Second-order coupling of numerical and physical wave tanks for 2D irregular waves. Part I: Formulation, implementation and numerical properties

Abstract

In this series of two papers, we report on the irregular wave extension of the second-order coupling theory of numerical and physical wave model described in [Z. Yang, S. Liu, H.B. Bingham and J. Li. Second-order theory for coupling numerical and physical wave tanks: Derivation, evaluation and experimental validation. Coast. Eng. 71, 37–51]. We also correct several errors which unfortunately appeared in that manuscript. In the present part I, the full second-order coupling theory for irregular wave is described in detail. The new second-order coupling signal is presented including both superharmonics and subharmonics and covering wavemaker configurations of the piston- and flap-types. The second-order dispersive correction allows for an improved nonlinear transfer of wave information between the two models. For practical implementation, the coupling equations are solved by a combined five-point Lagrange interpolation and the fourth-order Runge–Kutta scheme, with a numerical velocity time series which is decomposed by the Newton–Raphson iterative method. Analytical evaluations on the suppression of spurious free waves and the relative errors of the resultant bound waves have been conducted by considering a 2nd-order, bi-chromatic wave over a range of dimensionless water depth and oscillation frequency combinations, indicating that the resultant wave quality is significantly improved using the second-order coupling theory. A separate verification combining numerical and experimental model of the theory will be presented in Part II by the same authors.