Unidirectional flow over asymmetric and symmetric ripples

Abstract

Detailed measurements of velocity and turbulence over fixed sets of two‐dimensional asymmetric and symmetric ripples were collected in a flume equipped with a laser‐Doppler velocimeter. The measured velocity profiles show a region of strong wake influence extending 2–3 bedform heights above the bed and an outer, spatially uniform flow that has adjusted to the hydrodynamic roughness of the ripples. The measured velocities over ripples, when compared to measurements of flow over larger‐scale dunes of a similar geometry made by Nelson and Smith (1989), differ in two major respects: the velocity gradients are significantly larger in the outer region of the flow, and the velocity profiles exhibit no sharp inflection at the top of the lowest wake. A model for flow over bedforms that had provided excellent agreement with the dune measurements is modified herein in a physically reasonable manner to represent better the observed flow over ripples. The predictions of the modified model compare well with the velocity measurements made over sets of asymmetric and symmetric ripples in a unidirectional flow when the appropriate drag coefficients for the two bed geometries are used. Drag coefficients deduced from the measurements suggest a possible dependence on relative depth as well as ripple geometry. Hydrodynamic ripple roughnesses determined from the measured and calculated profiles have values of the same order as estimates made using several existing expressions for the roughness of bedforms and regular roughness arrays. However, the measurements and calculations also indicate that bottom roughness depends on more than the ripple height times ripple steepness length scale used in these formulations.