The scaling relation between channel width and the spacing of macroscale bed forms has long interested earth scientists and engineers. The current paper conceptualizes flow over such macro bed forms using perturbation theory. The objectives are to characterize the response of flow to pressure gradients that occur in convectively accelerating flow and convectively decelerating flow (CDF), as occurs in pools and riffles, and to determine how the response is modified by the width of the channel. Flume experiments are described that use idealized two-dimensional bed forms and an inner movable wall to isolate the effect of channel width. Ultrasonic Doppler velocimetry profilers operating at 40 Hz are used to measure velocity. Results show that the recovery of the shear velocity (u*) and Coles wake parameter (Π) follows a simple relaxation response toward uniform flow conditions that is insensitive to channel width, while the lateral concentration of flow (Ψ) and the principal Reynolds stress (-u′w′) occur as two-stage spreading and relaxation responses that follow a scaling relation on the order of 3-4 times the channel width, or approximately one half of the typical distance between pools. The -u′w′ increases during CDF, precisely in the location where mean bed velocity is at a minimum. It thus appears that hydrodynamic recovery from perturbation helps to explain the sensitivity of the scale of macro bed forms in rivers to channel width. Mobile beds and 3-D geometries should be tested to verify how mean flow and turbulent scales evolve as linked aspects of a complex response to perturbation.
ASJC Scopus subject areas
- Earth-Surface Processes