Analysis of Flood Flows in Mountain Streams with Boulders and Rocks by Using Non-Hydrostatic Quasi Three-dimensional Model (Q3D-FEBS)

Calculating accurate flood discharge and flow structures in mountain streams are necessary for discussing the propagation of flood flows, optimization of dam operations, and conservation of aquatic-habitats. Flood flows passing through the mountain streams are characterized by the resistance of a steep and irregular channel topography with boulders and rocks. Since local channel topography including the shapes of boulders and rocks does not appear in normal topographic surveys, the influence of non-uniform flow and form resistances of the boulders and rocks are expressed as the skin friction by the Manning equation in many cases. However, Manning’s roughness coefficients of the mountain streams have very large values and change with time and space. It is not good to analyze the flood flows in the mountain streams.

We developed a new non-hydrostatic quasi three-dimensional model (Q3D-FEBS). The Q3D-FEBS is the method to solve the depth integral flow equations in addition to the equation of motion on the bottom surface in order to properly incorporate the influence of the bed shapes into the flow analysis. It makes possible to estimation the form resistances of the boulders in the framework of the depth integral model by calculating the pressure distributions around the boulders. The Manning’s roughness coefficient of the mountain streams settles to a reasonable value by the Q3D-FEBS.

In this paper, the 2017 flood of the Takiyama River is analyzed by using 2D flow model and Q3D-FEBS based on observed water surface profiles for the reach where the detailed riverbed geometry including the shapes of boulders and rocks was measured. The results show that the value of n can be almost invariably determined from the flood flows and channel geometry by taking account of the three-dimensional flow velocities and non-hydrostatic pressure distributions around the boulders and rocks by using Q3D-FEBS. This makes it possible to estimate flood discharge hydrographs and flow structures from the reliable flood flow analysis in mountain streams.