Wind velocity profiles and shear stresses on a lake downwind from a canopy: Interpretation of three experiments in a wind tunnel

Abstract

We are interested in the shear stresses exerted by wind on a lake surface, especially if a lake has a small surface area. We have therefore begun to study the development of the atmospheric boundary layer over a small lake surrounded by a vegetation canopy of trees or cattails. Wind tunnel experiments have been performed to simulate the transition from a canopy to a flat solid surface. These experiments and the data collected are described in SAFL Report 492. In the first experiment we used several layers of chicken wire with a total height of 5cm, a porosity of 98% and a length of 2.4m (8 ft) in flow direction to represent the vegetation canopy, and the floor of the wind tunnel consisting of plywood was used to represent the lake. The chicken wire represents a porous step that ends at x=0. This experimental setup was considered to be a crude representation of a canopy of trees or other vegetation that ends at the shore of a lake. In a second experiment we used an array of pipe cleaners inserted in a styrofoam board to represent the canopy. The porosity of that canopy was 78%. In a third experiment we used a solid step with a smooth surface which could be a simplified representation of a high bank or buildings on the upwind side of a lake. Wind velocity profiles were measured downstream from the end of the canopy or step at distances up to x=7m. Using the velocity profile at x=0, the absolute roughness of the two canopies was determined to be 1.3 cm and 0.5 cm, respectively, and the displacement height was determined to be 2.3cm and 6.68cm. The roughness of the wind tunnel floor downstream from the canopy was determined to be 0.00003m =0.03mm. Three distinct layers were identified in the measured velocity profiles downstream from the canopy: the surface layer in response to the shear on the wind tunnel floor, an outer layer far above the canopy, and a mixing/blending layer in between. With sufficient distance downwind from the canopy the mixing layer should disappear, and the well-known logarithmic velocity profile should form. The shear stress on the surface downwind from the canopy was unaffected by wind sheltering after x/h=100, and the effect was less than 10% after x/h=60. A separated flow region formed downstream of each of the three canopies. The distance to reattachment was about 8 times the displacement height in the canopy. After a distance x/h=25 an internal boundary layer could be identified. It was characterized by rising shear stresses with distance from the canopy. Between x/d=8 and x/h=25 a turbulent shear layer touches down on the surface. Shear stresses in this range are highly variable, depending on canopy roughness and porosity. The velocities profiles downwind from the canopy are shaped by two attributes: the canopy roughness (z0) and the canopy porosity: the velocity profile at the end of the canopy is given by the canopy roughness, while the velocity profiles downwind from the canopy are shaped by both roughness and the porosity of the canopy. Wind velocity profiles took a much longer distance than x/h=100 to overcome the canopy effect. This leads to the conclusion that surface shear stresses make a much faster transition than velocity profiles downstream from the canopy. In other words, momentum transfer is faster than mass transfer downstream from the canopy.