The Ekman boundary-layer stress due to flow over a regular array of hills

The flow of water over a regular array of hills in a rotating laboratory experiment is studied as an analogue of planetary boundary layers. Gaussian-shaped hills of heighth = 1 cm andh = 1/3 cm covered the floor of a 228 cm diam rotating tank. The characteristic depth of the Ekman layer varied fromD = 0.1 cm toD = 0.3 cm and the Reynolds number for the Ekman layer varied up toRe = 150. The integrated boundary-layer stress as a function ofRe andD/h was determined by the rate of spin-up of the water after a small increase of the rotation rate.Selected functional relations were fitted to the empirical data by the method of least squares for the laminar and turbulent regimes of flow. These results indicate maximum non-linear effects of the hills and a minimum transition Reynolds number nearD/h = 0.2. The patterns of flow as indicated by dye tracers are briefly discussed. Peculiar circular bands of dye appear to be caused by the selective ejection of dye from the boundary layer when the circular flow is at a particular angle of incidence with respect to the triangular pattern of hills.The research reported herein was supported in part by the National Science Foundation under Grant NSF GA 4388.