Velocity Profiles in Steep Open‐Channel Flows

Abstract

Velocity measurements with a fiber‐optic laser‐Doppler anemometer were conducted in steep open‐channel flows over smooth and incompletely rough beds. The channel slopes were changed between 1/500 and 1/25 by steps, and as a result, the Froude number changed from 0.5 to 3. The law of the wall and the distributions of turbulence intensity were examined in more detail. The von $\acute{K}$rmán constant k in the log law was verified to be universally equal to 0.41. On the other hand, the integral constant A in the log law coincided with the usual value of 5.29 in subcritical flows, whereas it decreased with an increase of the bed slope in supercritical flows. This decrease of A was explained by a decrease of the damping factor B in the van Driest's mixing‐length formula. The decrease of B was well correlated with an increase of the friction velocity and the roughness. The streamwise turbulence intensity became smaller in the near‐wall region than the semiempirical universal formula as the friction velocity became larger.