In this dissertation, the effects of a shear-thinning fluid on the evolution of a hairpin vortex are investigated. The fluid viscosity is determined using a power law model and direct numerical simulations are performed using a pseudo-spectral code. The Reynolds number is defined using the initial maximum velocity and the initial viscosity at the wall. In the simulations, the Reynolds number and the initial strength of the hairpin vortex are fixed. We observe from 3D visualizations that the hairpin tends to lose its coherence more easily and breaks into small scale structures when the level of shear thinning is increased. The disintegration of the hairpin causes a decrease in the production of kinetic energy and an increase in dissipation. As a consequence, the transition to turbulence is delayed as the level of shear thinning is increased. In future work, we will investigate the effects of shear-thinning on fully developed turbulence, and we will study the effects of other rheological models such as the Carreau model.