Multivariate Hermite Expansion of Hydrodynamic Drag Loads on Tension Leg Platforms

Abstract

In this paper, a new method is proposed for the expansion of nonlinear drag forces in terms of multivariate Hermite polynomials correct up to the second order. The drag‐force formulation includes the effect of instantaneous wave surface profile and it caters for the waves and currents approaching from any arbitrary direction with respect to the platform orientation. These attributes are critical for a reliable treatment of the wave‐induced viscous effects on tension leg platforms (TLP). The viscous nonlinear drag force expressed in terms of Hermite polynomials is decomposed into the mean (zeroth‐order), viscous exciting and viscous damping terms (first‐order) and the slowly varying drift‐force term (second‐order). This decomposition permits spectral representation of the first‐order viscous forces in terms of the spectral density function of the water particle velocities. Accordingly, the second‐order viscous force can be described within the spectral framework by the spectral convolution or other related techniques involving the spectral density functions of the relative fluid‐structure velocities and the wave surface elevation. The response statistics derived from the frequency domain provides a very good agreement with the time‐domain simulation. The present approach based on an equivalent quadratization concept not only retains the important features of the nonlinear interactions in the frequency domain analysis, e.g., the spectral contents at the sum and difference frequencies, but also clearly offers accuracy comparable to the time‐domain approach at a fraction of the computational effort. Immediate applications of the present analysis approach are possible in the analysis of marine risers and suspended pipelines to ocean waves and currents.