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...