APPLICATIONS OF THE DIFFUSION HYDRODYNAMIC MODEL

OneDimensional Model

Application 1: Steady Flow in an Open Channel
Because the DHM is anticipated for use in modeling watershed phenomena, it is important that the channel models represent known flow characteristics. Unsteady flow is examined in the previous section. For steady flow, a steadystate, gradually varied flow problem is simulated by the 2D diffusion model. Figure 16 depicts both the water levels form the 2D diffusion model and from the gradually varied flow equation. For an 8000 cfs constant inflow rate, the water surface profiles from both the 2D diffusion model and the gradually varied flow equation match quite well. The discrepancies of these profiles occur at the break points where the upstream channel slope and downstream channel slope change. At the first break point where the upstream channel slope is equal to 0.001 and the downstream channel slope is equal to 0.005, the water surface level is assumed to be equal to the critical depth. However, Henderson (1966), notes that brink flow is typically less than the critical depth (Dc). The DHM water surface closely matches the 0.72 Dc brink depth.
It is clear to see that the DHM cannot simulate the hydraulic jump, but rather smoothes out the usually assumed "shock front". However, when considering unsteady flow, the DHM may be a reasonable approach for approximating the jump profile. For a higher inflow rate, 20,000 cfs, the surface water levels differ in the most upstream reach. Again, this is due to the downstream control, critical depth, of the gradually varied flow equation.

