An approach to determine coefficients of logarithmic velocity vertical profile in the bottom boundary layer
Velocity vertical profiles in the bottom boundary layer are important to understand the oceanic circulation. The logarithmic vertical profile, u=Alnz+B, is the universal profile for the horizontal velocity in the boundary layer, in which two coefficients (A and B) need to be determined. The two coefficients are the functions of the friction velocity (u* and the roughness length (z0) and they are calculated using u* and z0. However, the measurement of u* and z0 is a challenge. In the present study, an approach is developed to estimate the two coefficients (A and B) by using a series of flume laboratory experiments with flat boundary and regularly distributed cylinders as the rough boundaries. An acoustic doppler velocimeter (ADV) is used to measure the velocity vertical profiles of the steady flow. Using the measured velocity data, the regressed logarithmic profiles are obtained. Based on the series of the A and B values, the mathematical formula for A and B are statistically established as the function of the cylinder height, inflow velocity, and the water depth, which avoids the measurement of the friction velocity and the roughness length.
Journal of Oceanology and Limnology