急勾配斜面上におけるガリ形成の線形安定論

A mathematical model of the channelization on steep slopes is presented in this study. A linear stability analysis is performed with the use of the shallow water equations and the Exner equation extended for purely erosional beds. The analysis is found to be similar to that for channelization on mild slopes that the author has presented. The characteristic wavelength associated with the maximum growth rate is of the order of ten times the Froude-critical depth divided by the bed resistance coefiicient. The resistance coeffiicient is estimated of the order of 0.01; thus, the dominant channel spacing is of the order of 1000 times the Froude-critical depth.

Key Words : linear stability analysis, gully formation, steep slope