradesh -791112, India

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Abstract

In this paper, an analytical model for single-celled, steady, incompressible and axisymmetric atmospheric vortices is presented. The velocity components and pressure are derived by substituting the assumed special form of the radial dependent azimuthal velocity of Wood and White \cite{15} model into the governing equations. The azimuthal velocity component, vertical velocity component and pressure depend on radial and vertical coordinates whereas the radial velocity component depend only on the radial coordinate. The separation of variables method is applied for the solution of governing equations. This analytical model is then used to study the velocities and pressure of tornado-like stationary vortex. In this new approach, viscosity affects velocities as well as the pressure gradient. The radial velocity component decreases in magnitude as the Reynolds number increases. It is observed that the maximum azimuthal velocity weakens with altitude. The vertical profile of the azimuthal velocity increases up to some height and, once it attains maximum velocity, it start weakens gradually from the height of the maximum velocity and reduces zero asymptotically at higher altitudes. The peak of the radial pressure gradient decays with increasing altitude and has insignificant variation at higher altitudes. It is also observed that the axial pressure gradient falls with increasing Reynolds numbers.

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