Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2003-10-30
Nonlinear Sciences
Chaotic Dynamics
14 pages, 5 figure, electronically submitted to the Journal of Fluid Mechanics on 23 September 2003 (submission no. WRY 122)
Scientific paper
The present work discusses about a possible physical interpretation of the occurrence of turbulence in a dynamic fluid with mathematical modeling and computer simulation. Here turbulence is defined to be a phenomenon of random velocity field in the space-time continuum accompanied by chaotic occurrence of vortices. This interpretation is independent of the Navier-Stokes equations. I have reasoned how individual fluid percels are disintegrated with increasing Reynolds number (Re) (or increasing velocity or decreasing viscosity or both) leading to creation of smaller parcels with arbitrary speeds in arbitrary directions, which destroys the laminar structure of the fluid flow. I have modeled the occurrence of a vortex as a result of collision among fluid jets under certain conditions. Chaotic occurrence of such vortices further randomizes the velocity field. These together ultimately lead to turbulence. I have also shown an application of vortex formation in a dynamic fluid in atmospheric science., where it has been shown how an initial dusturbing cyclonic vortex is created by collision between two linear wind jets under certain conditions, which under favorable conditions, may mature into a severe tropical storm. Then a three dimensional mathematical modeling of the vortex (assuming that it is going to become a matured storm) has been proposed with computer simulations. This helps us to understand the mystery of origin of cyclonic and anticyclonic vortices in atmosphere and some of their observed asymmetries.
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