  Throughout the history of the study of turbulence in fluid dynamics, there
has yet to arise a unique definition or theoretical criterion for this
important phenomenon. There have been interesting conjectures made by Ruelle
[2], Muriel [3], and Getreuer, Albano and Muriel [6], however, attempting to
provide the sufficient criteria for the onset of turbulence. In this paper, a
classic equation in fluid dynamics, Burger's equation, is solved in one and two
dimensions, and these conjectures are illustrated. This illustration supports
these conjectures by showing that the proposed criteria do arise mathematically
from the solutions of an equation modelling fluid flows.
