Fully nonlinear interfacial periodic waves in a two-layer fluid with a rigid upper boundary and their loads on a cylindrical pile

Abstract

Based on the fully nonlinear potential flow theory, interfacial periodic gravity waves in a two-layer fluid with a rigid upper boundary are investigated quasi-analytically using the homotopy analysis method (HAM), and the corresponding wave loads on a cylindrical pile are estimated by Morison’s empirical formula. Because of the great freedom in the choices of auxiliary linear operators, initial guesses, and convergence-control parameter, convergent series solutions are obtained in the framework of the HAM. For Boussinesq wave loads on the cylinder in one wave period, there exists a phenomenon of peak–valley mismatch between the upper and lower layer inertial loads; the total drag, total inertial and global loads reach their own peaks almost at the same time when the upper layer load equals the lower layer load. As the wave height increases, the dominant load changes from inertial load to drag load. Previous theoretical studies about internal or interfacial periodic wave loads on a cylinder were mainly based on linear or weakly nonlinear wave models, which causes the lack of corresponding theoretical research in the frame of fully nonlinear wave theory. Compared with linear and weakly nonlinear wave models, the fully nonlinear wave model considered in this paper provides more accurate results for the maximal loads on a slender cylindrical pile exerted by Boussinesq interfacial periodic waves, especially for strongly nonlinear cases. All of these should enhance our understanding of internal periodic waves and their loads on a marine riser.