Velocity distribution in combined wave–current flows

This paper investigates why the measured velocity profiles in combined wave–current flows deviate from the log-law. Most of previous researchers attributed the velocity deviation to the wave Reynolds stress—View the MathML sourceρu˜v˜¯ only. However, this study shows that both the wave Reynolds stress and the momentum View the MathML sourceu¯v¯ driven by secondary flow and/or non-uniformity are responsible to the velocity deviation from the log-law. The theoretical investigation starts from the Reynolds equations and uses the simplified mixing-length hypothesis. The theoretical equation which describes the interaction of velocity distribution and View the MathML sourcev¯ in combined wave and current conditions from the bottom to the free surface is obtained, and the equation states that the non-zero wall-normal velocity View the MathML sourcev¯ that has been ignored in previous studies also plays an important role as the wave Reynolds stress to the velocity profile. By comparing the model with the available experimental data, it is seen that the model predicted the essential features of the experimental results.