Modified log-wake law in smooth rectangular open-channels

A modified log-wake law is proposed to describe turbulent velocity profiles in smooth rectangular open-channels. The new law consists of three components: a log term, a wake term, and a free surface term. The log term reflects the channel bed effect and predominates in terms of velocity magnitude; the wake term expresses the sidewall effect and can be neglected near the channel bed; and the free surface term satisfies the free surface boundary conditions. The modified log-wake law contains six parameters:(1) the von Karman constant kappa approximate to 0.42; (2) the wake strength Pi = kappa; (3) the bed shear velocity u(*b); (4) the sidewall shear velocity u(*w); (5) the maximum velocity u(max) or the integration constant A; and (6) the velocity gradient at the upper boundary. The analysis clearly shows that the wake function results from sidewall effects. The modified log-wake law can replicate the velocity dip phenomenon in narrow channels at width-depth ratios less than 5. When the width-depth ratio exceeds 5, the maximum velocity occurs at the free surface. Finally, the modified log-wake law compares very well with Coleman's, Lyn's and Muste and Patel's experimental data.