Double-averaged momentum and energy budgets for open-channel flows over self-affine bed roughness

Abstract

We explore the double-averaged momentum and energy conservation budgets for open-channel flows with hydraulically-rough beds. Three ‘self-affine’ roughness patterns were constructed with the spectra of surface height profiles designed to have power law scaling with exponents of -1, -5/3, and -3. Measurements were made using a ‘robotic’ stereoscopic PIV system that was programmed to record velocity fields in a sequence of planes on a periodic roughness tile. Our results showed that both secondary currents and roughness-induced near-bed spatial fluctuations of the time-averaged velocity contributed significantly to the dispersive stress. The distribution of drag force within the roughness canopy was shifted downwards for the ‘-3ʹ surface compared to the ‘-1ʹ surface reflecting increased penetration of the flow into the more open roughness structure. Production of turbulent energy via exchange with the double mean kinetic energy was found to be around three times larger than via exchange with the dispersive kinetic energy.