Bed forms of soft poroelastic material in an alluvial channel

Abstract

This study is to simulate stable bed forms of an alluvial channel with soft poroelastic bed caused by a constant current accompanied with water wave. Since a boundary layer exists within the soft porous bed near the homogeneous-water/porous-bed interface, conventional Stokes expansion, which only uses one parameter, ε 1= k 0 a, fails to estimate the second longitudinal wave inside the soft poroelastic bed. In order to overcome this difficulty, a boundary layer correction approach applying Biot’s theory of poroelasticity (J. Appl. Phys. 33 (4) (1962) 1482) for soft porous bed is proposed to simulate bed forms of dune, antidune, and flat bed by a two-parameter perturbation expansion based on ε 1 and ε 2= k 0/ k 2 in the present study. A new Runge–Kutta/Newton–Raphson method to find wave numbers is also proposed, which can trace bed forms of different categories continuously, including dune, antidune and flat bed. Although we do not use an empirical sediment transport formula as Kennedy (J. Fluid. Mech. 16 (1963) 521) did, the present result not only confirms the stable dune and antidune of Kennedy (1963), but also finds a rapidly damping wave that Kennedy (1963) could not get. The dimensionless lagged distance Re (k 0)δ in this study confirms Kennedy’s (1963) comment and is found to be 0, π, or 2π for stable dune and antidune when the dissipative parameter, log ( Im (k 0)/ Re (k 0)) , goes down.