Obstructed shear flows: similarities across systems and scales

In this paper, I show that a range of environmental flows are inherently dynamicallysimilar. These flows, which are partially obstructed by a permeable medium, are heretermed ‘obstructed shear flows’. Examples include aquatic flows over sediment beds,submerged vegetation canopies and coral reefs, as well as atmospheric flows over cropcanopies, forests and cities (‘urban canopies’). While the density and geometry of theobstructions may vary, the drag in each system generates a velocity profile with aninflection point. This renders the flow unstable. Consequently, it is expected that (a) thedominant interfacial turbulent structure in obstructed shear flows will be a Kelvin–Helmholtz-type vortex, and (b) that this instability will engender hydrodynamicsimilarities among obstructed shear flows. Such similarities have been hypothesizedbut not yet fully explored. An extensive review of existing data confirms these dynamicsimilarities on scales of O(mm) to O(10 m). The extent of shear penetration into theobstruction, which is a primary determinant of residence time in the obstruction, scalesupon the drag length scale. Other relationships that link the strength of turbulenceand the ‘slip’ velocity at the top of the obstruction to the friction velocity (u∗) are alsoevident. The relationships presented here provide predictive capability for flow andtransport in obstructed shear flows and suggest the possibility of a single frameworkto describe such flows on all scales.