Obstructed shear flows: similarities across systems and scales

Abstract

In this paper, I show that a range of environmental flows are inherently dynamically similar. These flows, which are partially obstructed by a permeable medium, are here termed ‘obstructed shear flows’. Examples include aquatic flows over sediment beds, submerged vegetation canopies and coral reefs, as well as atmospheric flows over crop canopies, forests and cities (‘urban canopies’). While the density and geometry of the obstructions may vary, the drag in each system generates a velocity profile with an inflection point. This renders the flow unstable. Consequently, it is expected that (a) the dominant interfacial turbulent structure in obstructed shear flows will be a Kelvin–Helmholtz-type vortex, and (b) that this instability will engender hydrodynamic similarities among obstructed shear flows. Such similarities have been hypothesized but not yet fully explored. An extensive review of existing data confirms these dynamic similarities on scales ofO(mm) toO(10 m). The extent of shear penetration into the obstruction, which is a primary determinant of residence time in the obstruction, scales upon the drag length scale. Other relationships that link the strength of turbulence and the ‘slip’ velocity at the top of the obstruction to the friction velocity (u∗) are also evident. The relationships presented here provide predictive capability for flow and transport in obstructed shear flows and suggest the possibility of a single framework to describe such flows on all scales.