The Stationary Concentrated Vortex Model

Oleg Onishchenko,Wendell Horton,Gary Verth,Samuel J Skirvin,Natalia Astafieva,Viktor Fedun,Oleg Pokhotelov

doi:10.3390/cli9030039

Oleg Onishchenko, Wendell Horton + Show 5 more

Open Access

https://doi.org/10.3390/cli9030039

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Abstract

A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere.

Highlights

The ubiquity of vortex motion in the Earth’s atmosphere stimulates a lot of interest from both a fundamental research and a practical point of view
The Sullivan vortex is probably the simplest two-cell dissipative vortex that can describe the flow in an intense dust devils or tornado vortices [8,10,53]
The new axially-symmetric model of a steady state vortex localised in the radial and vertical directions vortices with incompressible and inviscid flow which is a solution to the Euler equations has been proposed

Summary

Introduction

The ubiquity of vortex motion in the Earth’s atmosphere stimulates a lot of interest from both a fundamental research and a practical point of view. As well as understanding dust devils, detailed knowledge of the internal properties of the structure of concentrated vortices can be applied to the study of tornadoes and tropical cyclones In this regard, there is much motivation to search for new and physically accurate solutions of the hydrodynamic equations describing concentrated vortex fluid flow. The simplest model of a stationary concentrated vortex in an ideal incompressible fluid was studied previously by [37] In this model, the vortex, as well as the Burgers and Sullivan vortex models, is localised in the radial direction, but not vertically localised.

Vortex Models

Rankine Vortex

Burgers Vortex

The Sullivan Vortex

Vortex Model for an Incompressible and Inviscid Fluid

Conclusions