Effective Form Roughness of Ripples for Waves

Abstract

The effective roughness of ripple beds under a wave regime is investigated. An existing numerical model, KU-2DVW-00, with a mixing length hypothesis is used to simulate the wave boundary layer flow over ripples. The ripple-length-average bed shear stress or form drag friction is obtained from integration of the computed pressure field. The wave friction factor is generally expressed in terms of the ripple profile shape, the ratio between the amplitude of wave orbital velocity, and the representative amplitude of bed shear stress. The effects of three factors, the bed form shape, orbital velocity amplitude over ripple length, ripple steepness on the wave friction factor or form drag are examined. Three bed profiles were tested. Results show that the drag force at the bed for the sharp-crested arc is much larger than for other shapes. The computed bed friction for the sharp-crested shape is about two times larger than that for the sinusoidal shape. Then, the effective roughness for the sharp-crested ripple becomes about 3 times larger than that for the sinusoidal shape. The model results also show that the effective roughness over ripple height is proportional to the ripple steepness up to a limit, and remains almost constant above the limit.