Characteristics of turbulent flows in rivers can be significantly modified because of the presence of sediment particles and secondary currents/nonuniformity. This paper investigates why the measured vertical distributions of velocity deviate from the log law. In contrast to previous research that attributed the deviation to Richardson number only, this study demonstrates that like Reynolds shear stress (−), momentum flux (uv) caused by the nonzero wall-normal velocity v is also responsible for these deviations. Starting from Reynolds equations, this paper shows that the classical log law can be obtained only when v = 0; otherwise the velocity v results in the deviation. On the basis of experimental data available in the literature, this study shows that in an open channel, v is nonzero because of the coexistence of secondary currents and sediment and, subsequently, the Reynolds shear stress and streamwise velocity are affected. Equations for these interactions are obtained and solved numerically. The validity of the proposed model has been verified using experimental data, and good agreement between the predicted and observed profiles has been achieved.