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Analysis of Burgers' vortex model: Velocity profiles and vorticity distribution

Free vortices are observed in everyday life e.g. at sinks and bathtub drains. Till date, various studies have been made to analyze different analytical models on free surface vortices. The present work is designed to provide a better understanding on the phenomenon of vorticity and in the same context, Burgers' vortex model has been considered. Two main parameters of circulation and vortex core radius are defined. Mathematical models for velocity and vorticity have been analytically developed and the velocity profiles have been calculated utilizing computer aided codes. Vorticity and velocity plots have been generated for different combinations of viscosities and extensional strains; subsequently the effect of vortex stretching on vortex core radius is examined. Analysis revealed that most of the vorticity is distributed towards the vortex core while effect of strain rates and viscosity on the velocity profiles/vorticity distribution has also been critically analyzed. Analysis carried out in the current study will assist researchers to evaluate various free vortex models on same underlined principles. Subsequently, these models can be compared to assess the accuracy of each, validated with experimental results. Phenomenon discussed in the paper has significance in industry such as gravitation water vortex power plants, hydropower plants and Ranque-Hilsch refrigeration tubes. The vortex character also has implications in wildfires and tornadoes formation, nuclear power plants and flame stabilizers in combustion chambers of jet engines where undesirable effects of swirls have to be curtailed.