Drag on Naturally Rippled Beds Under Oscillatory Flows

Book excerpt: Laboratory tests measure the time-dependent drag on naturally rippled sand beds under oscillatory flows. The time integral of the product of this drag and the oscillatory flow velocity provide the energy dissipated per period. A positive kesplacement oscillatory flow tunnel provides amplitudes and periods of flow over a wide range of prototype conditions. With the test section split longitudinally into two channels, one containing the sand bed and the other having a smooth metallic bottom, the drag on the bed is obtained from the measured difference between pressure gradients in the two channels. Two sands are used, with diameters 0.55 and 0.18 mm. The experimental profiles are mostly natural and mature, but some are deliberately distorted. The experimental profiles are in process of growth from a bed initially flat. Bottom stress, including skin friction and profile drag components, is found to be a fairly complicated function of the phase and not proportional to the square of the simultaneous sinusoidal velocity far above the bed. Average values of the bottom stress and rates of energy dissipation are both typically an order of magnitude greater than for a flat surface roughened with fixed grains. Amplitudes and shapes of the curves of stress coefficient as function of phase are interpreted in terms of physical mechanisms and simple models--the profile drag as produced by flow separation at the crest with the growth of an attached vortex in its lee and the skin friction as produced by the flow, modified by a detached vortex, up the ripple face.