Bed forms of soft poroelastic material in an alluvial channel

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 homogeneo us-water/porous-bed interface, conventional Stokes expansion, which only us es one parameter, epsilon (1) = k(0)a, fails to estimate the second longitu dinal wave inside the soft poroelastic bed. In order to overcome this diffi culty, a boundary layer correction approach applying Blot's theory of poroe lasticity (J. Appl. Phys. 33 (4) (1962) 1482) for soft porous bed is propos ed to simulate bed forms of dune, antidune, and flat bed by a two-parameter perturbation expansion based on epsilon (1) and epsilon (2) = k(0)/k(2) in the present study. A new Runge-Kutta/Newton-Raphson method to find wave nu mbers is also proposed, which can trace bed forms of different categories c ontinuously, including dune, antidune and flat bed. Although we do not use an empirical sediment transport formula as Kennedy (J. Fluid. Mech. 16 (196 3) 521) did, the present result not only confirms the stable dune and antid une of Kennedy (1963), but also finds a rapidly damping wave that Kennedy ( 1963) could not get. The dimensionless lagged distance Re(k(0))delta in thi s study confirms Kennedy's (1963) comment and is found to be 0, pi, or 2 pi for stable dune and antidune when the dissipative parameter, log (Im (k(0) )/Re(k(0))), goes down. (C) 2001 Elsevier Science Ltd. All rights reserved.