Reynolds stress and sand transport over a foredune

Reynolds shear stress (RS=-u′ w′) and sand transport patterns over a vegetated foredune are explored using three-dimensional velocity data from ultrasonic anemometers (at 0·2 and 1·2m) and sand transport intensity from laser particle counters (at 0·014m). A mid-latitude cyclone on 3-4 May 2010 generated storm-force winds (exceeding 20ms^-1) that shifted from offshore to obliquely alongshore. Quadrant analysis was used to characterize the spatial variation of RS quadrant components (Q1 through Q4) and their relative contributions were parameterized using the flow exuberance relation, EX_FL=(Q1+Q3)/(Q2+Q4). The magnitudes of RS and sand transport varied somewhat independently over the dune as controlled by topographic forcing effects on flow dynamics. A 'flow exuberance effect' was evident such that Q2 (ejection-like) and Q4 (sweep-like) quadrants (that contribute positively to RS) dominated on the beach, dune toe, and lower stoss, whereas Q1 and Q3 (that contribute negatively to RS) dominated near the crest. This exuberance effect was not expressed, however, in sand transport patterns. Instead, Q1 and Q4, with above-average streamwise velocity fluctuations (+u′), were most frequently associated with sand transport. Q4 activity corresponded with most sand transport at the beach, toe, and stoss locations (52, 60, 100%). At the crest, 25 to 86% of transport was associated with Q1 while Q4 corresponded with most of the remaining transport (13 to 59%). Thus, the relationship between sand transport and RS is not as straightforward as in traditional equations that relate flux to stress in increasing fashion. Generally, RS was poorly associated with sand transport partly because Q1 and Q4 contributions offset each other in RS calculations. Thus, large amounts of transport can occur with small RS. Turbulent kinetic energy or Reynolds normal stresses (u′², w′²) may provide stronger associations with sand transport over dunes, although challenges exist on how to normalize and compare these quantities.