Turbulence model for water flow over two-dimensional bed forms

A boundary-fitted numerical model adopting the general conservation of mass and momentum equation is applied to free surface water flow over a two-dimensional topography. A three-layer near-wall k-epsilon turbulence model is used to partly account for the effect of the separated-reattaching region in front of each sand wave. A modification of the streamline curvature is introduced to achieve a proper response to the degree of anisotropy between the normal stresses. The geometric shape of the train of sand waves is simulated by introducing a general curvilinear coordinate system. The numerical results were compared with the available experimental data reported by Raudkivi in 1963 and 1966, and more recently by Van Mierlo and De Ruiter, in 1988, and overall agreement has been satisfactory. Detailed calculations indicate that the two-equation k-epsilon model with careful modifications can yield good predictions for the sand-wave problem. The present model provides a basis for the extended study of bed-load transport: and resistance to flow arising from the movement of sediment bedforms.