Numerical solutions of mixture equations describing balances of mass and momentum in debris flows clearly illustrate the physical distinctions between flows of dry grains, water, and mixtures of grains and water. These distinctions are particularly evident during initiation of flow on a slope. Flows of either dry grains or water are characterized by rapidly advancing, tapered flow fronts and gradually thickening tails, whereas mixtures of grains and water are characterized by development of steep, bulbous flow snouts and gradually tapering tails. The latter flow morphology applies whether the grains and water are mixed prior to flow initiation or are mixed into water during erosion of sediment by flow of water over a dry bed. Sorting of the granular mixture during flow creates a coarse-grained, unpressurized flow front. Combined with development and maintenance of high pore pressures in the fine-grained core of the debris flow, the coarse-grained front creates and maintains characteristic debris-flow morphology. Successful modeling of this phenomenon relies on data acquired in controlled laboratory experiments, which constrain interactions of the pressurized debris-flow cores with unpressurized, bulbous snouts. A dynamic product of this interaction that is also simulated is development of a sequence of separate waves, each with a pressurized core and unpressurized snout. Understanding of this complex behavior and how it develops through the interaction of simple mechanisms is necessary to successfully model debris flows.