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International Journal of Fluid Mechanics Research
ESCI SJR: 0.22 SNIP: 0.446 CiteScore™: 0.5

ISSN Print: 2152-5102
ISSN Online: 2152-5110

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v32.i4.40
pages 439-453

Mathematical Modeling of Geophysical Vortex Flow

Harmindar S. Takhar
Engineering Department, Manchester Metropolitan University, Oxford Rd., Manchester, M15GD, UK
O. Anwar Bég
Fluid Mechanics, Nanosystems and Propulsion, Aeronautical and Mechanical Engineering, School of Computing, Science and Engineering, Newton Building, University of Salford, Manchester M54WT, United Kingdom

ABSTRACT

A mathematical model is developed of the geophysical vortex flow using an order-of-magnitude analysis based on a laminar, steady axisymmetric vortex motion in a cylindrical frame of reference. A similarity method is adopted. The classical solution of Long (J. Fluid. Mech., 11, p. 611, 1961; Rossby number > 1) is reexamined. It is shown that true similarity solutions for the intermediate case of the Rossby number ∼ 1 do not exist, since this implies the physically impossible vortex flow wherein the fluxes of radial momentum and angular momentum are simultaneously zero. Numerical solutions are presented for our model using a shooting method with graphs depicting the variation of pressure and also axial, azimuthal, and radial velocities with non-dimensional radius parameter. The results are discussed with applications to tornado swirl and compared to the earlier studies by Long and Herbert.


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