Theoretical analysis for the interaction between the river flow and the seepage flow

Abstract

Many previous studies have been carried on the interaction between river flow and the seepage flow in the environmental point of view, but these hardly touch on the boundary conditions or the limitations for the interactions. The subsurface layer below the river is known as the hyporheic layer and it is a saturated band of sediment that surrounds river flow and forms a linkage between the river and the aquifer. The large velocity difference between the river flow layer and the seepage flow layer causes the instability of the flows. Due to this flow instability, a reciprocating flow motion is generated between the hyporheic layer and the above. Linear stability analysis technique is used to understand the stability of the natural flows in rivers as well as the flows occurred in the air by many researchers. In this study a linear stability analysis is carried out to presents the interaction between the river flow and seepage flow. Reynolds averaged Navier-Stokes equations and Brinkman-Forchheimer equations are used in order to formulate the river flow and seepage flow interaction. The open channel flow is analyzed by mixing length turbulent model and Spectral collocation method incorporated with the Chebyshev polynomials are used to perform the numerical solution of the perturbed equations. Instability diagrams are discussed with several slopes of the layers against the dimensionless particle diameter and wave numbers. It has been noted that the instability occurs even in the range of small dimensionless particle diameter with relatively high wave numbers if there is a seepage layer beneath the flow and the instability region increases with the slope when the wave numbers are at small values.