Development of Physically Realistic Numerical Model for Blinking Vortex System

Abstract

The blinking vortex system defines a method of mixing where two vortices turn on and off alternately. Research suggests that systems of this nature are sensitive to the initial conditions. This thesis aims to build off the authors previous paper, "Experimental and Numerical Analysis of Chaotic Advection in 2-D Blinking Vortex Flow System", to create a more accurate numerical model of a blinking vortex system [9]. The model previously created in the PHYS 452: Advanced Physics Lab course did not account for multiple important physical characteristics of the fluid system, which resulted in the model being unusable to predict physical behavior. Therefore, a new set of differential equations, based on the Navier-Stokes equations is used to model the blinking vortex system. Using the experimental results obtained in PHYS 452, the improved numerical model is compared to physical results. Using the positive Lyapunov exponent as a point of comparison, it is revealed that the improved numerical model is very accurate in predicting physical behavior. By accounting for the fluid's momentum and viscosity with the Navier-Stokes equations, a viable numerical model for the blinking vortex system was created.