Dislocations play an important role in the deformation behaviors of metals. They not only interact via long-range elastic stress, but also interact with shortrange interactions; they annihilate, tangle, get stuck, and unstuck. These interaction between dislocations lead to interesting dislocation wall formation at the mesoscales. A recently developed continuum dislocation dynamics model that shows dislocation wall structures, is presented and explored in two and three dimensions. We discuss both mathematical and numerical aspects of simulating the model; the validity of our methods are explored and we show that the model has physical analogies to turbulence. We explain why and how the walls are formed in our continuum dislocation dynamics model. We propose modifications for more traditional slip dynamical laws, which lead them to form dislocation wall structures. Furthermore, we argue that defect physics may generate more singular structures than the density jumps that have traditionally been observed within fluid dynamics, and that development and enhancement of mathematical and numerical schemes will be necessary to incorporate the microscale defect physics that ought to determine the evolution of the singularity (replacing traditional entropy conditions).