Eight-Phase Integration of Powers of Bed Shear Velocity for Entrainment and Bed Load Vector

Abstract

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%.