Abstract
The instability of shallow water flow has been studied since a long time ago. It has been found from linear stability analysis that, when the Froude number is larger than approximately two, uniform flow becomes unstable, resulting in the evolution of a terrain of waves, which are called roll waves. In this study, a linear stability analysis is performed with the use of the shallow water equation extended for flow on permeable beds in order to investigate the instability of flow on permeable river beds and the resulting water exchange between river flow and the seepage flow beneath the beds. The analysis reveals that flow is unstable in the range of sufficiently large wavenumbers and Froude numbers when the permeable layer is sufficiently thicker than the flow on the bed. In the range of instability, water exchange between river flow and the hyporheic layer beneath river beds is expected to be activated.
