Kim, H.; Min, B.; Lee, S.; Park, D., and Yoo, J., 2018. Eight-phase integration of powers of bed shear velocity for entrainment and bed load vector. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 1151–1155. Coconut Creek (Florida), ISSN 0749-0208.
Assume that the entrainment rate is a function of the bed shear velocity to a power with a scale factor, and the two components of the bed load are the cosine and sine of the power for the entrainment with another scale factor. The power n may be between 2 to 6 depending on their authors. There have been parameterization trials, to obtain wave-phase-average bed shear stress from current only and wave-related properties. They involve stirring factors, which requires other complicated manipulations. Here a guideline for numerical integration is proposed instead of parameterization. Bed shear velocity vector is assumed to be composed of constant current and sinusoidal wave components. 8 phases in a wave period is sufficient for accurate answers of the three properties for the power between 2 and 6, the errors of which are less than 5.1%.