Abstract
ABSTRACT Li, S. and Liu, Y., 2018. Analytical and explicit solutions to implicit wave friction-factor equations based on the Lambert W function. Calculation of the friction factor of turbulent oscillatory fluid flow is a significant issue in accessing bed shear stress and sediment entrainment in coastal areas. A fast, robust calculation is necessary for intensive scientific simulations. However, some widely used friction-factor equations belong to the group of implicit and transcendental equations. Common procedures for obtaining accurate solutions are based on root-solving techniques such as the Newton–Raphson iterative method, with substantial computation cost and potential failure of solution convergence. The present note offers a simple and highly accurate procedure for explicitly calculating the friction factors. First, explicit analytical solutions of the friction-factor equations are derived using the Lambert W function, which is a newly recognized elementary transcendental function. Then, the anal...
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